jiangly算法模板收集
声明
本博客体量较大，原更新于 GitHub，但是使用不太方便，于是在这里额外部署了一份。
自用！非本人原创，仅作整理归档。大部分代码来自于 CodeForces Jiangly 的提交，部分来自于GYM、牛客、Atcoder。文章博客链接，文章 GitHub 链接。
灵感参考链接：GitHub/beiyouwuyanzu/cf_code_jiangly 。
目录
目录
- 声明
- 目录
- 一、杂类
- 二、图与网络
- 三、数论、几何、多项式
- 四、数据结构
- 五、字符串
一、杂类
点击展开本章节
int128 库函数自定义
/** int128 库函数自定义
* 2024-08-14: https://ac.nowcoder.com/acm/contest/view-submission?submissionId=70979004&returnHomeType=1&uid=329687984
* 2024-09-17: https://qoj.ac/submission/571481
**/
using i128 = __int128;
std::ostream &operator<<(std::ostream &os, i128 n) {
if (n == 0) {
return os << 0;
}
std::string s;
while (n > 0) {
s += char('0' + n % 10);
n /= 10;
}
std::reverse(s.begin(), s.end());
return os << s;
}
i128 toi128(const std::string &s) {
i128 n = 0;
for (auto c : s) {
n = n * 10 + (c - '0');
}
return n;
}
i128 sqrti128(i128 n) {
i128 lo = 0, hi = 1E16;
while (lo < hi) {
i128 x = (lo + hi + 1) / 2;
if (x * x <= n) {
lo = x;
} else {
hi = x - 1;
}
}
return lo;
}
i128 gcd(i128 a, i128 b) {
while (b) {
a %= b;
std::swap(a, b);
}
return a;
}
常用库函数重载
using i64 = long long;
using i128 = __int128;
/** 上取整下取整
* 2023-10-15: https://codeforces.com/contest/293/submission/228297248
**/
i64 ceilDiv(i64 n, i64 m) {
if (n >= 0) {
return (n + m - 1) / m;
} else {
return n / m;
}
}
i64 floorDiv(i64 n, i64 m) {
if (n >= 0) {
return n / m;
} else {
return (n - m + 1) / m;
}
}
/** 最大值赋值
* 2023-09-30: https://codeforces.com/contest/1874/submission/226069129
**/
template<class T>
void chmax(T &a, T b) {
if (a < b) {
a = b;
}
}
/** 最大公约数
* -: -
**/
i128 gcd(i128 a, i128 b) {
return b ? gcd(b, a % b) : a;
}
/** 精确开平方
* 2024-03-02: https://qoj.ac/submission/343317
**/
i64 sqrt(i64 n) {
i64 s = std::sqrt(n);
while (s * s > n) {
s--;
}
while ((s + 1) * (s + 1) <= n) {
s++;
}
return s;
}
/** 精确开平方
* 2023-09-19: https://qoj.ac/submission/183430
**/
i64 get(i64 n) {
i64 u = std::sqrt(2.0L * n);
while (u * (u + 1) / 2 < n) {
u++;
}
while (u * (u - 1) / 2 + 1 > n) {
u--;
}
return u;
}
/** 求 Log
* 2024-07-23: https://codeforces.com/contest/1995/submission/272110180
**/
int logi(int a, int b) {
int t = 0;
i64 v = 1;
while (v < b) {
v *= a;
t++;
}
return t;
}
int llog(int a, int b) {
if (a <= b) {
int l = logi(a, b);
return (l == 0 ? 0 : std::__lg(2 * l - 1));
}
int l = logi(b, a + 1) - 1;
assert(l > 0);
return -std::__lg(l);
}
字符调整
/** 大小写转换、获取字母序
* 2024-03-16: https://qoj.ac/submission/355156
**/
void rev(std::string &s) {
int l = s.size();
for (int i = 1; i < l; i += 2) {
if (std::isupper(s[i])) {
s[i] = std::tolower(s[i]);
} else {
s[i] = std::toupper(s[i]);
}
}
}
int get(char c) {
int x;
if (std::islower(c)) {
x = c - 'a';
} else {
x = 26 + c - 'A';
}
return x;
}
二分算法
二分算法（整数域）
/** 二分算法（整数域）： 前驱
* 2023-09-18: https://qoj.ac/submission/182628
**/
int lo = 1, hi = 1E9;
while (lo < hi) {
int m = (lo + hi + 1) / 2;
if (check(m)) {
lo = m;
} else {
hi = m - 1;
}
}
std::cout << lo << "\n";
/** 二分算法（整数域）：后继
* 2023-09-18: https://qoj.ac/submission/182752
**/
int lo = 1, hi = n;
while (lo < hi) {
int m = (lo + hi) / 2;
if (check(m)) {
hi = m;
} else {
lo = m + 1;
}
}
std::cout << lo << "\n";
二分算法（实数域）
/** 二分算法（实数域）
* 2023-10-21: https://qoj.ac/submission/222042
**/
auto check = [&](double t) {
// write
};
double lo = 0;
double hi = 1E12;
while (hi - lo > std::max(1.0, lo) * eps) {
double x = (lo + hi) / 2;
if (check(x)) {
hi = x;
} else {
lo = x;
}
}
std::cout << lo << "\n";
/** 二分算法（实数域）
* 2023-09-15: https://qoj.ac/submission/179994
**/
using i64 = long long;
using real = long double;
constexpr real eps = 1E-7;
auto get = [&](const auto &f) {
real lo = -1E4, hi = 1E4;
while (hi - lo > 3 * eps) {
real x1 = (lo + hi - eps) / 2;
real x2 = (lo + hi + eps) / 2;
if (f(x1) > f(x2)) {
lo = x1;
} else {
hi = x2;
}
}
return f((lo + hi) / 2);
};
std::cout << get([&](real px) {
return get([&](real py) {
// write
});
}) << "\n";
二、图与网络
点击展开本章节
强连通分量缩点（SCC）
/** 强连通分量缩点（SCC）
* 2023-06-18: https://codeforces.com/contest/1835/submission/210147209
**/
struct SCC {
int n;
std::vector<std::vector<int>> adj;
std::vector<int> stk;
std::vector<int> dfn, low, bel;
int cur, cnt;
SCC() {}
SCC(int n) {
init(n);
}
void init(int n) {
this->n = n;
adj.assign(n, {});
dfn.assign(n, -1);
low.resize(n);
bel.assign(n, -1);
stk.clear();
cur = cnt = 0;
}
void addEdge(int u, int v) {
adj[u].push_back(v);
}
void dfs(int x) {
dfn[x] = low[x] = cur++;
stk.push_back(x);
for (auto y : adj[x]) {
if (dfn[y] == -1) {
dfs(y);
low[x] = std::min(low[x], low[y]);
} else if (bel[y] == -1) {
low[x] = std::min(low[x], dfn[y]);
}
}
if (dfn[x] == low[x]) {
int y;
do {
y = stk.back();
bel[y] = cnt;
stk.pop_back();
} while (y != x);
cnt++;
}
}
std::vector<int> work() {
for (int i = 0; i < n; i++) {
if (dfn[i] == -1) {
dfs(i);
}
}
return bel;
}
};
割边与割边缩点（EBCC）
/** 割边与割边缩点（EBCC）
* 2023-05-11: https://codeforces.com/contest/118/submission/205426518
**/
std::set<std::pair<int, int>> E;
struct EBCC {
int n;
std::vector<std::vector<int>> adj;
std::vector<int> stk;
std::vector<int> dfn, low, bel;
int cur, cnt;
EBCC() {}
EBCC(int n) {
init(n);
}
void init(int n) {
this->n = n;
adj.assign(n, {});
dfn.assign(n, -1);
low.resize(n);
bel.assign(n, -1);
stk.clear();
cur = cnt = 0;
}
void addEdge(int u, int v) {
adj[u].push_back(v);
adj[v].push_back(u);
}
void dfs(int x, int p) {
dfn[x] = low[x] = cur++;
stk.push_back(x);
for (auto y : adj[x]) {
if (y == p) {
continue;
}
if (dfn[y] == -1) {
E.emplace(x, y);
dfs(y, x);
low[x] = std::min(low[x], low[y]);
} else if (bel[y] == -1 && dfn[y] < dfn[x]) {
E.emplace(x, y);
low[x] = std::min(low[x], dfn[y]);
}
}
if (dfn[x] == low[x]) {
int y;
do {
y = stk.back();
bel[y] = cnt;
stk.pop_back();
} while (y != x);
cnt++;
}
}
std::vector<int> work() {
dfs(0, -1);
return bel;
}
struct Graph {
int n;
std::vector<std::pair<int, int>> edges;
std::vector<int> siz;
std::vector<int> cnte;
};
Graph compress() {
Graph g;
g.n = cnt;
g.siz.resize(cnt);
g.cnte.resize(cnt);
for (int i = 0; i < n; i++) {
g.siz[bel[i]]++;
for (auto j : adj[i]) {
if (bel[i] < bel[j]) {
g.edges.emplace_back(bel[i], bel[j]);
} else if (i < j) {
g.cnte[bel[i]]++;
}
}
}
return g;
}
};
二分图最大权匹配（MaxAssignment 基于KM）
/** 二分图最大权匹配（MaxAssignment 基于KM）
* 2022-04-10: https://atcoder.jp/contests/abc247/submissions/30867023
* 2023-09-21: https://qoj.ac/submission/184824
**/
constexpr int inf = 1E7;
template<class T>
struct MaxAssignment {
public:
T solve(int nx, int ny, std::vector<std::vector<T>> a) {
assert(0 <= nx && nx <= ny);
assert(int(a.size()) == nx);
for (int i = 0; i < nx; ++i) {
assert(int(a[i].size()) == ny);
for (auto x : a[i])
assert(x >= 0);
}
auto update = [&](int x) {
for (int y = 0; y < ny; ++y) {
if (lx[x] + ly[y] - a[x][y] < slack[y]) {
slack[y] = lx[x] + ly[y] - a[x][y];
slackx[y] = x;
}
}
};
costs.resize(nx + 1);
costs[0] = 0;
lx.assign(nx, std::numeric_limits<T>::max());
ly.assign(ny, 0);
xy.assign(nx, -1);
yx.assign(ny, -1);
slackx.resize(ny);
for (int cur = 0; cur < nx; ++cur) {
std::queue<int> que;
visx.assign(nx, false);
visy.assign(ny, false);
slack.assign(ny, std::numeric_limits<T>::max());
p.assign(nx, -1);
for (int x = 0; x < nx; ++x) {
if (xy[x] == -1) {
que.push(x);
visx[x] = true;
update(x);
}
}
int ex, ey;
bool found = false;
while (!found) {
while (!que.empty() && !found) {
auto x = que.front();
que.pop();
for (int y = 0; y < ny; ++y) {
if (a[x][y] == lx[x] + ly[y] && !visy[y]) {
if (yx[y] == -1) {
ex = x;
ey = y;
found = true;
break;
}
que.push(yx[y]);
p[yx[y]] = x;
visy[y] = visx[yx[y]] = true;
update(yx[y]);
}
}
}
if (found)
break;
T delta = std::numeric_limits<T>::max();
for (int y = 0; y < ny; ++y)
if (!visy[y])
delta = std::min(delta, slack[y]);
for (int x = 0; x < nx; ++x)
if (visx[x])
lx[x] -= delta;
for (int y = 0; y < ny; ++y) {
if (visy[y]) {
ly[y] += delta;
} else {
slack[y] -= delta;
}
}
for (int y = 0; y < ny; ++y) {
if (!visy[y] && slack[y] == 0) {
if (yx[y] == -1) {
ex = slackx[y];
ey = y;
found = true;
break;
}
que.push(yx[y]);
p[yx[y]] = slackx[y];
visy[y] = visx[yx[y]] = true;
update(yx[y]);
}
}
}
costs[cur + 1] = costs[cur];
for (int x = ex, y = ey, ty; x != -1; x = p[x], y = ty) {
costs[cur + 1] += a[x][y];
if (xy[x] != -1)
costs[cur + 1] -= a[x][xy[x]];
ty = xy[x];
xy[x] = y;
yx[y] = x;
}
}
return costs[nx];
}
std::vector<int> assignment() {
return xy;
}
std::pair<std::vector<T>, std::vector<T>> labels() {
return std::make_pair(lx, ly);
}
std::vector<T> weights() {
return costs;
}
private:
std::vector<T> lx, ly, slack, costs;
std::vector<int> xy, yx, p, slackx;
std::vector<bool> visx, visy;
};
一般图最大匹配（Graph 带花树算法）【久远】
/** 一般图最大匹配（Graph 带花树算法）
* 2024-09-13: https://qoj.ac/submission/562904
**/
struct Graph {
int n;
std::vector<std::vector<int>> e;
Graph(int n) : n(n), e(n) {}
void addEdge(int u, int v) {
e[u].push_back(v);
e[v].push_back(u);
}
std::vector<int> findMatching(int m, const auto &init) {
std::vector<int> match(n, -1), vis(n), link(n), f(n), dep(n);
for (auto [x, y] : init) {
match[x] = y;
match[y] = x;
}
// disjoint set union
auto find = [&](int u) {
while (f[u] != u)
u = f[u] = f[f[u]];
return u;
};
auto lca = [&](int u, int v) {
u = find(u);
v = find(v);
while (u != v) {
if (dep[u] < dep[v])
std::swap(u, v);
u = find(link[match[u]]);
}
return u;
};
std::queue<int> que;
auto blossom = [&](int u, int v, int p) {
while (find(u) != p) {
link[u] = v;
v = match[u];
if (vis[v] == 0) {
vis[v] = 1;
que.push(v);
}
f[u] = f[v] = p;
u = link[v];
}
};
// find an augmenting path starting from u and augment (if exist)
auto augment = [&](int u) {
while (!que.empty())
que.pop();
std::iota(f.begin(), f.end(), 0);
// vis = 0 corresponds to inner vertices, vis = 1 corresponds to outer vertices
std::fill(vis.begin(), vis.end(), -1);
que.push(u);
vis[u] = 1;
dep[u] = 0;
int y = -1;
while (!que.empty()){
int u = que.front();
que.pop();
if (u >= m) {
y = u;
}
for (auto v : e[u]) {
if (vis[v] == -1) {
vis[v] = 0;
link[v] = u;
dep[v] = dep[u] + 1;
// found an augmenting path
if (match[v] == -1) {
for (int x = v, y = u, temp; y != -1; x = temp, y = x == -1 ? -1 : link[x]) {
temp = match[y];
match[x] = y;
match[y] = x;
}
return;
}
vis[match[v]] = 1;
dep[match[v]] = dep[u] + 2;
que.push(match[v]);
} else if (vis[v] == 1 && find(v) != find(u)) {
// found a blossom
int p = lca(u, v);
blossom(u, v, p);
blossom(v, u, p);
}
}
}
if (y != -1) {
for (int x = -1, temp; y != -1; x = temp, y = x == -1 ? -1 : link[x]) {
temp = match[y];
if (x != -1) {
match[x] = y;
}
match[y] = x;
}
}
};
// find a maximal matching greedily (decrease constant)
// auto greedy = [&]() {
// for (int u = 0; u < n; ++u) {
// if (match[u] != -1)
// continue;
// for (auto v : e[u]) {
// if (match[v] == -1) {
// match[u] = v;
// match[v] = u;
// break;
// }
// }
// }
// };
// greedy();
for (int u = 0; u < m; ++u)
if (match[u] == -1)
augment(u);
return match;
}
};
/** 一般图最大匹配（Graph 带花树算法）【久远】
* 2021-12-24: https://codeforces.com/contest/1615/submission/140509278
* 2022-08-28: https://codeforces.com/gym/103260/submission/169975982
**/
struct Graph {
int n;
std::vector<std::vector<int>> e;
Graph(int n) : n(n), e(n) {}
void addEdge(int u, int v) {
e[u].push_back(v);
e[v].push_back(u);
}
std::vector<int> findMatching() {
std::vector<int> match(n, -1), vis(n), link(n), f(n), dep(n);
// disjoint set union
auto find = [&](int u) {
while (f[u] != u)
u = f[u] = f[f[u]];
return u;
};
auto lca = [&](int u, int v) {
u = find(u);
v = find(v);
while (u != v) {
if (dep[u] < dep[v])
std::swap(u, v);
u = find(link[match[u]]);
}
return u;
};
std::queue<int> que;
auto blossom = [&](int u, int v, int p) {
while (find(u) != p) {
link[u] = v;
v = match[u];
if (vis[v] == 0) {
vis[v] = 1;
que.push(v);
}
f[u] = f[v] = p;
u = link[v];
}
};
// find an augmenting path starting from u and augment (if exist)
auto augment = [&](int u) {
while (!que.empty())
que.pop();
std::iota(f.begin(), f.end(), 0);
// vis = 0 corresponds to inner vertices, vis = 1 corresponds to outer vertices
std::fill(vis.begin(), vis.end(), -1);
que.push(u);
vis[u] = 1;
dep[u] = 0;
while (!que.empty()){
int u = que.front();
que.pop();
for (auto v : e[u]) {
if (vis[v] == -1) {
vis[v] = 0;
link[v] = u;
dep[v] = dep[u] + 1;
// found an augmenting path
if (match[v] == -1) {
for (int x = v, y = u, temp; y != -1; x = temp, y = x == -1 ? -1 : link[x]) {
temp = match[y];
match[x] = y;
match[y] = x;
}
return;
}
vis[match[v]] = 1;
dep[match[v]] = dep[u] + 2;
que.push(match[v]);
} else if (vis[v] == 1 && find(v) != find(u)) {
// found a blossom
int p = lca(u, v);
blossom(u, v, p);
blossom(v, u, p);
}
}
}
};
// find a maximal matching greedily (decrease constant)
auto greedy = [&]() {
for (int u = 0; u < n; ++u) {
if (match[u] != -1)
continue;
for (auto v : e[u]) {
if (match[v] == -1) {
match[u] = v;
match[v] = u;
break;
}
}
}
};
greedy();
for (int u = 0; u < n; ++u)
if (match[u] == -1)
augment(u);
return match;
}
};
TwoSat（2-Sat）
/** TwoSat（2-Sat）
* 2023-09-29: https://atcoder.jp/contests/arc161/submissions/46031530
**/
struct TwoSat {
int n;
std::vector<std::vector<int>> e;
std::vector<bool> ans;
TwoSat(int n) : n(n), e(2 * n), ans(n) {}
void addClause(int u, bool f, int v, bool g) {
e[2 * u + !f].push_back(2 * v + g);
e[2 * v + !g].push_back(2 * u + f);
}
bool satisfiable() {
std::vector<int> id(2 * n, -1), dfn(2 * n, -1), low(2 * n, -1);
std::vector<int> stk;
int now = 0, cnt = 0;
std::function<void(int)> tarjan = [&](int u) {
stk.push_back(u);
dfn[u] = low[u] = now++;
for (auto v : e[u]) {
if (dfn[v] == -1) {
tarjan(v);
low[u] = std::min(low[u], low[v]);
} else if (id[v] == -1) {
low[u] = std::min(low[u], dfn[v]);
}
}
if (dfn[u] == low[u]) {
int v;
do {
v = stk.back();
stk.pop_back();
id[v] = cnt;
} while (v != u);
++cnt;
}
};
for (int i = 0; i < 2 * n; ++i) if (dfn[i] == -1) tarjan(i);
for (int i = 0; i < n; ++i) {
if (id[2 * i] == id[2 * i + 1]) return false;
ans[i] = id[2 * i] > id[2 * i + 1];
}
return true;
}
std::vector<bool> answer() { return ans; }
};
最大流
最大流（Flow 旧版其一，整数应用）
/** 最大流（Flow 旧版其一，整数应用）
* 2022-09-03: https://codeforces.com/contest/1717/submission/170688062
**/
template<class T>
struct Flow {
const int n;
struct Edge {
int to;
T cap;
Edge(int to, T cap) : to(to), cap(cap) {}
};
std::vector<Edge> e;
std::vector<std::vector<int>> g;
std::vector<int> cur, h;
Flow(int n) : n(n), g(n) {}
bool bfs(int s, int t) {
h.assign(n, -1);
std::queue<int> que;
h[s] = 0;
que.push(s);
while (!que.empty()) {
const int u = que.front();
que.pop();
for (int i : g[u]) {
auto [v, c] = e[i];
if (c > 0 && h[v] == -1) {
h[v] = h[u] + 1;
if (v == t) {
return true;
}
que.push(v);
}
}
}
return false;
}
T dfs(int u, int t, T f) {
if (u == t) {
return f;
}
auto r = f;
for (int &i = cur[u]; i < int(g[u].size()); ++i) {
const int j = g[u][i];
auto [v, c] = e[j];
if (c > 0 && h[v] == h[u] + 1) {
auto a = dfs(v, t, std::min(r, c));
e[j].cap -= a;
e[j ^ 1].cap += a;
r -= a;
if (r == 0) {
return f;
}
}
}
return f - r;
}
void addEdge(int u, int v, T c) {
g[u].push_back(e.size());
e.emplace_back(v, c);
g[v].push_back(e.size());
e.emplace_back(u, 0);
}
T maxFlow(int s, int t) {
T ans = 0;
while (bfs(s, t)) {
cur.assign(n, 0);
ans += dfs(s, t, std::numeric_limits<T>::max());
}
return ans;
}
};
最大流（Flow 旧版其二，浮点数应用）
/** 最大流（Flow 旧版其二，浮点数应用）
* 2022-04-09: https://cf.dianhsu.com/gym/104288/submission/201412765
**/
template<class T>
struct Flow {
const int n;
struct Edge {
int to;
T cap;
Edge(int to, T cap) : to(to), cap(cap) {}
};
std::vector<Edge> e;
std::vector<std::vector<int>> g;
std::vector<int> cur, h;
Flow(int n) : n(n), g(n) {}
bool bfs(int s, int t) {
h.assign(n, -1);
std::queue<int> que;
h[s] = 0;
que.push(s);
while (!que.empty()) {
const int u = que.front();
que.pop();
for (int i : g[u]) {
auto [v, c] = e[i];
if (c > 0 && h[v] == -1) {
h[v] = h[u] + 1;
if (v == t) {
return true;
}
que.push(v);
}
}
}
return false;
}
T dfs(int u, int t, T f) {
if (u == t) {
return f;
}
auto r = f;
double res = 0;
for (int &i = cur[u]; i < int(g[u].size()); ++i) {
const int j = g[u][i];
auto [v, c] = e[j];
if (c > 0 && h[v] == h[u] + 1) {
auto a = dfs(v, t, std::min(r, c));
res += a;
e[j].cap -= a;
e[j ^ 1].cap += a;
r -= a;
if (r == 0) {
return f;
}
}
}
return res;
}
void addEdge(int u, int v, T c) {
g[u].push_back(e.size());
e.emplace_back(v, c);
g[v].push_back(e.size());
e.emplace_back(u, 0);
}
T maxFlow(int s, int t) {
T ans = 0;
while (bfs(s, t)) {
cur.assign(n, 0);
ans += dfs(s, t, 1E100);
}
return ans;
}
};
最大流（MaxFlow 新版）
/** 最大流（MaxFlow 新版）
* 2023-07-21: https://ac.nowcoder.com/acm/contest/view-submission?submissionId=62915815
**/
constexpr int inf = 1E9;
template<class T>
struct MaxFlow {
struct _Edge {
int to;
T cap;
_Edge(int to, T cap) : to(to), cap(cap) {}
};
int n;
std::vector<_Edge> e;
std::vector<std::vector<int>> g;
std::vector<int> cur, h;
MaxFlow() {}
MaxFlow(int n) {
init(n);
}
void init(int n) {
this->n = n;
e.clear();
g.assign(n, {});
cur.resize(n);
h.resize(n);
}
bool bfs(int s, int t) {
h.assign(n, -1);
std::queue<int> que;
h[s] = 0;
que.push(s);
while (!que.empty()) {
const int u = que.front();
que.pop();
for (int i : g[u]) {
auto [v, c] = e[i];
if (c > 0 && h[v] == -1) {
h[v] = h[u] + 1;
if (v == t) {
return true;
}
que.push(v);
}
}
}
return false;
}
T dfs(int u, int t, T f) {
if (u == t) {
return f;
}
auto r = f;
for (int &i = cur[u]; i < int(g[u].size()); ++i) {
const int j = g[u][i];
auto [v, c] = e[j];
if (c > 0 && h[v] == h[u] + 1) {
auto a = dfs(v, t, std::min(r, c));
e[j].cap -= a;
e[j ^ 1].cap += a;
r -= a;
if (r == 0) {
return f;
}
}
}
return f - r;
}
void addEdge(int u, int v, T c) {
g[u].push_back(e.size());
e.emplace_back(v, c);
g[v].push_back(e.size());
e.emplace_back(u, 0);
}
T flow(int s, int t) {
T ans = 0;
while (bfs(s, t)) {
cur.assign(n, 0);
ans += dfs(s, t, std::numeric_limits<T>::max());
}
return ans;
}
std::vector<bool> minCut() {
std::vector<bool> c(n);
for (int i = 0; i < n; i++) {
c[i] = (h[i] != -1);
}
return c;
}
struct Edge {
int from;
int to;
T cap;
T flow;
};
std::vector<Edge> edges() {
std::vector<Edge> a;
for (int i = 0; i < e.size(); i += 2) {
Edge x;
x.from = e[i + 1].to;
x.to = e[i].to;
x.cap = e[i].cap + e[i + 1].cap;
x.flow = e[i + 1].cap;
a.push_back(x);
}
return a;
}
};
费用流
费用流（MCFGraph 旧版）
/** 费用流（MCFGraph 旧版）
* 2022-12-12: https://codeforces.com/contest/1766/submission/184974697
*
* 下方为最小费用**最大流**模板，如需求解最小费用**可行流**，需要去除建边限制
**/
struct MCFGraph {
struct Edge {
int v, c, f;
Edge(int v, int c, int f) : v(v), c(c), f(f) {}
};
const int n;
std::vector<Edge> e;
std::vector<std::vector<int>> g;
std::vector<i64> h, dis;
std::vector<int> pre;
bool dijkstra(int s, int t) {
dis.assign(n, std::numeric_limits<i64>::max());
pre.assign(n, -1);
std::priority_queue<std::pair<i64, int>, std::vector<std::pair<i64, int>>, std::greater<std::pair<i64, int>>> que;
dis[s] = 0;
que.emplace(0, s);
while (!que.empty()) {
i64 d = que.top().first;
int u = que.top().second;
que.pop();
if (dis[u] < d) continue;
for (int i : g[u]) {
int v = e[i].v;
int c = e[i].c;
int f = e[i].f;
if (c > 0 && dis[v] > d + h[u] - h[v] + f) {
dis[v] = d + h[u] - h[v] + f;
pre[v] = i;
que.emplace(dis[v], v);
}
}
}
return dis[t] != std::numeric_limits<i64>::max();
}
MCFGraph(int n) : n(n), g(n) {}
void addEdge(int u, int v, int c, int f) {
// if (f < 0) {
g[u].push_back(e.size());
e.emplace_back(v, 0, f);
g[v].push_back(e.size());
e.emplace_back(u, c, -f);
// } else {
// g[u].push_back(e.size());
// e.emplace_back(v, c, f);
// g[v].push_back(e.size());
// e.emplace_back(u, 0, -f);
// }
}
std::pair<int, i64> flow(int s, int t) {
int flow = 0;
i64 cost = 0;
h.assign(n, 0);
while (dijkstra(s, t)) {
for (int i = 0; i < n; ++i) h[i] += dis[i];
int aug = std::numeric_limits<int>::max();
for (int i = t; i != s; i = e[pre[i] ^ 1].v) aug = std::min(aug, e[pre[i]].c);
for (int i = t; i != s; i = e[pre[i] ^ 1].v) {
e[pre[i]].c -= aug;
e[pre[i] ^ 1].c += aug;
}
flow += aug;
cost += i64(aug) * h[t];
}
return std::make_pair(flow, cost);
}
};
费用流（MinCostFlow 新版）
/** 费用流（MinCostFlow 新版）
* 2023-11-09: https://qoj.ac/submission/244680
**/
template<class T>
struct MinCostFlow {
struct _Edge {
int to;
T cap;
T cost;
_Edge(int to_, T cap_, T cost_) : to(to_), cap(cap_), cost(cost_) {}
};
int n;
std::vector<_Edge> e;
std::vector<std::vector<int>> g;
std::vector<T> h, dis;
std::vector<int> pre;
bool dijkstra(int s, int t) {
dis.assign(n, std::numeric_limits<T>::max());
pre.assign(n, -1);
std::priority_queue<std::pair<T, int>, std::vector<std::pair<T, int>>, std::greater<std::pair<T, int>>> que;
dis[s] = 0;
que.emplace(0, s);
while (!que.empty()) {
T d = que.top().first;
int u = que.top().second;
que.pop();
if (dis[u] != d) {
continue;
}
for (int i : g[u]) {
int v = e[i].to;
T cap = e[i].cap;
T cost = e[i].cost;
if (cap > 0 && dis[v] > d + h[u] - h[v] + cost) {
dis[v] = d + h[u] - h[v] + cost;
pre[v] = i;
que.emplace(dis[v], v);
}
}
}
return dis[t] != std::numeric_limits<T>::max();
}
MinCostFlow() {}
MinCostFlow(int n_) {
init(n_);
}
void init(int n_) {
n = n_;
e.clear();
g.assign(n, {});
}
void addEdge(int u, int v, T cap, T cost) {
g[u].push_back(e.size());
e.emplace_back(v, cap, cost);
g[v].push_back(e.size());
e.emplace_back(u, 0, -cost);
}
std::pair<T, T> flow(int s, int t) {
T flow = 0;
T cost = 0;
h.assign(n, 0);
while (dijkstra(s, t)) {
for (int i = 0; i < n; ++i) {
h[i] += dis[i];
}
T aug = std::numeric_limits<int>::max();
for (int i = t; i != s; i = e[pre[i] ^ 1].to) {
aug = std::min(aug, e[pre[i]].cap);
}
for (int i = t; i != s; i = e[pre[i] ^ 1].to) {
e[pre[i]].cap -= aug;
e[pre[i] ^ 1].cap += aug;
}
flow += aug;
cost += aug * h[t];
}
return std::make_pair(flow, cost);
}
struct Edge {
int from;
int to;
T cap;
T cost;
T flow;
};
std::vector<Edge> edges() {
std::vector<Edge> a;
for (int i = 0; i < e.size(); i += 2) {
Edge x;
x.from = e[i + 1].to;
x.to = e[i].to;
x.cap = e[i].cap + e[i + 1].cap;
x.cost = e[i].cost;
x.flow = e[i + 1].cap;
a.push_back(x);
}
return a;
}
};
树链剖分（HLD）
/** 树链剖分（HLD）
* 2023-08-31: https://codeforces.com/contest/1863/submission/221214363
**/
struct HLD {
int n;
std::vector<int> siz, top, dep, parent, in, out, seq;
std::vector<std::vector<int>> adj;
int cur;
HLD() {}
HLD(int n) {
init(n);
}
void init(int n) {
this->n = n;
siz.resize(n);
top.resize(n);
dep.resize(n);
parent.resize(n);
in.resize(n);
out.resize(n);
seq.resize(n);
cur = 0;
adj.assign(n, {});
}
void addEdge(int u, int v) {
adj[u].push_back(v);
adj[v].push_back(u);
}
void work(int root = 0) {
top[root] = root;
dep[root] = 0;
parent[root] = -1;
dfs1(root);
dfs2(root);
}
void dfs1(int u) {
if (parent[u] != -1) {
adj[u].erase(std::find(adj[u].begin(), adj[u].end(), parent[u]));
}
siz[u] = 1;
for (auto &v : adj[u]) {
parent[v] = u;
dep[v] = dep[u] + 1;
dfs1(v);
siz[u] += siz[v];
if (siz[v] > siz[adj[u][0]]) {
std::swap(v, adj[u][0]);
}
}
}
void dfs2(int u) {
in[u] = cur++;
seq[in[u]] = u;
for (auto v : adj[u]) {
top[v] = v == adj[u][0] ? top[u] : v;
dfs2(v);
}
out[u] = cur;
}
int lca(int u, int v) {
while (top[u] != top[v]) {
if (dep[top[u]] > dep[top[v]]) {
u = parent[top[u]];
} else {
v = parent[top[v]];
}
}
return dep[u] < dep[v] ? u : v;
}
int dist(int u, int v) {
return dep[u] + dep[v] - 2 * dep[lca(u, v)];
}
int jump(int u, int k) {
if (dep[u] < k) {
return -1;
}
int d = dep[u] - k;
while (dep[top[u]] > d) {
u = parent[top[u]];
}
return seq[in[u] - dep[u] + d];
}
bool isAncester(int u, int v) {
return in[u] <= in[v] && in[v] < out[u];
}
int rootedParent(int u, int v) {
std::swap(u, v);
if (u == v) {
return u;
}
if (!isAncester(u, v)) {
return parent[u];
}
auto it = std::upper_bound(adj[u].begin(), adj[u].end(), v, [&](int x, int y) {
return in[x] < in[y];
}) - 1;
return *it;
}
int rootedSize(int u, int v) {
if (u == v) {
return n;
}
if (!isAncester(v, u)) {
return siz[v];
}
return n - siz[rootedParent(u, v)];
}
int rootedLca(int a, int b, int c) {
return lca(a, b) ^ lca(b, c) ^ lca(c, a);
}
};
三、数论、几何、多项式
点击展开本章节
快速幂
/** 快速幂 - 普通版
* 2023-10-09: https://atcoder.jp/contests/tenka1-2017/submissions/46411797
**/
int power(int a, i64 b, int p) {
int res = 1;
for (; b; b /= 2, a = 1LL * a * a % p) {
if (b % 2) {
res = 1LL * res * a % p;
}
}
return res;
}
/** 快速幂 - 手写乘法
* 2023-09-27: https://qoj.ac/submission/189343
**/
using i64 = long long;
i64 mul(i64 a, i64 b, i64 p) {
i64 c = a * b - i64(1.0L * a * b / p) * p;
c %= p;
if (c < 0) {
c += p;
}
return c;
}
i64 power(i64 a, i64 b, i64 p) {
i64 res = 1;
for (; b; b /= 2, a = mul(a, a, p)) {
if (b % 2) {
res = mul(res, a, p);
}
}
return res;
}
基姆拉尔森公式
/** 基姆拉尔森公式
* 2023-09-05: https://qoj.ac/submission/164735
**/
const int d[] = {31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31};
bool isLeap(int y) {
return y % 400 == 0 || (y % 4 == 0 && y % 100 != 0);
}
int daysInMonth(int y, int m) {
return d[m - 1] + (isLeap(y) && m == 2);
}
int getDay(int y, int m, int d) {
int ans = 0;
for (int i = 1970; i < y; i++) {
ans += 365 + isLeap(i);
}
for (int i = 1; i < m; i++) {
ans += daysInMonth(y, i);
}
ans += d;
return (ans + 2) % 7 + 1;
}
欧拉筛
/** 欧拉筛
* 2023-11-14: https://qoj.ac/submission/251234
**/
std::vector<int> minp, primes;
void sieve(int n) {
minp.assign(n + 1, 0);
primes.clear();
for (int i = 2; i <= n; i++) {
if (minp[i] == 0) {
minp[i] = i;
primes.push_back(i);
}
for (auto p : primes) {
if (i * p > n) {
break;
}
minp[i * p] = p;
if (p == minp[i]) {
break;
}
}
}
}
bool isprime(int n) {
return minp[n] == n;
}
/** 欧拉筛
* 2023-03-22: https://yukicoder.me/submissions/851524
**/
void sieve(int n) {
minp.assign(n + 1, 0);
phi.assign(n + 1, 0);
primes.clear();
for (int i = 2; i <= n; i++) {
if (minp[i] == 0) {
minp[i] = i;
phi[i] = i - 1;
primes.push_back(i);
}
for (auto p : primes) {
if (i * p > n) {
break;
}
minp[i * p] = p;
if (p == minp[i]) {
phi[i * p] = phi[i] * p;
break;
}
phi[i * p] = phi[i] * (p - 1);
}
}
for (int i = 2; i <= n; i++) {
phi[i] += phi[i - 1];
}
}
莫比乌斯函数筛（莫比乌斯反演）
/** 莫比乌斯函数筛（莫比乌斯反演）
* 2023-03-04: https://atcoder.jp/contests/tupc2022/submissions/39391116
* 2023-04-07: https://yukicoder.me/submissions/857472
**/
std::unordered_map<int, Z> fMu;
std::vector<int> minp, primes, phi, mu;
std::vector<i64> sphi;
void sieve(int n) {
minp.assign(n + 1, 0);
phi.assign(n + 1, 0);
sphi.assign(n + 1, 0);
mu.assign(n + 1, 0);
primes.clear();
phi[1] = 1;
mu[1] = 1;
for (int i = 2; i <= n; i++) {
if (minp[i] == 0) {
minp[i] = i;
phi[i] = i - 1;
mu[i] = -1;
primes.push_back(i);
}
for (auto p : primes) {
if (i * p > n) {
break;
}
minp[i * p] = p;
if (p == minp[i]) {
phi[i * p] = phi[i] * p;
break;
}
phi[i * p] = phi[i] * (p - 1);
mu[i * p] = -mu[i];
}
}
for (int i = 1; i <= n; i++) {
sphi[i] = sphi[i - 1] + phi[i];
mu[i] += mu[i - 1];
}
}
Z sumMu(int n) {
if (n <= N) {
return mu[n];
}
if (fMu.count(n)) {
return fMu[n];
}
if (n == 0) {
return 0;
}
Z ans = 1;
for (int l = 2, r; l <= n; l = r + 1) {
r = n / (n / l);
ans -= (r - l + 1) * sumMu(n / l);
}
return ans;
}
扩展欧几里得（exgcd）
/** 扩展欧几里得（exgcd）
* 2024-08-07: https://codeforces.com/contest/1993/submission/275110715
**/
i64 exgcd(i64 a, i64 b, i64 &x, i64 &y) {
if (b == 0) {
x = 1;
y = 0;
return a;
}
i64 g = exgcd(b, a % b, y, x);
y -= a / b * x;
return g;
}
// ax + b = 0 (mod m)
std::pair<i64, i64> sol(i64 a, i64 b, i64 m) {
assert(m > 0);
b *= -1;
i64 x, y;
i64 g = exgcd(a, m, x, y);
if (g < 0) {
g *= -1;
x *= -1;
y *= -1;
}
if (b % g != 0) {
return {-1, -1};
}
x = x * (b / g) % (m / g);
if (x < 0) {
x += m / g;
}
return {x, m / g};
}
/** 扩展欧几里得（exgcd）
* 2023-09-05: https://qoj.ac/submission/165983
**/
std::array<i64, 3> exgcd(i64 a, i64 b) {
if (!b) {
return {a, 1, 0};
}
auto [g, x, y] = exgcd(b, a % b);
return {g, y, x - a / b * y};
}
欧拉函数
欧拉函数（求解单个数的欧拉函数）
/** 欧拉函数（求解单个数的欧拉函数）
* 2023-10-09: https://atcoder.jp/contests/tenka1-2017/submissions/46411797
**/
int phi(int n) {
int res = n;
for (int i = 2; i * i <= n; i++) {
if (n % i == 0) {
while (n % i == 0) {
n /= i;
}
res = res / i * (i - 1);
}
}
if (n > 1) {
res = res / n * (n - 1);
}
return res;
}
欧拉函数（求解全部数的欧拉函数）
/** 欧拉函数（求解全部数的欧拉函数）
* 2023-09-24: https://qoj.ac/submission/187055
**/
constexpr int N = 1E7;
constexpr int P = 1000003;
bool isprime[N + 1];
int phi[N + 1];
std::vector<int> primes;
std::fill(isprime + 2, isprime + N + 1, true);
phi[1] = 1;
for (int i = 2; i <= N; i++) {
if (isprime[i]) {
primes.push_back(i);
phi[i] = i - 1;
}
for (auto p : primes) {
if (i * p > N) {
break;
}
isprime[i * p] = false;
if (i % p == 0) {
phi[i * p] = phi[i] * p;
break;
}
phi[i * p] = phi[i] * (p - 1);
}
}
组合数
组合数（小范围预处理，逆元+杨辉三角）
/** 组合数（小范围预处理，逆元+杨辉三角）
* 2024-03-14: https://qoj.ac/submission/353877
* 2023-10-06: https://qoj.ac/submission/203196
**/
constexpr int P = 1000000007;
constexpr int L = 10000;
int fac[L + 1], invfac[L + 1];
int sumbinom[L + 1][7];
int binom(int n, int m) {
if (n < m || m < 0) {
return 0;
}
return 1LL * fac[n] * invfac[m] % P * invfac[n - m] % P;
}
int power(int a, int b) {
int res = 1;
for (; b; b /= 2, a = 1LL * a * a % P) {
if (b % 2) {
res = 1LL * res * a % P;
}
}
return res;
}
int main() {
fac[0] = 1;
for (int i = 1; i <= L; i++) {
fac[i] = 1LL * fac[i - 1] * i % P;
}
invfac[L] = power(fac[L], P - 2);
for (int i = L; i; i--) {
invfac[i - 1] = 1LL * invfac[i] * i % P;
}
sumbinom[0][0] = 1;
for (int i = 1; i <= L; i++) {
for (int j = 0; j < 7; j++) {
sumbinom[i][j] = (sumbinom[i - 1][j] + sumbinom[i - 1][(j + 6) % 7]) % P;
}
}
}
组合数（Comb, with. ModIntBase）
/** 组合数（Comb, with. ModIntBase）
* 2024-08-06: https://codeforces.com/contest/1999/submission/274744751
**/
struct Comb {
int n;
std::vector<Z> _fac;
std::vector<Z> _invfac;
std::vector<Z> _inv;
Comb() : n{0}, _fac{1}, _invfac{1}, _inv{0} {}
Comb(int n) : Comb() {
init(n);
}
void init(int m) {
if (m <= n) return;
_fac.resize(m + 1);
_invfac.resize(m + 1);
_inv.resize(m + 1);
for (int i = n + 1; i <= m; i++) {
_fac[i] = _fac[i - 1] * i;
}
_invfac[m] = _fac[m].inv();
for (int i = m; i > n; i--) {
_invfac[i - 1] = _invfac[i] * i;
_inv[i] = _invfac[i] * _fac[i - 1];
}
n = m;
}
Z fac(int m) {
if (m > n) init(2 * m);
return _fac[m];
}
Z invfac(int m) {
if (m > n) init(2 * m);
return _invfac[m];
}
Z inv(int m) {
if (m > n) init(2 * m);
return _inv[m];
}
Z binom(int n, int m) {
if (n < m || m < 0) return 0;
return fac(n) * invfac(m) * invfac(n - m);
}
} comb;
素数测试与因式分解（Miller-Rabin & Pollard-Rho）
/** 素数测试与因式分解（Miller-Rabin & Pollard-Rho）
* 2023-05-16: https://cf.dianhsu.com/gym/104354/submission/206130894
**/
i64 mul(i64 a, i64 b, i64 m) {
return static_cast<__int128>(a) * b % m;
}
i64 power(i64 a, i64 b, i64 m) {
i64 res = 1 % m;
for (; b; b >>= 1, a = mul(a, a, m))
if (b & 1)
res = mul(res, a, m);
return res;
}
bool isprime(i64 n) {
if (n < 2)
return false;
static constexpr int A[] = {2, 3, 5, 7, 11, 13, 17, 19, 23};
int s = __builtin_ctzll(n - 1);
i64 d = (n - 1) >> s;
for (auto a : A) {
if (a == n)
return true;
i64 x = power(a, d, n);
if (x == 1 || x == n - 1)
continue;
bool ok = false;
for (int i = 0; i < s - 1; ++i) {
x = mul(x, x, n);
if (x == n - 1) {
ok = true;
break;
}
}
if (!ok)
return false;
}
return true;
}
std::vector<i64> factorize(i64 n) {
std::vector<i64> p;
std::function<void(i64)> f = [&](i64 n) {
if (n <= 10000) {
for (int i = 2; i * i <= n; ++i)
for (; n % i == 0; n /= i)
p.push_back(i);
if (n > 1)
p.push_back(n);
return;
}
if (isprime(n)) {
p.push_back(n);
return;
}
auto g = [&](i64 x) {
return (mul(x, x, n) + 1) % n;
};
i64 x0 = 2;
while (true) {
i64 x = x0;
i64 y = x0;
i64 d = 1;
i64 power = 1, lam = 0;
i64 v = 1;
while (d == 1) {
y = g(y);
++lam;
v = mul(v, std::abs(x - y), n);
if (lam % 127 == 0) {
d = std::gcd(v, n);
v = 1;
}
if (power == lam) {
x = y;
power *= 2;
lam = 0;
d = std::gcd(v, n);
v = 1;
}
}
if (d != n) {
f(d);
f(n / d);
return;
}
++x0;
}
};
f(n);
std::sort(p.begin(), p.end());
return p;
}
平面几何
平面几何（Point）
长度过长，点击查看
/** 平面几何（Point）
* 2023-09-22: https://qoj.ac/submission/185408
**/
template<class T>
struct Point {
T x;
T y;
Point(const T &x_ = 0, const T &y_ = 0) : x(x_), y(y_) {}
template<class U>
operator Point<U>() {
return Point<U>(U(x), U(y));
}
Point &operator+=(const Point &p) & {
x += p.x;
y += p.y;
return *this;
}
Point &operator-=(const Point &p) & {
x -= p.x;
y -= p.y;
return *this;
}
Point &operator*=(const T &v) & {
x *= v;
y *= v;
return *this;
}
Point &operator/=(const T &v) & {
x /= v;
y /= v;
return *this;
}
Point operator-() const {
return Point(-x, -y);
}
friend Point operator+(Point a, const Point &b) {
return a += b;
}
friend Point operator-(Point a, const Point &b) {
return a -= b;
}
friend Point operator*(Point a, const T &b) {
return a *= b;
}
friend Point operator/(Point a, const T &b) {
return a /= b;
}
friend Point operator*(const T &a, Point b) {
return b *= a;
}
friend bool operator==(const Point &a, const Point &b) {
return a.x == b.x && a.y == b.y;
}
friend std::istream &operator>>(std::istream &is, Point &p) {
return is >> p.x >> p.y;
}
friend std::ostream &operator<<(std::ostream &os, const Point &p) {
return os << "(" << p.x << ", " << p.y << ")";
}
};
template<class T>
struct Line {
Point<T> a;
Point<T> b;
Line(const Point<T> &a_ = Point<T>(), const Point<T> &b_ = Point<T>()) : a(a_), b(b_) {}
};
template<class T>
T dot(const Point<T> &a, const Point<T> &b) {
return a.x * b.x + a.y * b.y;
}
template<class T>
T cross(const Point<T> &a, const Point<T> &b) {
return a.x * b.y - a.y * b.x;
}
template<class T>
T square(const Point<T> &p) {
return dot(p, p);
}
template<class T>
double length(const Point<T> &p) {
return std::sqrt(square(p));
}
template<class T>
double length(const Line<T> &l) {
return length(l.a - l.b);
}
template<class T>
Point<T> normalize(const Point<T> &p) {
return p / length(p);
}
template<class T>
bool parallel(const Line<T> &l1, const Line<T> &l2) {
return cross(l1.b - l1.a, l2.b - l2.a) == 0;
}
template<class T>
double distance(const Point<T> &a, const Point<T> &b) {
return length(a - b);
}
template<class T>
double distancePL(const Point<T> &p, const Line<T> &l) {
return std::abs(cross(l.a - l.b, l.a - p)) / length(l);
}
template<class T>
double distancePS(const Point<T> &p, const Line<T> &l) {
if (dot(p - l.a, l.b - l.a) < 0) {
return distance(p, l.a);
}
if (dot(p - l.b, l.a - l.b) < 0) {
return distance(p, l.b);
}
return distancePL(p, l);
}
template<class T>
Point<T> rotate(const Point<T> &a) {
return Point(-a.y, a.x);
}
template<class T>
int sgn(const Point<T> &a) {
return a.y > 0 || (a.y == 0 && a.x > 0) ? 1 : -1;
}
template<class T>
bool pointOnLineLeft(const Point<T> &p, const Line<T> &l) {
return cross(l.b - l.a, p - l.a) > 0;
}
template<class T>
Point<T> lineIntersection(const Line<T> &l1, const Line<T> &l2) {
return l1.a + (l1.b - l1.a) * (cross(l2.b - l2.a, l1.a - l2.a) / cross(l2.b - l2.a, l1.a - l1.b));
}
template<class T>
bool pointOnSegment(const Point<T> &p, const Line<T> &l) {
return cross(p - l.a, l.b - l.a) == 0 && std::min(l.a.x, l.b.x) <= p.x && p.x <= std::max(l.a.x, l.b.x)
&& std::min(l.a.y, l.b.y) <= p.y && p.y <= std::max(l.a.y, l.b.y);
}
template<class T>
bool pointInPolygon(const Point<T> &a, const std::vector<Point<T>> &p) {
int n = p.size();
for (int i = 0; i < n; i++) {
if (pointOnSegment(a, Line(p[i], p[(i + 1) % n]))) {
return true;
}
}
int t = 0;
for (int i = 0; i < n; i++) {
auto u = p[i];
auto v = p[(i + 1) % n];
if (u.x < a.x && v.x >= a.x && pointOnLineLeft(a, Line(v, u))) {
t ^= 1;
}
if (u.x >= a.x && v.x < a.x && pointOnLineLeft(a, Line(u, v))) {
t ^= 1;
}
}
return t == 1;
}
// 0 : not intersect
// 1 : strictly intersect
// 2 : overlap
// 3 : intersect at endpoint
template<class T>
std::tuple<int, Point<T>, Point<T>> segmentIntersection(const Line<T> &l1, const Line<T> &l2) {
if (std::max(l1.a.x, l1.b.x) < std::min(l2.a.x, l2.b.x)) {
return {0, Point<T>(), Point<T>()};
}
if (std::min(l1.a.x, l1.b.x) > std::max(l2.a.x, l2.b.x)) {
return {0, Point<T>(), Point<T>()};
}
if (std::max(l1.a.y, l1.b.y) < std::min(l2.a.y, l2.b.y)) {
return {0, Point<T>(), Point<T>()};
}
if (std::min(l1.a.y, l1.b.y) > std::max(l2.a.y, l2.b.y)) {
return {0, Point<T>(), Point<T>()};
}
if (cross(l1.b - l1.a, l2.b - l2.a) == 0) {
if (cross(l1.b - l1.a, l2.a - l1.a) != 0) {
return {0, Point<T>(), Point<T>()};
} else {
auto maxx1 = std::max(l1.a.x, l1.b.x);
auto minx1 = std::min(l1.a.x, l1.b.x);
auto maxy1 = std::max(l1.a.y, l1.b.y);
auto miny1 = std::min(l1.a.y, l1.b.y);
auto maxx2 = std::max(l2.a.x, l2.b.x);
auto minx2 = std::min(l2.a.x, l2.b.x);
auto maxy2 = std::max(l2.a.y, l2.b.y);
auto miny2 = std::min(l2.a.y, l2.b.y);
Point<T> p1(std::max(minx1, minx2), std::max(miny1, miny2));
Point<T> p2(std::min(maxx1, maxx2), std::min(maxy1, maxy2));
if (!pointOnSegment(p1, l1)) {
std::swap(p1.y, p2.y);
}
if (p1 == p2) {
return {3, p1, p2};
} else {
return {2, p1, p2};
}
}
}
auto cp1 = cross(l2.a - l1.a, l2.b - l1.a);
auto cp2 = cross(l2.a - l1.b, l2.b - l1.b);
auto cp3 = cross(l1.a - l2.a, l1.b - l2.a);
auto cp4 = cross(l1.a - l2.b, l1.b - l2.b);
if ((cp1 > 0 && cp2 > 0) || (cp1 < 0 && cp2 < 0) || (cp3 > 0 && cp4 > 0) || (cp3 < 0 && cp4 < 0)) {
return {0, Point<T>(), Point<T>()};
}
Point p = lineIntersection(l1, l2);
if (cp1 != 0 && cp2 != 0 && cp3 != 0 && cp4 != 0) {
return {1, p, p};
} else {
return {3, p, p};
}
}
template<class T>
double distanceSS(const Line<T> &l1, const Line<T> &l2) {
if (std::get<0>(segmentIntersection(l1, l2)) != 0) {
return 0.0;
}
return std::min({distancePS(l1.a, l2), distancePS(l1.b, l2), distancePS(l2.a, l1), distancePS(l2.b, l1)});
}
template<class T>
bool segmentInPolygon(const Line<T> &l, const std::vector<Point<T>> &p) {
int n = p.size();
if (!pointInPolygon(l.a, p)) {
return false;
}
if (!pointInPolygon(l.b, p)) {
return false;
}
for (int i = 0; i < n; i++) {
auto u = p[i];
auto v = p[(i + 1) % n];
auto w = p[(i + 2) % n];
auto [t, p1, p2] = segmentIntersection(l, Line(u, v));
if (t == 1) {
return false;
}
if (t == 0) {
continue;
}
if (t == 2) {
if (pointOnSegment(v, l) && v != l.a && v != l.b) {
if (cross(v - u, w - v) > 0) {
return false;
}
}
} else {
if (p1 != u && p1 != v) {
if (pointOnLineLeft(l.a, Line(v, u))
|| pointOnLineLeft(l.b, Line(v, u))) {
return false;
}
} else if (p1 == v) {
if (l.a == v) {
if (pointOnLineLeft(u, l)) {
if (pointOnLineLeft(w, l)
&& pointOnLineLeft(w, Line(u, v))) {
return false;
}
} else {
if (pointOnLineLeft(w, l)
|| pointOnLineLeft(w, Line(u, v))) {
return false;
}
}
} else if (l.b == v) {
if (pointOnLineLeft(u, Line(l.b, l.a))) {
if (pointOnLineLeft(w, Line(l.b, l.a))
&& pointOnLineLeft(w, Line(u, v))) {
return false;
}
} else {
if (pointOnLineLeft(w, Line(l.b, l.a))
|| pointOnLineLeft(w, Line(u, v))) {
return false;
}
}
} else {
if (pointOnLineLeft(u, l)) {
if (pointOnLineLeft(w, Line(l.b, l.a))
|| pointOnLineLeft(w, Line(u, v))) {
return false;
}
} else {
if (pointOnLineLeft(w, l)
|| pointOnLineLeft(w, Line(u, v))) {
return false;
}
}
}
}
}
}
return true;
}
template<class T>
std::vector<Point<T>> hp(std::vector<Line<T>> lines) {
std::sort(lines.begin(), lines.end(), [&](auto l1, auto l2) {
auto d1 = l1.b - l1.a;
auto d2 = l2.b - l2.a;
if (sgn(d1) != sgn(d2)) {
return sgn(d1) == 1;
}
return cross(d1, d2) > 0;
});
std::deque<Line<T>> ls;
std::deque<Point<T>> ps;
for (auto l : lines) {
if (ls.empty()) {
ls.push_back(l);
continue;
}
while (!ps.empty() && !pointOnLineLeft(ps.back(), l)) {
ps.pop_back();
ls.pop_back();
}
while (!ps.empty() && !pointOnLineLeft(ps[0], l)) {
ps.pop_front();
ls.pop_front();
}
if (cross(l.b - l.a, ls.back().b - ls.back().a) == 0) {
if (dot(l.b - l.a, ls.back().b - ls.back().a) > 0) {
if (!pointOnLineLeft(ls.back().a, l)) {
assert(ls.size() == 1);
ls[0] = l;
}
continue;
}
return {};
}
ps.push_back(lineIntersection(ls.back(), l));
ls.push_back(l);
}
while (!ps.empty() && !pointOnLineLeft(ps.back(), ls[0])) {
ps.pop_back();
ls.pop_back();
}
if (ls.size() <= 2) {
return {};
}
ps.push_back(lineIntersection(ls[0], ls.back()));
return std::vector(ps.begin(), ps.end());
}
using real = long double;
using P = Point<real>;
constexpr real eps = 0;
平面几何（with. std::complex）
/** 平面几何（with. complex）
* 2023-09-04: https://qoj.ac/submission/164445
**/
using Point = std::complex<long double>;
#define x real
#define y imag
long double dot(const Point &a, const Point &b) {
return (std::conj(a) * b).x();
}
long double cross(const Point &a, const Point &b) {
return (std::conj(a) * b).y();
}
long double length(const Point &a) {
return std::sqrt(dot(a, a));
}
long double dist(const Point &a, const Point &b) {
return length(a - b);
}
long double get(const Point &a, const Point &b, const Point &c, const Point &d) {
auto e = a + (b - a) * cross(c - a, d - a) / cross(b - a, d - c);
return dist(d, e);
}
立体几何（Point）
/** 立体几何（Point）
* 2023-09-25 (i64): https://qoj.ac/submission/188519
* 2023-09-28 (double): https://qoj.ac/submission/190463
**/
using i64 = long long;
using real = double;
struct Point {
real x = 0;
real y = 0;
real z = 0;
};
Point operator+(const Point &a, const Point &b) {
return {a.x + b.x, a.y + b.y, a.z + b.z};
}
Point operator-(const Point &a, const Point &b) {
return {a.x - b.x, a.y - b.y, a.z - b.z};
}
Point operator*(const Point &a, real b) {
return {a.x * b, a.y * b, a.z * b};
}
Point operator/(const Point &a, real b) {
return {a.x / b, a.y / b, a.z / b};
}
real length(const Point &a) {
return std::hypot(a.x, a.y, a.z);
}
Point normalize(const Point &a) {
real l = length(a);
return {a.x / l, a.y / l, a.z / l};
}
real getAng(real a, real b, real c) {
return std::acos((a * a + b * b - c * c) / 2 / a / b);
}
std::ostream &operator<<(std::ostream &os, const Point &a) {
return os << "(" << a.x << ", " << a.y << ", " << a.z << ")";
}
real dot(const Point &a, const Point &b) {
return a.x * b.x + a.y * b.y + a.z * b.z;
}
Point cross(const Point &a, const Point &b) {
return {
a.y * b.z - a.z * b.y,
a.z * b.x - a.x * b.z,
a.x * b.y - a.y * b.x
};
}
静态凸包
静态凸包（with. Point，旧版）
/** 静态凸包（with. Point，旧版）
* 2023-04-09: https://cf.dianhsu.com/gym/104288/submission/201412835
**/
struct Point {
i64 x;
i64 y;
Point(i64 x = 0, i64 y = 0) : x(x), y(y) {}
};
bool operator==(const Point &a, const Point &b) {
return a.x == b.x && a.y == b.y;
}
Point operator+(const Point &a, const Point &b) {
return Point(a.x + b.x, a.y + b.y);
}
Point operator-(const Point &a, const Point &b) {
return Point(a.x - b.x, a.y - b.y);
}
i64 dot(const Point &a, const Point &b) {
return a.x * b.x + a.y * b.y;
}
i64 cross(const Point &a, const Point &b) {
return a.x * b.y - a.y * b.x;
}
void norm(std::vector<Point> &h) {
int i = 0;
for (int j = 0; j < int(h.size()); j++) {
if (h[j].y < h[i].y || (h[j].y == h[i].y && h[j].x < h[i].x)) {
i = j;
}
}
std::rotate(h.begin(), h.begin() + i, h.end());
}
int sgn(const Point &a) {
return a.y > 0 || (a.y == 0 && a.x > 0) ? 0 : 1;
}
std::vector<Point> getHull(std::vector<Point> p) {
std::vector<Point> h, l;
std::sort(p.begin(), p.end(), [&](auto a, auto b) {
if (a.x != b.x) {
return a.x < b.x;
} else {
return a.y < b.y;
}
});
p.erase(std::unique(p.begin(), p.end()), p.end());
if (p.size() <= 1) {
return p;
}
for (auto a : p) {
while (h.size() > 1 && cross(a - h.back(), a - h[h.size() - 2]) <= 0) {
h.pop_back();
}
while (l.size() > 1 && cross(a - l.back(), a - l[l.size() - 2]) >= 0) {
l.pop_back();
}
l.push_back(a);
h.push_back(a);
}
l.pop_back();
std::reverse(h.begin(), h.end());
h.pop_back();
l.insert(l.end(), h.begin(), h.end());
return l;
}
静态凸包（with. Point，新版）
/** 静态凸包（with. Point，新版）
* 2024-04-06: https://qoj.ac/submission/379920)
**/
struct Point {
i64 x;
i64 y;
Point() : x{0}, y{0} {}
Point(i64 x_, i64 y_) : x{x_}, y{y_} {}
};
i64 dot(Point a, Point b) {
return a.x * b.x + a.y * b.y;
}
i64 cross(Point a, Point b) {
return a.x * b.y - a.y * b.x;
}
Point operator+(Point a, Point b) {
return Point(a.x + b.x, a.y + b.y);
}
Point operator-(Point a, Point b) {
return Point(a.x - b.x, a.y - b.y);
}
auto getHull(std::vector<Point> p) {
std::sort(p.begin(), p.end(),
[&](auto a, auto b) {
return a.x < b.x || (a.x == b.x && a.y < b.y);
});
std::vector<Point> hi, lo;
for (auto p : p) {
while (hi.size() > 1 && cross(hi.back() - hi[hi.size() - 2], p - hi.back()) >= 0) {
hi.pop_back();
}
while (!hi.empty() && hi.back().x == p.x) {
hi.pop_back();
}
hi.push_back(p);
while (lo.size() > 1 && cross(lo.back() - lo[lo.size() - 2], p - lo.back()) <= 0) {
lo.pop_back();
}
if (lo.empty() || lo.back().x < p.x) {
lo.push_back(p);
}
}
return std::make_pair(hi, lo);
}
const double inf = INFINITY;
静态凸包（with. complex）
/** 静态凸包（with. complex）
* 2022-02-04: https://loj.ac/s/1370861
**/
using Point = std::complex<i64>;
#define x real
#define y imag
auto dot(const Point &a, const Point &b) {
return (std::conj(a) * b).x();
}
auto cross(const Point &a, const Point &b) {
return (std::conj(a) * b).y();
}
auto rot(const Point &p) {
return Point(-p.y(), p.x());
}
auto complexHull(std::vector<Point> a) {
std::sort(a.begin(), a.end(), [&](auto a, auto b) {
if (a.x() != b.x()) {
return a.x() < b.x();
} else {
return a.y() < b.y();
}
});
std::vector<Point> l, h;
for (auto p : a) {
while (l.size() > 1 && cross(l.back() - l[l.size() - 2], p - l.back()) <= 0) {
l.pop_back();
}
while (h.size() > 1 && cross(h.back() - h[h.size() - 2], p - h.back()) >= 0) {
h.pop_back();
}
l.push_back(p);
h.push_back(p);
}
std::reverse(h.begin(), h.end());
h.insert(h.end(), l.begin() + 1, l.end() - 1);
return h;
}
int sgn(Point p) {
if (p.y() > 0 || (p.y() == 0 && p.x() < 0)) {
return 0;
} else {
return 1;
}
}
多项式
长度过长，点击查看
### 多项式（Poly，旧版）/** 多项式（Poly，旧版）
* 2021-06-16: https://codeforces.com/gym/103119/submission/119653035
**/
constexpr int C = 1024;
constexpr int P = 998244353;
std::vector<int> rev, roots{0, 1};
int power(int a, int b) {
int res = 1;
for (; b; b >>= 1, a = 1ll * a * a % P)
if (b & 1)
res = 1ll * res * a % P;
return res;
}
void dft(std::vector<int> &a) {
int n = a.size();
if (int(rev.size()) != n) {
int k = __builtin_ctz(n) - 1;
rev.resize(n);
for (int i = 0; i < n; ++i)
rev[i] = rev[i >> 1] >> 1 | (i & 1) << k;
}
for (int i = 0; i < n; ++i)
if (rev[i] < i)
std::swap(a[i], a[rev[i]]);
if (int(roots.size()) < n) {
int k = __builtin_ctz(roots.size());
roots.resize(n);
while ((1 << k) < n) {
int e = power(3, (P - 1) >> (k + 1));
for (int i = 1 << (k - 1); i < (1 << k); ++i) {
roots[2 * i] = roots[i];
roots[2 * i + 1] = 1ll * roots[i] * e % P;
}
++k;
}
}
for (int k = 1; k < n; k *= 2) {
for (int i = 0; i < n; i += 2 * k) {
for (int j = 0; j < k; ++j) {
int u = a[i + j];
int v = 1ll * a[i + j + k] * roots[k + j] % P;
int x = u + v;
if (x >= P)
x -= P;
a[i + j] = x;
x = u - v;
if (x < 0)
x += P;
a[i + j + k] = x;
}
}
}
}
void idft(std::vector<int> &a) {
int n = a.size();
std::reverse(a.begin() + 1, a.end());
dft(a);
int inv = power(n, P - 2);
for (int i = 0; i < n; ++i)
a[i] = 1ll * a[i] * inv % P;
}
struct Poly {
std::vector<int> a;
Poly() {}
Poly(int a0) {
if (a0)
a = {a0};
}
Poly(const std::vector<int> &a1) : a(a1) {
while (!a.empty() && !a.back())
a.pop_back();
}
int size() const {
return a.size();
}
int operator[](int idx) const {
if (idx < 0 || idx >= size())
return 0;
return a[idx];
}
Poly mulxk(int k) const {
auto b = a;
b.insert(b.begin(), k, 0);
return Poly(b);
}
Poly modxk(int k) const {
k = std::min(k, size());
return Poly(std::vector<int>(a.begin(), a.begin() + k));
}
Poly divxk(int k) const {
if (size() <= k)
return Poly();
return Poly(std::vector<int>(a.begin() + k, a.end()));
}
friend Poly operator+(const Poly a, const Poly &b) {
std::vector<int> res(std::max(a.size(), b.size()));
for (int i = 0; i < int(res.size()); ++i) {
res[i] = a[i] + b[i];
if (res[i] >= P)
res[i] -= P;
}
return Poly(res);
}
friend Poly operator-(const Poly a, const Poly &b) {
std::vector<int> res(std::max(a.size(), b.size()));
for (int i = 0; i < int(res.size()); ++i) {
res[i] = a[i] - b[i];
if (res[i] < 0)
res[i] += P;
}
return Poly(res);
}
friend Poly operator*(Poly a, Poly b) {
int sz = 1, tot = a.size() + b.size() - 1;
while (sz < tot)
sz *= 2;
a.a.resize(sz);
b.a.resize(sz);
dft(a.a);
dft(b.a);
for (int i = 0; i < sz; ++i)
a.a[i] = 1ll * a[i] * b[i] % P;
idft(a.a);
return Poly(a.a);
}
Poly &operator+=(Poly b) {
return (*this) = (*this) + b;
}
Poly &operator-=(Poly b) {
return (*this) = (*this) - b;
}
Poly &operator*=(Poly b) {
return (*this) = (*this) * b;
}
Poly deriv() const {
if (a.empty())
return Poly();
std::vector<int> res(size() - 1);
for (int i = 0; i < size() - 1; ++i)
res[i] = 1ll * (i + 1) * a[i + 1] % P;
return Poly(res);
}
Poly integr() const {
if (a.empty())
return Poly();
std::vector<int> res(size() + 1);
for (int i = 0; i < size(); ++i)
res[i + 1] = 1ll * a[i] * power(i + 1, P - 2) % P;
return Poly(res);
}
Poly inv(int m) const {
Poly x(power(a[0], P - 2));
int k = 1;
while (k < m) {
k *= 2;
x = (x * (2 - modxk(k) * x)).modxk(k);
}
return x.modxk(m);
}
Poly log(int m) const {
return (deriv() * inv(m)).integr().modxk(m);
}
Poly exp(int m) const {
Poly x(1);
int k = 1;
while (k < m) {
k *= 2;
x = (x * (1 - x.log(k) + modxk(k))).modxk(k);
}
return x.modxk(m);
}
Poly sqrt(int m) const {
Poly x(1);
int k = 1;
while (k < m) {
k *= 2;
x = (x + (modxk(k) * x.inv(k)).modxk(k)) * ((P + 1) / 2);
}
return x.modxk(m);
}
Poly mulT(Poly b) const {
if (b.size() == 0)
return Poly();
int n = b.size();
std::reverse(b.a.begin(), b.a.end());
return ((*this) * b).divxk(n - 1);
}
std::vector<int> eval(std::vector<int> x) const {
if (size() == 0)
return std::vector<int>(x.size(), 0);
const int n = std::max(int(x.size()), size());
std::vector<Poly> q(4 * n);
std::vector<int> ans(x.size());
x.resize(n);
std::function<void(int, int, int)> build = [&](int p, int l, int r) {
if (r - l == 1) {
q[p] = std::vector<int>{1, (P - x[l]) % P};
} else {
int m = (l + r) / 2;
build(2 * p, l, m);
build(2 * p + 1, m, r);
q[p] = q[2 * p] * q[2 * p + 1];
}
};
build(1, 0, n);
std::function<void(int, int, int, const Poly &)> work = [&](int p, int l, int r, const Poly &num) {
if (r - l == 1) {
if (l < int(ans.size()))
ans[l] = num[0];
} else {
int m = (l + r) / 2;
work(2 * p, l, m, num.mulT(q[2 * p + 1]).modxk(m - l));
work(2 * p + 1, m, r, num.mulT(q[2 * p]).modxk(r - m));
}
};
work(1, 0, n, mulT(q[1].inv(n)));
return ans;
}
};
using i64 = long long;
void dft(std::vector<std::vector<int>> &a) {
int n = a.size();
for (auto &v : a) {
dft(v);
}
for (int i = 0; i < int(a[0].size()); i++) {
std::vector<int> v(n);
for (int j = 0; j < n; j++) {
v[j] = a[j][i];
}
dft(v);
for (int j = 0; j < n; j++) {
a[j][i] = v[j];
}
}
}
void idft(std::vector<std::vector<int>> &a) {
int n = a.size();
for (auto &v : a) {
idft(v);
}
for (int i = 0; i < int(a[0].size()); i++) {
std::vector<int> v(n);
for (int j = 0; j < n; j++) {
v[j] = a[j][i];
}
idft(v);
for (int j = 0; j < n; j++) {
a[j][i] = v[j];
}
}
}
auto inv(const std::vector<std::vector<int>> &a) {
int m = 1;
std::vector g(1, std::vector{Poly(a[0]).inv(C).a});
while (m < C) {
std::vector a0(4 * m, std::vector<int>(4 * C));
for (int i = 0; i < 2 * m; i++) {
for (int j = 0; j < C; j++) {
a0[i][j] = a[i][j];
}
}
dft(a0);
g.resize(4 * m);
for (auto &v : g) {
v.resize(4 * C);
}
dft(g);
for (int i = 0; i < 4 * m; i++) {
for (int j = 0; j < 4 * C; j++) {
g[i][j] = i64(g[i][j]) * (2 + i64(P - a0[i][j]) * g[i][j] % P) % P;
}
}
idft(g);
m *= 2;
g.resize(m);
for (auto &v : g) {
v.resize(C);
}
}
return g;
}
多项式（Poly, with. Z）
/** 多项式（Poly, with. Z）
* 2023-02-06: https://atcoder.jp/contests/arc155/submissions/38664055
**/
constexpr int P = 998244353;
using i64 = long long;
// assume -P <= x < 2P
int norm(int x) {
if (x < 0) {
x += P;
}
if (x >= P) {
x -= P;
}
return x;
}
template<class T>
T power(T a, i64 b) {
T res = 1;
for (; b; b /= 2, a *= a) {
if (b % 2) {
res *= a;
}
}
return res;
}
struct Z {
int x;
Z(int x = 0) : x(norm(x)) {}
Z(i64 x) : x(norm(x % P)) {}
int val() const {
return x;
}
Z operator-() const {
return Z(norm(P - x));
}
Z inv() const {
assert(x != 0);
return power(*this, P - 2);
}
Z &operator*=(const Z &rhs) {
x = i64(x) * rhs.x % P;
return *this;
}
Z &operator+=(const Z &rhs) {
x = norm(x + rhs.x);
return *this;
}
Z &operator-=(const Z &rhs) {
x = norm(x - rhs.x);
return *this;
}
Z &operator/=(const Z &rhs) {
return *this *= rhs.inv();
}
friend Z operator*(const Z &lhs, const Z &rhs) {
Z res = lhs;
res *= rhs;
return res;
}
friend Z operator+(const Z &lhs, const Z &rhs) {
Z res = lhs;
res += rhs;
return res;
}
friend Z operator-(const Z &lhs, const Z &rhs) {
Z res = lhs;
res -= rhs;
return res;
}
friend Z operator/(const Z &lhs, const Z &rhs) {
Z res = lhs;
res /= rhs;
return res;
}
friend std::istream &operator>>(std::istream &is, Z &a) {
i64 v;
is >> v;
a = Z(v);
return is;
}
friend std::ostream &operator<<(std::ostream &os, const Z &a) {
return os << a.val();
}
};
std::vector<int> rev;
std::vector<Z> roots{0, 1};
void dft(std::vector<Z> &a) {
int n = a.size();
if (int(rev.size()) != n) {
int k = __builtin_ctz(n) - 1;
rev.resize(n);
for (int i = 0; i < n; i++) {
rev[i] = rev[i >> 1] >> 1 | (i & 1) << k;
}
}
for (int i = 0; i < n; i++) {
if (rev[i] < i) {
std::swap(a[i], a[rev[i]]);
}
}
if (int(roots.size()) < n) {
int k = __builtin_ctz(roots.size());
roots.resize(n);
while ((1 << k) < n) {
Z e = power(Z(3), (P - 1) >> (k + 1));
for (int i = 1 << (k - 1); i < (1 << k); i++) {
roots[2 * i] = roots[i];
roots[2 * i + 1] = roots[i] * e;
}
k++;
}
}
for (int k = 1; k < n; k *= 2) {
for (int i = 0; i < n; i += 2 * k) {
for (int j = 0; j < k; j++) {
Z u = a[i + j];
Z v = a[i + j + k] * roots[k + j];
a[i + j] = u + v;
a[i + j + k] = u - v;
}
}
}
}
void idft(std::vector<Z> &a) {
int n = a.size();
std::reverse(a.begin() + 1, a.end());
dft(a);
Z inv = (1 - P) / n;
for (int i = 0; i < n; i++) {
a[i] *= inv;
}
}
struct Poly {
std::vector<Z> a;
Poly() {}
explicit Poly(int size, std::function<Z(int)> f = [](int) { return 0; }) : a(size) {
for (int i = 0; i < size; i++) {
a[i] = f(i);
}
}
Poly(const std::vector<Z> &a) : a(a) {}
Poly(const std::initializer_list<Z> &a) : a(a) {}
int size() const {
return a.size();
}
void resize(int n) {
a.resize(n);
}
Z operator[](int idx) const {
if (idx < size()) {
return a[idx];
} else {
return 0;
}
}
Z &operator[](int idx) {
return a[idx];
}
Poly mulxk(int k) const {
auto b = a;
b.insert(b.begin(), k, 0);
return Poly(b);
}
Poly modxk(int k) const {
k = std::min(k, size());
return Poly(std::vector<Z>(a.begin(), a.begin() + k));
}
Poly divxk(int k) const {
if (size() <= k) {
return Poly();
}
return Poly(std::vector<Z>(a.begin() + k, a.end()));
}
friend Poly operator+(const Poly &a, const Poly &b) {
std::vector<Z> res(std::max(a.size(), b.size()));
for (int i = 0; i < int(res.size()); i++) {
res[i] = a[i] + b[i];
}
return Poly(res);
}
friend Poly operator-(const Poly &a, const Poly &b) {
std::vector<Z> res(std::max(a.size(), b.size()));
for (int i = 0; i < int(res.size()); i++) {
res[i] = a[i] - b[i];
}
return Poly(res);
}
friend Poly operator-(const Poly &a) {
std::vector<Z> res(a.size());
for (int i = 0; i < int(res.size()); i++) {
res[i] = -a[i];
}
return Poly(res);
}
friend Poly operator*(Poly a, Poly b) {
if (a.size() == 0 || b.size() == 0) {
return Poly();
}
if (a.size() < b.size()) {
std::swap(a, b);
}
if (b.size() < 128) {
Poly c(a.size() + b.size() - 1);
for (int i = 0; i < a.size(); i++) {
for (int j = 0; j < b.size(); j++) {
c[i + j] += a[i] * b[j];
}
}
return c;
}
int sz = 1, tot = a.size() + b.size() - 1;
while (sz < tot) {
sz *= 2;
}
a.a.resize(sz);
b.a.resize(sz);
dft(a.a);
dft(b.a);
for (int i = 0; i < sz; ++i) {
a.a[i] = a[i] * b[i];
}
idft(a.a);
a.resize(tot);
return a;
}
friend Poly operator*(Z a, Poly b) {
for (int i = 0; i < int(b.size()); i++) {
b[i] *= a;
}
return b;
}
friend Poly operator*(Poly a, Z b) {
for (int i = 0; i < int(a.size()); i++) {
a[i] *= b;
}
return a;
}
Poly &operator+=(Poly b) {
return (*this) = (*this) + b;
}
Poly &operator-=(Poly b) {
return (*this) = (*this) - b;
}
Poly &operator*=(Poly b) {
return (*this) = (*this) * b;
}
Poly &operator*=(Z b) {
return (*this) = (*this) * b;
}
Poly deriv() const {
if (a.empty()) {
return Poly();
}
std::vector<Z> res(size() - 1);
for (int i = 0; i < size() - 1; ++i) {
res[i] = (i + 1) * a[i + 1];
}
return Poly(res);
}
Poly integr() const {
std::vector<Z> res(size() + 1);
for (int i = 0; i < size(); ++i) {
res[i + 1] = a[i] / (i + 1);
}
return Poly(res);
}
Poly inv(int m) const {
Poly x{a[0].inv()};
int k = 1;
while (k < m) {
k *= 2;
x = (x * (Poly{2} - modxk(k) * x)).modxk(k);
}
return x.modxk(m);
}
Poly log(int m) const {
return (deriv() * inv(m)).integr().modxk(m);
}
Poly exp(int m) const {
Poly x{1};
int k = 1;
while (k < m) {
k *= 2;
x = (x * (Poly{1} - x.log(k) + modxk(k))).modxk(k);
}
return x.modxk(m);
}
Poly pow(int k, int m) const {
int i = 0;
while (i < size() && a[i].val() == 0) {
i++;
}
if (i == size() || 1LL * i * k >= m) {
return Poly(std::vector<Z>(m));
}
Z v = a[i];
auto f = divxk(i) * v.inv();
return (f.log(m - i * k) * k).exp(m - i * k).mulxk(i * k) * power(v, k);
}
Poly sqrt(int m) const {
Poly x{1};
int k = 1;
while (k < m) {
k *= 2;
x = (x + (modxk(k) * x.inv(k)).modxk(k)) * ((P + 1) / 2);
}
return x.modxk(m);
}
Poly mulT(Poly b) const {
if (b.size() == 0) {
return Poly();
}
int n = b.size();
std::reverse(b.a.begin(), b.a.end());
return ((*this) * b).divxk(n - 1);
}
std::vector<Z> eval(std::vector<Z> x) const {
if (size() == 0) {
return std::vector<Z>(x.size(), 0);
}
const int n = std::max(int(x.size()), size());
std::vector<Poly> q(4 * n);
std::vector<Z> ans(x.size());
x.resize(n);
std::function<void(int, int, int)> build = [&](int p, int l, int r) {
if (r - l == 1) {
q[p] = Poly{1, -x[l]};
} else {
int m = (l + r) / 2;
build(2 * p, l, m);
build(2 * p + 1, m, r);
q[p] = q[2 * p] * q[2 * p + 1];
}
};
build(1, 0, n);
std::function<void(int, int, int, const Poly &)> work = [&](int p, int l, int r, const Poly &num) {
if (r - l == 1) {
if (l < int(ans.size())) {
ans[l] = num[0];
}
} else {
int m = (l + r) / 2;
work(2 * p, l, m, num.mulT(q[2 * p + 1]).modxk(m - l));
work(2 * p + 1, m, r, num.mulT(q[2 * p]).modxk(r - m));
}
};
work(1, 0, n, mulT(q[1].inv(n)));
return ans;
}
};
多项式（Poly, with. MInt & MLong）
/** 多项式（Poly, with. MInt & MLong）
* 2023-09-20: https://atcoder.jp/contests/arc163/submissions/45737810
* 2024-07-28: https://codeforces.com/contest/1991/submission/273204889
**/
template<class T>
constexpr T power(T a, i64 b) {
T res = 1;
for (; b; b /= 2, a *= a) {
if (b % 2) {
res *= a;
}
}
return res;
}
template<int P>
struct MInt {
int x;
constexpr MInt() : x{} {}
constexpr MInt(i64 x) : x{norm(x % getMod())} {}
static int Mod;
constexpr static int getMod() {
if (P > 0) {
return P;
} else {
return Mod;
}
}
constexpr static void setMod(int Mod_) {
Mod = Mod_;
}
constexpr int norm(int x) const {
if (x < 0) {
x += getMod();
}
if (x >= getMod()) {
x -= getMod();
}
return x;
}
constexpr int val() const {
return x;
}
explicit constexpr operator int() const {
return x;
}
constexpr MInt operator-() const {
MInt res;
res.x = norm(getMod() - x);
return res;
}
constexpr MInt inv() const {
assert(x != 0);
return power(*this, getMod() - 2);
}
constexpr MInt &operator*=(MInt rhs) & {
x = 1LL * x * rhs.x % getMod();
return *this;
}
constexpr MInt &operator+=(MInt rhs) & {
x = norm(x + rhs.x);
return *this;
}
constexpr MInt &operator-=(MInt rhs) & {
x = norm(x - rhs.x);
return *this;
}
constexpr MInt &operator/=(MInt rhs) & {
return *this *= rhs.inv();
}
friend constexpr MInt operator*(MInt lhs, MInt rhs) {
MInt res = lhs;
res *= rhs;
return res;
}
friend constexpr MInt operator+(MInt lhs, MInt rhs) {
MInt res = lhs;
res += rhs;
return res;
}
friend constexpr MInt operator-(MInt lhs, MInt rhs) {
MInt res = lhs;
res -= rhs;
return res;
}
friend constexpr MInt operator/(MInt lhs, MInt rhs) {
MInt res = lhs;
res /= rhs;
return res;
}
friend constexpr std::istream &operator>>(std::istream &is, MInt &a) {
i64 v;
is >> v;
a = MInt(v);
return is;
}
friend constexpr std::ostream &operator<<(std::ostream &os, const MInt &a) {
return os << a.val();
}
friend constexpr bool operator==(MInt lhs, MInt rhs) {
return lhs.val() == rhs.val();
}
friend constexpr bool operator!=(MInt lhs, MInt rhs) {
return lhs.val() != rhs.val();
}
};
template<>
int MInt<0>::Mod = 1;
template<int V, int P>
constexpr MInt<P> CInv = MInt<P>(V).inv();
constexpr int P = 998244353;
using Z = MInt<P>;
std::vector<int> rev;
template<int P>
std::vector<MInt<P>> roots{0, 1};
template<int P>
constexpr MInt<P> findPrimitiveRoot() {
MInt<P> i = 2;
int k = __builtin_ctz(P - 1);
while (true) {
if (power(i, (P - 1) / 2) != 1) {
break;
}
i += 1;
}
return power(i, (P - 1) >> k);
}
template<int P>
constexpr MInt<P> primitiveRoot = findPrimitiveRoot<P>();
template<>
constexpr MInt<998244353> primitiveRoot<998244353> {31};
template<int P>
constexpr void dft(std::vector<MInt<P>> &a) {
int n = a.size();
if (int(rev.size()) != n) {
int k = __builtin_ctz(n) - 1;
rev.resize(n);
for (int i = 0; i < n; i++) {
rev[i] = rev[i >> 1] >> 1 | (i & 1) << k;
}
}
for (int i = 0; i < n; i++) {
if (rev[i] < i) {
std::swap(a[i], a[rev[i]]);
}
}
if (roots<P>.size() < n) {
int k = __builtin_ctz(roots<P>.size());
roots<P>.resize(n);
while ((1 << k) < n) {
auto e = power(primitiveRoot<P>, 1 << (__builtin_ctz(P - 1) - k - 1));
for (int i = 1 << (k - 1); i < (1 << k); i++) {
roots<P>[2 * i] = roots<P>[i];
roots<P>[2 * i + 1] = roots<P>[i] * e;
}
k++;
}
}
for (int k = 1; k < n; k *= 2) {
for (int i = 0; i < n; i += 2 * k) {
for (int j = 0; j < k; j++) {
MInt<P> u = a[i + j];
MInt<P> v = a[i + j + k] * roots<P>[k + j];
a[i + j] = u + v;
a[i + j + k] = u - v;
}
}
}
}
template<int P>
constexpr void idft(std::vector<MInt<P>> &a) {
int n = a.size();
std::reverse(a.begin() + 1, a.end());
dft(a);
MInt<P> inv = (1 - P) / n;
for (int i = 0; i < n; i++) {
a[i] *= inv;
}
}
template<int P = 998244353>
struct Poly : public std::vector<MInt<P>> {
using Value = MInt<P>;
Poly() : std::vector<Value>() {}
explicit constexpr Poly(int n) : std::vector<Value>(n) {}
explicit constexpr Poly(const std::vector<Value> &a) : std::vector<Value>(a) {}
constexpr Poly(const std::initializer_list<Value> &a) : std::vector<Value>(a) {}
template<class InputIt, class = std::_RequireInputIter<InputIt>>
explicit constexpr Poly(InputIt first, InputIt last) : std::vector<Value>(first, last) {}
template<class F>
explicit constexpr Poly(int n, F f) : std::vector<Value>(n) {
for (int i = 0; i < n; i++) {
(*this)[i] = f(i);
}
}
constexpr Poly shift(int k) const {
if (k >= 0) {
auto b = *this;
b.insert(b.begin(), k, 0);
return b;
} else if (this->size() <= -k) {
return Poly();
} else {
return Poly(this->begin() + (-k), this->end());
}
}
constexpr Poly trunc(int k) const {
Poly f = *this;
f.resize(k);
return f;
}
constexpr friend Poly operator+(const Poly &a, const Poly &b) {
Poly res(std::max(a.size(), b.size()));
for (int i = 0; i < a.size(); i++) {
res[i] += a[i];
}
for (int i = 0; i < b.size(); i++) {
res[i] += b[i];
}
return res;
}
constexpr friend Poly operator-(const Poly &a, const Poly &b) {
Poly res(std::max(a.size(), b.size()));
for (int i = 0; i < a.size(); i++) {
res[i] += a[i];
}
for (int i = 0; i < b.size(); i++) {
res[i] -= b[i];
}
return res;
}
constexpr friend Poly operator-(const Poly &a) {
std::vector<Value> res(a.size());
for (int i = 0; i < int(res.size()); i++) {
res[i] = -a[i];
}
return Poly(res);
}
constexpr friend Poly operator*(Poly a, Poly b) {
if (a.size() == 0 || b.size() == 0) {
return Poly();
}
if (a.size() < b.size()) {
std::swap(a, b);
}
int n = 1, tot = a.size() + b.size() - 1;
while (n < tot) {
n *= 2;
}
if (((P - 1) & (n - 1)) != 0 || b.size() < 128) {
Poly c(a.size() + b.size() - 1);
for (int i = 0; i < a.size(); i++) {
for (int j = 0; j < b.size(); j++) {
c[i + j] += a[i] * b[j];
}
}
return c;
}
a.resize(n);
b.resize(n);
dft(a);
dft(b);
for (int i = 0; i < n; ++i) {
a[i] *= b[i];
}
idft(a);
a.resize(tot);
return a;
}
constexpr friend Poly operator*(Value a, Poly b) {
for (int i = 0; i < int(b.size()); i++) {
b[i] *= a;
}
return b;
}
constexpr friend Poly operator*(Poly a, Value b) {
for (int i = 0; i < int(a.size()); i++) {
a[i] *= b;
}
return a;
}
constexpr friend Poly operator/(Poly a, Value b) {
for (int i = 0; i < int(a.size()); i++) {
a[i] /= b;
}
return a;
}
constexpr Poly &operator+=(Poly b) {
return (*this) = (*this) + b;
}
constexpr Poly &operator-=(Poly b) {
return (*this) = (*this) - b;
}
constexpr Poly &operator*=(Poly b) {
return (*this) = (*this) * b;
}
constexpr Poly &operator*=(Value b) {
return (*this) = (*this) * b;
}
constexpr Poly &operator/=(Value b) {
return (*this) = (*this) / b;
}
constexpr Poly deriv() const {
if (this->empty()) {
return Poly();
}
Poly res(this->size() - 1);
for (int i = 0; i < this->size() - 1; ++i) {
res[i] = (i + 1) * (*this)[i + 1];
}
return res;
}
constexpr Poly integr() const {
Poly res(this->size() + 1);
for (int i = 0; i < this->size(); ++i) {
res[i + 1] = (*this)[i] / (i + 1);
}
return res;
}
constexpr Poly inv(int m) const {
Poly x{(*this)[0].inv()};
int k = 1;
while (k < m) {
k *= 2;
x = (x * (Poly{2} - trunc(k) * x)).trunc(k);
}
return x.trunc(m);
}
constexpr Poly log(int m) const {
return (deriv() * inv(m)).integr().trunc(m);
}
constexpr Poly exp(int m) const {
Poly x{1};
int k = 1;
while (k < m) {
k *= 2;
x = (x * (Poly{1} - x.log(k) + trunc(k))).trunc(k);
}
return x.trunc(m);
}
constexpr Poly pow(int k, int m) const {
int i = 0;
while (i < this->size() && (*this)[i] == 0) {
i++;
}
if (i == this->size() || 1LL * i * k >= m) {
return Poly(m);
}
Value v = (*this)[i];
auto f = shift(-i) * v.inv();
return (f.log(m - i * k) * k).exp(m - i * k).shift(i * k) * power(v, k);
}
constexpr Poly sqrt(int m) const {
Poly x{1};
int k = 1;
while (k < m) {
k *= 2;
x = (x + (trunc(k) * x.inv(k)).trunc(k)) * CInv<2, P>;
}
return x.trunc(m);
}
constexpr Poly mulT(Poly b) const {
if (b.size() == 0) {
return Poly();
}
int n = b.size();
std::reverse(b.begin(), b.end());
return ((*this) * b).shift(-(n - 1));
}
constexpr std::vector<Value> eval(std::vector<Value> x) const {
if (this->size() == 0) {
return std::vector<Value>(x.size(), 0);
}
const int n = std::max(x.size(), this->size());
std::vector<Poly> q(4 * n);
std::vector<Value> ans(x.size());
x.resize(n);
std::function<void(int, int, int)> build = [&](int p, int l, int r) {
if (r - l == 1) {
q[p] = Poly{1, -x[l]};
} else {
int m = (l + r) / 2;
build(2 * p, l, m);
build(2 * p + 1, m, r);
q[p] = q[2 * p] * q[2 * p + 1];
}
};
build(1, 0, n);
std::function<void(int, int, int, const Poly &)> work = [&](int p, int l, int r, const Poly &num) {
if (r - l == 1) {
if (l < int(ans.size())) {
ans[l] = num[0];
}
} else {
int m = (l + r) / 2;
work(2 * p, l, m, num.mulT(q[2 * p + 1]).trunc(m - l));
work(2 * p + 1, m, r, num.mulT(q[2 * p]).trunc(r - m));
}
};
work(1, 0, n, mulT(q[1].inv(n)));
return ans;
}
};
template<int P = 998244353>
Poly<P> berlekampMassey(const Poly<P> &s) {
Poly<P> c;
Poly<P> oldC;
int f = -1;
for (int i = 0; i < s.size(); i++) {
auto delta = s[i];
for (int j = 1; j <= c.size(); j++) {
delta -= c[j - 1] * s[i - j];
}
if (delta == 0) {
continue;
}
if (f == -1) {
c.resize(i + 1);
f = i;
} else {
auto d = oldC;
d *= -1;
d.insert(d.begin(), 1);
MInt<P> df1 = 0;
for (int j = 1; j <= d.size(); j++) {
df1 += d[j - 1] * s[f + 1 - j];
}
assert(df1 != 0);
auto coef = delta / df1;
d *= coef;
Poly<P> zeros(i - f - 1);
zeros.insert(zeros.end(), d.begin(), d.end());
d = zeros;
auto temp = c;
c += d;
if (i - temp.size() > f - oldC.size()) {
oldC = temp;
f = i;
}
}
}
c *= -1;
c.insert(c.begin(), 1);
return c;
}
template<int P = 998244353>
MInt<P> linearRecurrence(Poly<P> p, Poly<P> q, i64 n) {
int m = q.size() - 1;
while (n > 0) {
auto newq = q;
for (int i = 1; i <= m; i += 2) {
newq[i] *= -1;
}
auto newp = p * newq;
newq = q * newq;
for (int i = 0; i < m; i++) {
p[i] = newp[i * 2 + n % 2];
}
for (int i = 0; i <= m; i++) {
q[i] = newq[i * 2];
}
n /= 2;
}
return p[0] / q[0];
}
struct Comb {
int n;
std::vector<Z> _fac;
std::vector<Z> _invfac;
std::vector<Z> _inv;
Comb() : n{0}, _fac{1}, _invfac{1}, _inv{0} {}
Comb(int n) : Comb() {
init(n);
}
void init(int m) {
m = std::min(m, Z::getMod() - 1);
if (m <= n) return;
_fac.resize(m + 1);
_invfac.resize(m + 1);
_inv.resize(m + 1);
for (int i = n + 1; i <= m; i++) {
_fac[i] = _fac[i - 1] * i;
}
_invfac[m] = _fac[m].inv();
for (int i = m; i > n; i--) {
_invfac[i - 1] = _invfac[i] * i;
_inv[i] = _invfac[i] * _fac[i - 1];
}
n = m;
}
Z fac(int m) {
if (m > n) init(2 * m);
return _fac[m];
}
Z invfac(int m) {
if (m > n) init(2 * m);
return _invfac[m];
}
Z inv(int m) {
if (m > n) init(2 * m);
return _inv[m];
}
Z binom(int n, int m) {
if (n < m || m < 0) return 0;
return fac(n) * invfac(m) * invfac(n - m);
}
} comb;
Poly<P> get(int n, int m) {
if (m == 0) {
return Poly(n + 1);
}
if (m % 2 == 1) {
auto f = get(n, m - 1);
Z p = 1;
for (int i = 0; i <= n; i++) {
f[n - i] += comb.binom(n, i) * p;
p *= m;
}
return f;
}
auto f = get(n, m / 2);
auto fm = f;
for (int i = 0; i <= n; i++) {
fm[i] *= comb.fac(i);
}
Poly pw(n + 1);
pw[0] = 1;
for (int i = 1; i <= n; i++) {
pw[i] = pw[i - 1] * (m / 2);
}
for (int i = 0; i <= n; i++) {
pw[i] *= comb.invfac(i);
}
fm = fm.mulT(pw);
for (int i = 0; i <= n; i++) {
fm[i] *= comb.invfac(i);
}
return f + fm;
}
多项式乘法
/** 多项式乘法
* 2024-03-10: https://qoj.ac/submission/350298
**/
constexpr int P = 998244353;
int power(int a, int b) {
int res = 1;
for (; b; b /= 2, a = 1LL * a * a % P) {
if (b % 2) {
res = 1LL * res * a % P;
}
}
return res;
}
std::vector<int> rev, roots {0, 1};
void dft(std::vector<int> &a) {
int n = a.size();
if (int(rev.size()) != n) {
int k = __builtin_ctz(n) - 1;
rev.resize(n);
for (int i = 0; i < n; i++) {
rev[i] = rev[i >> 1] >> 1 | (i & 1) << k;
}
}
for (int i = 0; i < n; i++) {
if (rev[i] < i) {
std::swap(a[i], a[rev[i]]);
}
}
if (roots.size() < n) {
int k = __builtin_ctz(roots.size());
roots.resize(n);
while ((1 << k) < n) {
int e = power(31, 1 << (__builtin_ctz(P - 1) - k - 1));
for (int i = 1 << (k - 1); i < (1 << k); i++) {
roots[2 * i] = roots[i];
roots[2 * i + 1] = 1LL * roots[i] * e % P;
}
k++;
}
}
for (int k = 1; k < n; k *= 2) {
for (int i = 0; i < n; i += 2 * k) {
for (int j = 0; j < k; j++) {
int u = a[i + j];
int v = 1LL * a[i + j + k] * roots[k + j] % P;
a[i + j] = (u + v) % P;
a[i + j + k] = (u - v) % P;
}
}
}
}
void idft(std::vector<int> &a) {
int n = a.size();
std::reverse(a.begin() + 1, a.end());
dft(a);
int inv = (1 - P) / n;
for (int i = 0; i < n; i++) {
a[i] = 1LL * a[i] * inv % P;
}
}
std::vector<int> mul(std::vector<int> a, std::vector<int> b) {
int n = 1, tot = a.size() + b.size() - 1;
while (n < tot) {
n *= 2;
}
if (tot < 128) {
std::vector<int> c(a.size() + b.size() - 1);
for (int i = 0; i < a.size(); i++) {
for (int j = 0; j < b.size(); j++) {
c[i + j] = (c[i + j] + 1LL * a[i] * b[j]) % P;
}
}
return c;
}
a.resize(n);
b.resize(n);
dft(a);
dft(b);
for (int i = 0; i < n; i++) {
a[i] = 1LL * a[i] * b[i] % P;
}
idft(a);
a.resize(tot);
return a;
}
生成函数
生成函数（q-int）
/** 生成函数（q-int）
* 2023-09-04: https://qoj.ac/submission/163986
**/
using i64 = long long;
using i128 = __int128;
i64 power(i64 a, i64 b, i64 p) {
i64 res = 1;
for (; b; b /= 2, a = i128(a) * a % p) {
if (b % 2) {
res = i128(res) * a % p;
}
}
return res;
}
std::pair<int, int> qint(int q, int n, int p) {
q %= p;
for (int x = 2; x * x <= n; x++) {
if (n % x == 0) {
auto [v1, e1] = qint(q, x, p);
auto [v2, e2] = qint(power(q, x, p), n / x, p);
return {1LL * v1 * v2 % p, e1 + e2};
}
}
if (q == 1) {
if (n == p) {
return {0, 1};
}
return {n, 0};
}
// std::cerr << q << " " << n << " " << p << "\n";
i64 v = 1 - power(q, n, 1LL * p * p);
if (v < 0) {
v += 1LL * p * p;
}
assert(v != 0);
int inv = power(1 - q + p, p - 2, p);
if (v % p == 0) {
return {(v / p) * inv % p, 1};
} else {
return {v % p * inv % p, 0};
}
}
生成函数（q-Binomial）
/** 生成函数（q-Binomial）
* 2023-09-04: https://qoj.ac/submission/164128
**/
int power(int a, int b, int p) {
int res = 1;
for (; b; b /= 2, a = 1LL * a * a % p) {
if (b % 2) {
res = 1LL * res * a % p;
}
}
return res;
}
int qint(int n, int q, int p) {
return 1LL * (power(q, n, p) - 1) * power(q - 1, p - 2, p) % p;
}
int qBinomial(int n, int k, int q, int p) {
if (q == 0) {
return 1;
}
int r = 0;
int x = 1;
do {
x = 1LL * x * q % p;
r++;
} while (x != 1);
if (n / r > k / r + (n - k) / r) {
return 0;
}
int num = 1, den = 1;
for (int i = 1; i <= k % r; i++) {
num = 1LL * num * qint(n % r - i + 1, q, p) % p;
den = 1LL * den * qint(i, q, p) % p;
}
n /= r, k /= r;
while (n > 0 || k > 0) {
if (n % p < k % p) {
return 0;
}
for (int i = 1; i <= k % p; i++) {
num = 1LL * num * (n % p - i + 1) % p;
den = 1LL * den * i % p;
}
n /= p, k /= p;
}
int ans = 1LL * num * power(den, p - 2, p) % p;
return ans;
}
生成函数（Binomial 任意模数二项式）
/** 生成函数（Binomial 任意模数二项式）
* 2023-08-22: https://codeforces.com/contest/896/submission/219861532
**/
std::vector<std::pair<int, int>> factorize(int n) {
std::vector<std::pair<int, int>> factors;
for (int i = 2; static_cast<long long>(i) * i <= n; i++) {
if (n % i == 0) {
int t = 0;
for (; n % i == 0; n /= i)
++t;
factors.emplace_back(i, t);
}
}
if (n > 1)
factors.emplace_back(n, 1);
return factors;
}
constexpr int power(int base, i64 exp) {
int res = 1;
for (; exp > 0; base *= base, exp /= 2) {
if (exp % 2 == 1) {
res *= base;
}
}
return res;
}
constexpr int power(int base, i64 exp, int mod) {
int res = 1 % mod;
for (; exp > 0; base = 1LL * base * base % mod, exp /= 2) {
if (exp % 2 == 1) {
res = 1LL * res * base % mod;
}
}
return res;
}
int inverse(int a, int m) {
int g = m, r = a, x = 0, y = 1;
while (r != 0) {
int q = g / r;
g %= r;
std::swap(g, r);
x -= q * y;
std::swap(x, y);
}
return x < 0 ? x + m : x;
}
int solveModuloEquations(const std::vector<std::pair<int, int>> &e) {
int m = 1;
for (std::size_t i = 0; i < e.size(); i++) {
m *= e[i].first;
}
int res = 0;
for (std::size_t i = 0; i < e.size(); i++) {
int p = e[i].first;
res = (res + 1LL * e[i].second * (m / p) * inverse(m / p, p)) % m;
}
return res;
}
constexpr int N = 1E5;
class Binomial {
const int mod;
private:
const std::vector<std::pair<int, int>> factors;
std::vector<int> pk;
std::vector<std::vector<int>> prod;
static constexpr i64 exponent(i64 n, int p) {
i64 res = 0;
for (n /= p; n > 0; n /= p) {
res += n;
}
return res;
}
int product(i64 n, std::size_t i) {
int res = 1;
int p = factors[i].first;
for (; n > 0; n /= p) {
res = 1LL * res * power(prod[i].back(), n / pk[i], pk[i]) % pk[i] * prod[i][n % pk[i]] % pk[i];
}
return res;
}
public:
Binomial(int mod) : mod(mod), factors(factorize(mod)) {
pk.resize(factors.size());
prod.resize(factors.size());
for (std::size_t i = 0; i < factors.size(); i++) {
int p = factors[i].first;
int k = factors[i].second;
pk[i] = power(p, k);
prod[i].resize(std::min(N + 1, pk[i]));
prod[i][0] = 1;
for (int j = 1; j < prod[i].size(); j++) {
if (j % p == 0) {
prod[i][j] = prod[i][j - 1];
} else {
prod[i][j] = 1LL * prod[i][j - 1] * j % pk[i];
}
}
}
}
int operator()(i64 n, i64 m) {
if (n < m || m < 0) {
return 0;
}
std::vector<std::pair<int, int>> ans(factors.size());
for (int i = 0; i < factors.size(); i++) {
int p = factors[i].first;
int k = factors[i].second;
int e = exponent(n, p) - exponent(m, p) - exponent(n - m, p);
if (e >= k) {
ans[i] = std::make_pair(pk[i], 0);
} else {
int pn = product(n, i);
int pm = product(m, i);
int pd = product(n - m, i);
int res = 1LL * pn * inverse(pm, pk[i]) % pk[i] * inverse(pd, pk[i]) % pk[i] * power(p, e) % pk[i];
ans[i] = std::make_pair(pk[i], res);
}
}
return solveModuloEquations(ans);
}
};
自适应辛普森法（Simpson）
/** 自适应辛普森法（Simpson）
* 2020-09-25: https://codeforces.com/gym/100198/submission/93747918
* 2021-01-28: https://codeforces.com/gym/100553/submission/105639142
* 2023-09-02: https://qoj.ac/submission/161388
**/
const double Pi = std::acos(-1.0);
constexpr double EPS = 1e-9;
double v, r, d;
double f(double x) {
double s = std::sin(x);
return 1 / v / (std::sqrt(s * s + 3) - s);
}
double simpson(double l, double r) {
return (f(l) + 4 * f((l + r) / 2) + f(r)) * (r - l) / 6;
}
double integral(double l, double r, double eps, double st) {
double mid = (l + r) / 2;
double sl = simpson(l, mid);
double sr = simpson(mid, r);
if (std::abs(sl + sr - st) <= 15 * eps)
return sl + sr + (sl + sr - st) / 15;
return integral(l, mid, eps / 2, sl) + integral(mid, r, eps / 2, sr);
}
double integral(double l, double r) {
return integral(l, r, EPS, simpson(l, r));
}
矩阵（Matrix）
/** 矩阵（Matrix）
* 2024-03-14: https://qoj.ac/submission/353771
**/
using i64 = long long;
using u64 = unsigned long long;
using Matrix = std::array<u64, 65>;
Matrix operator*(const Matrix &a, const Matrix &b) {
Matrix c{};
for (int i = 0; i <= 64; i++) {
for (int j = 0; j <= 64; j++) {
if (j == 64 ? i == 64 : (a[i] >> j & 1)) {
c[i] ^= b[j];
}
}
}
return c;
}
u64 operator*(u64 a, const Matrix &b) {
u64 c = 0;
for (int i = 0; i <= 64; i++) {
if (i == 64 || (a >> i & 1)) {
c ^= b[i];
}
}
return c;
}
Matrix readMatrix() {
int m;
std::cin >> m;
Matrix f{};
for (int i = 0; i < m; i++) {
int s, o;
u64 A;
std::cin >> s >> o >> A;
if (o == 0) {
for (int j = 0; j < 64; j++) {
if (A >> ((j + s) % 64) & 1) {
f[64] ^= 1ULL << ((j + s) % 64);
} else {
f[j] ^= 1ULL << ((j + s) % 64);
}
}
} else {
for (int j = 0; j < 64; j++) {
if (A >> ((j + s) % 64) & 1) {
f[j] ^= 1ULL << ((j + s) % 64);
}
}
}
}
u64 B;
std::cin >> B;
f[64] ^= B;
return f;
}
高斯消元法（gaussian elimination）【久远】
/** 高斯消元法（gaussian elimination）【久远】
* 2020-08-30: https://codeforces.com/gym/102129/submission/91334513
**/
std::vector<int> operator*(const std::vector<int> &lhs, const std::vector<int> &rhs) {
std::vector<int> res(lhs.size() + rhs.size() - 1);
for (int i = 0; i < int(lhs.size()); ++i)
for (int j = 0; j < int(rhs.size()); ++j)
res[i + j] = (res[i + j] + 1ll * lhs[i] * rhs[j]) % P;
return res;
}
std::vector<int> operator%(const std::vector<int> &lhs, const std::vector<int> &rhs) {
auto res = lhs;
int m = rhs.size() - 1;
int inv = power(rhs.back(), P - 2);
for (int i = res.size() - 1; i >= m; --i) {
int x = 1ll * inv * res[i] % P;
for (int j = 0; j < m; ++j)
res[i - m + j] = (res[i - m + j] + 1ll * (P - x) * rhs[j]) % P;
}
if (int(res.size()) > m)
res.resize(m);
return res;
}
std::vector<int> gauss(std::vector<std::vector<int>> a, std::vector<int> b) {
int n = a.size();
for (int i = 0; i < n; ++i) {
int r = i;
while (a[r][i] == 0)
++r;
std::swap(a[i], a[r]);
std::swap(b[i], b[r]);
int inv = power(a[i][i], P - 2);
for (int j = i; j < n; ++j)
a[i][j] = 1ll * a[i][j] * inv % P;
b[i] = 1ll * b[i] * inv % P;
for (int j = 0; j < n; ++j) {
if (i == j)
continue;
int x = a[j][i];
for (int k = i; k < n; ++k)
a[j][k] = (a[j][k] + 1ll * (P - x) * a[i][k]) % P;
b[j] = (b[j] + 1ll * (P - x) * b[i]) % P;
}
}
return b;
}
/** 高斯消元法（gaussian elimination）【久远】
* 2020-12-02: https://www.codechef.com/viewsolution/39942900
**/
std::vector<double> gauss(std::vector<std::vector<double>> a, std::vector<double> b) {
int n = a.size();
for (int i = 0; i < n; ++i) {
double x = a[i][i];
for (int j = i; j < n; ++j) a[i][j] /= x;
b[i] /= x;
for (int j = 0; j < n; ++j) {
if (i == j) continue;
x = a[j][i];
for (int k = i; k < n; ++k) a[j][k] -= a[i][k] * x;
b[j] -= b[i] * x;
}
}
return b;
}
四、数据结构
点击展开本章节
树状数组
树状数组（Fenwick 旧版）
/** 树状数组（Fenwick 旧版）
* 2023-08-11: https://ac.nowcoder.com/acm/contest/view-submission?submissionId=63382128
**/
template <typename T>
struct Fenwick {
int n;
std::vector<T> a;
Fenwick(int n = 0) {
init(n);
}
void init(int n) {
this->n = n;
a.assign(n, T());
}
void add(int x, T v) {
for (int i = x + 1; i <= n; i += i & -i) {
a[i - 1] += v;
}
}
T sum(int x) {
auto ans = T();
for (int i = x; i > 0; i -= i & -i) {
ans += a[i - 1];
}
return ans;
}
T rangeSum(int l, int r) {
return sum(r) - sum(l);
}
int kth(T k) {
int x = 0;
for (int i = 1 << std::__lg(n); i; i /= 2) {
if (x + i <= n && k >= a[x + i - 1]) {
x += i;
k -= a[x - 1];
}
}
return x;
}
};
树状数组（Fenwick 新版）
/** 树状数组（Fenwick 新版）
* 2023-12-28: https://codeforces.com/contest/1915/submission/239262801
**/
template <typename T>
struct Fenwick {
int n;
std::vector<T> a;
Fenwick(int n_ = 0) {
init(n_);
}
void init(int n_) {
n = n_;
a.assign(n, T{});
}
void add(int x, const T &v) {
for (int i = x + 1; i <= n; i += i & -i) {
a[i - 1] = a[i - 1] + v;
}
}
T sum(int x) {
T ans{};
for (int i = x; i > 0; i -= i & -i) {
ans = ans + a[i - 1];
}
return ans;
}
T rangeSum(int l, int r) {
return sum(r) - sum(l);
}
int select(const T &k) {
int x = 0;
T cur{};
for (int i = 1 << std::__lg(n); i; i /= 2) {
if (x + i <= n && cur + a[x + i - 1] <= k) {
x += i;
cur = cur + a[x - 1];
}
}
return x;
}
};
并查集
并查集（DSU）
/** 并查集（DSU）
* 2023-08-04: https://ac.nowcoder.com/acm/contest/view-submission?submissionId=63239142
**/
struct DSU {
std::vector<int> f, siz;
DSU() {}
DSU(int n) {
init(n);
}
void init(int n) {
f.resize(n);
std::iota(f.begin(), f.end(), 0);
siz.assign(n, 1);
}
int find(int x) {
while (x != f[x]) {
x = f[x] = f[f[x]];
}
return x;
}
bool same(int x, int y) {
return find(x) == find(y);
}
bool merge(int x, int y) {
x = find(x);
y = find(y);
if (x == y) {
return false;
}
siz[x] += siz[y];
f[y] = x;
return true;
}
int size(int x) {
return siz[find(x)];
}
};
可撤销并查集（DSU With Rollback）
/** 可撤销并查集（DSU With Rollback）
* 2024-09-17: https://qoj.ac/submission/569639
**/
struct DSU {
std::vector<int> siz;
std::vector<int> f;
std::vector<std::array<int, 2>> his;
DSU(int n) : siz(n + 1, 1), f(n + 1) {
std::iota(f.begin(), f.end(), 0);
}
int find(int x) {
while (f[x] != x) {
x = f[x];
}
return x;
}
bool merge(int x, int y) {
x = find(x);
y = find(y);
if (x == y) {
return false;
}
if (siz[x] < siz[y]) {
std::swap(x, y);
}
his.push_back({x, y});
siz[x] += siz[y];
f[y] = x;
return true;
}
int time() {
return his.size();
}
void revert(int tm) {
while (his.size() > tm) {
auto [x, y] = his.back();
his.pop_back();
f[y] = y;
siz[x] -= siz[y];
}
}
};
线段树
线段树（SegmentTree+Info 区间加+单点修改）
/** 线段树（SegmentTree+Info 区间加+单点修改）
* 2023-09-13: https://qoj.ac/submission/178310
**/
struct SegmentTree {
int n;
std::vector<int> tag;
std::vector<Info> info;
SegmentTree(int n_) : n(n_), tag(4 * n), info(4 * n) {}
void pull(int p) {
info[p] = info[2 * p] + info[2 * p + 1];
}
void add(int p, int v) {
tag[p] += v;
info[p].max += v;
}
void push(int p) {
add(2 * p, tag[p]);
add(2 * p + 1, tag[p]);
tag[p] = 0;
}
Info query(int p, int l, int r, int x, int y) {
if (l >= y || r <= x) {
return {};
}
if (l >= x && r <= y) {
return info[p];
}
int m = (l + r) / 2;
push(p);
return query(2 * p, l, m, x, y) + query(2 * p + 1, m, r, x, y);
}
Info query(int x, int y) {
return query(1, 0, n, x, y);
}
void rangeAdd(int p, int l, int r, int x, int y, int v) {
if (l >= y || r <= x) {
return;
}
if (l >= x && r <= y) {
return add(p, v);
}
int m = (l + r) / 2;
push(p);
rangeAdd(2 * p, l, m, x, y, v);
rangeAdd(2 * p + 1, m, r, x, y, v);
pull(p);
}
void rangeAdd(int x, int y, int v) {
rangeAdd(1, 0, n, x, y, v);
}
void modify(int p, int l, int r, int x, const Info &v) {
if (r - l == 1) {
info[p] = v;
return;
}
int m = (l + r) / 2;
push(p);
if (x < m) {
modify(2 * p, l, m, x, v);
} else {
modify(2 * p + 1, m, r, x, v);
}
pull(p);
}
void modify(int x, const Info &v) {
modify(1, 0, n, x, v);
}
};
线段树（SegmentTree 区间乘+单点加）
/** 线段树（SegmentTree 区间乘+单点加）
* 2023-10-18: https://cf.dianhsu.com/gym/104417/submission/223800089
**/
struct SegmentTree {
int n;
std::vector<int> tag, sum;
SegmentTree(int n_) : n(n_), tag(4 * n, 1), sum(4 * n) {}
void pull(int p) {
sum[p] = (sum[2 * p] + sum[2 * p + 1]) % P;
}
void mul(int p, int v) {
tag[p] = 1LL * tag[p] * v % P;
sum[p] = 1LL * sum[p] * v % P;
}
void push(int p) {
mul(2 * p, tag[p]);
mul(2 * p + 1, tag[p]);
tag[p] = 1;
}
int query(int p, int l, int r, int x, int y) {
if (l >= y || r <= x) {
return 0;
}
if (l >= x && r <= y) {
return sum[p];
}
int m = (l + r) / 2;
push(p);
return (query(2 * p, l, m, x, y) + query(2 * p + 1, m, r, x, y)) % P;
}
int query(int x, int y) {
return query(1, 0, n, x, y);
}
void rangeMul(int p, int l, int r, int x, int y, int v) {
if (l >= y || r <= x) {
return;
}
if (l >= x && r <= y) {
return mul(p, v);
}
int m = (l + r) / 2;
push(p);
rangeMul(2 * p, l, m, x, y, v);
rangeMul(2 * p + 1, m, r, x, y, v);
pull(p);
}
void rangeMul(int x, int y, int v) {
rangeMul(1, 0, n, x, y, v);
}
void add(int p, int l, int r, int x, int v) {
if (r - l == 1) {
sum[p] = (sum[p] + v) % P;
return;
}
int m = (l + r) / 2;
push(p);
if (x < m) {
add(2 * p, l, m, x, v);
} else {
add(2 * p + 1, m, r, x, v);
}
pull(p);
}
void add(int x, int v) {
add(1, 0, n, x, v);
}
};
线段树（SegmentTree+Info 初始赋值+单点修改+查找前驱后继）
/** 线段树（SegmentTree+Info 初始赋值+单点修改+查找前驱后继）
* 2023-07-17: https://ac.nowcoder.com/acm/contest/view-submission?submissionId=62804432
* 2024-06-25: https://codeforces.com/contest/1982/submission/267353839
**/
template<class Info>
struct SegmentTree {
int n;
std::vector<Info> info;
SegmentTree() : n(0) {}
SegmentTree(int n_, Info v_ = Info()) {
init(n_, v_);
}
template<class T>
SegmentTree(std::vector<T> init_) {
init(init_);
}
void init(int n_, Info v_ = Info()) {
init(std::vector(n_, v_));
}
template<class T>
void init(std::vector<T> init_) {
n = init_.size();
info.assign(4 << std::__lg(n), Info());
std::function<void(int, int, int)> build = [&](int p, int l, int r) {
if (r - l == 1) {
info[p] = init_[l];
return;
}
int m = (l + r) / 2;
build(2 * p, l, m);
build(2 * p + 1, m, r);
pull(p);
};
build(1, 0, n);
}
void pull(int p) {
info[p] = info[2 * p] + info[2 * p + 1];
}
void modify(int p, int l, int r, int x, const Info &v) {
if (r - l == 1) {
info[p] = v;
return;
}
int m = (l + r) / 2;
if (x < m) {
modify(2 * p, l, m, x, v);
} else {
modify(2 * p + 1, m, r, x, v);
}
pull(p);
}
void modify(int p, const Info &v) {
modify(1, 0, n, p, v);
}
Info rangeQuery(int p, int l, int r, int x, int y) {
if (l >= y || r <= x) {
return Info();
}
if (l >= x && r <= y) {
return info[p];
}
int m = (l + r) / 2;
return rangeQuery(2 * p, l, m, x, y) + rangeQuery(2 * p + 1, m, r, x, y);
}
Info rangeQuery(int l, int r) {
return rangeQuery(1, 0, n, l, r);
}
template<class F>
int findFirst(int p, int l, int r, int x, int y, F &&pred) {
if (l >= y || r <= x) {
return -1;
}
if (l >= x && r <= y && !pred(info[p])) {
return -1;
}
if (r - l == 1) {
return l;
}
int m = (l + r) / 2;
int res = findFirst(2 * p, l, m, x, y, pred);
if (res == -1) {
res = findFirst(2 * p + 1, m, r, x, y, pred);
}
return res;
}
template<class F>
int findFirst(int l, int r, F &&pred) {
return findFirst(1, 0, n, l, r, pred);
}
template<class F>
int findLast(int p, int l, int r, int x, int y, F &&pred) {
if (l >= y || r <= x) {
return -1;
}
if (l >= x && r <= y && !pred(info[p])) {
return -1;
}
if (r - l == 1) {
return l;
}
int m = (l + r) / 2;
int res = findLast(2 * p + 1, m, r, x, y, pred);
if (res == -1) {
res = findLast(2 * p, l, m, x, y, pred);
}
return res;
}
template<class F>
int findLast(int l, int r, F &&pred) {
return findLast(1, 0, n, l, r, pred);
}
};
线段树（SegmentTree+Info+Merge 初始赋值+单点修改+区间合并）
/** 线段树（SegmentTree+Info+Merge 初始赋值+单点修改+区间合并）
* 2022-04-23: https://codeforces.com/contest/1672/submission/154766851
**/
template<class Info,
class Merge = std::plus<Info>>
struct SegmentTree {
const int n;
const Merge merge;
std::vector<Info> info;
SegmentTree(int n) : n(n), merge(Merge()), info(4 << std::__lg(n)) {}
SegmentTree(std::vector<Info> init) : SegmentTree(init.size()) {
std::function<void(int, int, int)> build = [&](int p, int l, int r) {
if (r - l == 1) {
info[p] = init[l];
return;
}
int m = (l + r) / 2;
build(2 * p, l, m);
build(2 * p + 1, m, r);
pull(p);
};
build(1, 0, n);
}
void pull(int p) {
info[p] = merge(info[2 * p], info[2 * p + 1]);
}
void modify(int p, int l, int r, int x, const Info &v) {
if (r - l == 1) {
info[p] = v;
return;
}
int m = (l + r) / 2;
if (x < m) {
modify(2 * p, l, m, x, v);
} else {
modify(2 * p + 1, m, r, x, v);
}
pull(p);
}
void modify(int p, const Info &v) {
modify(1, 0, n, p, v);
}
Info rangeQuery(int p, int l, int r, int x, int y) {
if (l >= y || r <= x) {
return Info();
}
if (l >= x && r <= y) {
return info[p];
}
int m = (l + r) / 2;
return merge(rangeQuery(2 * p, l, m, x, y), rangeQuery(2 * p + 1, m, r, x, y));
}
Info rangeQuery(int l, int r) {
return rangeQuery(1, 0, n, l, r);
}
};
懒标记线段树（LazySegmentTree）
/** 懒标记线段树（LazySegmentTree）
* 2023-03-03: https://atcoder.jp/contests/joi2023yo2/submissions/39363123
* 2023-03-12: https://codeforces.com/contest/1804/submission/197106837
* 2023-07-17: https://ac.nowcoder.com/acm/contest/view-submission?submissionId=62804432
* 2023-11-12: https://qoj.ac/submission/249505
* 2024-08-14: https://ac.nowcoder.com/acm/contest/view-submission?submissionId=70980889&returnHomeType=1&uid=329687984
**/
template<class Info, class Tag>
struct LazySegmentTree {
int n;
std::vector<Info> info;
std::vector<Tag> tag;
LazySegmentTree() : n(0) {}
LazySegmentTree(int n_, Info v_ = Info()) {
init(n_, v_);
}
template<class T>
LazySegmentTree(std::vector<T> init_) {
init(init_);
}
void init(int n_, Info v_ = Info()) {
init(std::vector(n_, v_));
}
template<class T>
void init(std::vector<T> init_) {
n = init_.size();
info.assign(4 << std::__lg(n), Info());
tag.assign(4 << std::__lg(n), Tag());
std::function<void(int, int, int)> build = [&](int p, int l, int r) {
if (r - l == 1) {
info[p] = init_[l];
return;
}
int m = (l + r) / 2;
build(2 * p, l, m);
build(2 * p + 1, m, r);
pull(p);
};
build(1, 0, n);
}
void pull(int p) {
info[p] = info[2 * p] + info[2 * p + 1];
}
void apply(int p, const Tag &v) {
info[p].apply(v);
tag[p].apply(v);
}
void push(int p) {
apply(2 * p, tag[p]);
apply(2 * p + 1, tag[p]);
tag[p] = Tag();
}
void modify(int p, int l, int r, int x, const Info &v) {
if (r - l == 1) {
info[p] = v;
return;
}
int m = (l + r) / 2;
push(p);
if (x < m) {
modify(2 * p, l, m, x, v);
} else {
modify(2 * p + 1, m, r, x, v);
}
pull(p);
}
void modify(int p, const Info &v) {
modify(1, 0, n, p, v);
}
Info rangeQuery(int p, int l, int r, int x, int y) {
if (l >= y || r <= x) {
return Info();
}
if (l >= x && r <= y) {
return info[p];
}
int m = (l + r) / 2;
push(p);
return rangeQuery(2 * p, l, m, x, y) + rangeQuery(2 * p + 1, m, r, x, y);
}
Info rangeQuery(int l, int r) {
return rangeQuery(1, 0, n, l, r);
}
void rangeApply(int p, int l, int r, int x, int y, const Tag &v) {
if (l >= y || r <= x) {
return;
}
if (l >= x && r <= y) {
apply(p, v);
return;
}
int m = (l + r) / 2;
push(p);
rangeApply(2 * p, l, m, x, y, v);
rangeApply(2 * p + 1, m, r, x, y, v);
pull(p);
}
void rangeApply(int l, int r, const Tag &v) {
return rangeApply(1, 0, n, l, r, v);
}
void half(int p, int l, int r) {
if (info[p].act == 0) {
return;
}
if ((info[p].min + 1) / 2 == (info[p].max + 1) / 2) {
apply(p, {-(info[p].min + 1) / 2});
return;
}
int m = (l + r) / 2;
push(p);
half(2 * p, l, m);
half(2 * p + 1, m, r);
pull(p);
}
void half() {
half(1, 0, n);
}
template<class F>
int findFirst(int p, int l, int r, int x, int y, F &&pred) {
if (l >= y || r <= x) {
return -1;
}
if (l >= x && r <= y && !pred(info[p])) {
return -1;
}
if (r - l == 1) {
return l;
}
int m = (l + r) / 2;
push(p);
int res = findFirst(2 * p, l, m, x, y, pred);
if (res == -1) {
res = findFirst(2 * p + 1, m, r, x, y, pred);
}
return res;
}
template<class F>
int findFirst(int l, int r, F &&pred) {
return findFirst(1, 0, n, l, r, pred);
}
template<class F>
int findLast(int p, int l, int r, int x, int y, F &&pred) {
if (l >= y || r <= x) {
return -1;
}
if (l >= x && r <= y && !pred(info[p])) {
return -1;
}
if (r - l == 1) {
return l;
}
int m = (l + r) / 2;
push(p);
int res = findLast(2 * p + 1, m, r, x, y, pred);
if (res == -1) {
res = findLast(2 * p, l, m, x, y, pred);
}
return res;
}
template<class F>
int findLast(int l, int r, F &&pred) {
return findLast(1, 0, n, l, r, pred);
}
void maintainL(int p, int l, int r, int pre) {
if (info[p].difl > 0 && info[p].maxlowl < pre) {
return;
}
if (r - l == 1) {
info[p].max = info[p].maxlowl;
info[p].maxl = info[p].maxr = l;
info[p].maxlowl = info[p].maxlowr = -inf;
return;
}
int m = (l + r) / 2;
push(p);
maintainL(2 * p, l, m, pre);
pre = std::max(pre, info[2 * p].max);
maintainL(2 * p + 1, m, r, pre);
pull(p);
}
void maintainL() {
maintainL(1, 0, n, -1);
}
void maintainR(int p, int l, int r, int suf) {
if (info[p].difr > 0 && info[p].maxlowr < suf) {
return;
}
if (r - l == 1) {
info[p].max = info[p].maxlowl;
info[p].maxl = info[p].maxr = l;
info[p].maxlowl = info[p].maxlowr = -inf;
return;
}
int m = (l + r) / 2;
push(p);
maintainR(2 * p + 1, m, r, suf);
suf = std::max(suf, info[2 * p + 1].max);
maintainR(2 * p, l, m, suf);
pull(p);
}
void maintainR() {
maintainR(1, 0, n, -1);
}
};
struct Tag {
int x = 0;
void apply(const Tag &t) & {
x = std::max(x, t.x);
}
};
struct Info {
int x = 0;
void apply(const Tag &t) & {
x = std::max(x, t.x);
}
};
Info operator+(const Info &a, const Info &b) {
return {std::max(a.x, b.x)};
}
取模类
长度过长，点击查看
取模类（Z 旧版）
/** 取模类（Z 旧版）
* 2022-06-12: https://codeforces.com/contest/1697/submission/160317720
**/
constexpr int P = 998244353;
using i64 = long long;
// assume -P <= x < 2P
int norm(int x) {
if (x < 0) {
x += P;
}
if (x >= P) {
x -= P;
}
return x;
}
template<class T>
T power(T a, i64 b) {
T res = 1;
for (; b; b /= 2, a *= a) {
if (b % 2) {
res *= a;
}
}
return res;
}
struct Z {
int x;
Z(int x = 0) : x(norm(x)) {}
Z(i64 x) : x(norm(x % P)) {}
int val() const {
return x;
}
Z operator-() const {
return Z(norm(P - x));
}
Z inv() const {
assert(x != 0);
return power(*this, P - 2);
}
Z &operator*=(const Z &rhs) {
x = i64(x) * rhs.x % P;
return *this;
}
Z &operator+=(const Z &rhs) {
x = norm(x + rhs.x);
return *this;
}
Z &operator-=(const Z &rhs) {
x = norm(x - rhs.x);
return *this;
}
Z &operator/=(const Z &rhs) {
return *this *= rhs.inv();
}
friend Z operator*(const Z &lhs, const Z &rhs) {
Z res = lhs;
res *= rhs;
return res;
}
friend Z operator+(const Z &lhs, const Z &rhs) {
Z res = lhs;
res += rhs;
return res;
}
friend Z operator-(const Z &lhs, const Z &rhs) {
Z res = lhs;
res -= rhs;
return res;
}
friend Z operator/(const Z &lhs, const Z &rhs) {
Z res = lhs;
res /= rhs;
return res;
}
friend std::istream &operator>>(std::istream &is, Z &a) {
i64 v;
is >> v;
a = Z(v);
return is;
}
friend std::ostream &operator<<(std::ostream &os, const Z &a) {
return os << a.val();
}
};
取模类（MLong & MInt 新版）
/** 取模类（MLong & MInt 新版）
* 2023-08-14: https://ac.nowcoder.com/acm/contest/view-submission?submissionId=63433564
*
* 根据输入内容动态修改 MOD 的方法：Z::setMod(p) 。
**/
template<class T>
constexpr T power(T a, i64 b) {
T res = 1;
for (; b; b /= 2, a *= a) {
if (b % 2) {
res *= a;
}
}
return res;
}
constexpr i64 mul(i64 a, i64 b, i64 p) {
i64 res = a * b - i64(1.L * a * b / p) * p;
res %= p;
if (res < 0) {
res += p;
}
return res;
}
template<i64 P>
struct MLong {
i64 x;
constexpr MLong() : x{} {}
constexpr MLong(i64 x) : x{norm(x % getMod())} {}
static i64 Mod;
constexpr static i64 getMod() {
if (P > 0) {
return P;
} else {
return Mod;
}
}
constexpr static void setMod(i64 Mod_) {
Mod = Mod_;
}
constexpr i64 norm(i64 x) const {
if (x < 0) {
x += getMod();
}
if (x >= getMod()) {
x -= getMod();
}
return x;
}
constexpr i64 val() const {
return x;
}
explicit constexpr operator i64() const {
return x;
}
constexpr MLong operator-() const {
MLong res;
res.x = norm(getMod() - x);
return res;
}
constexpr MLong inv() const {
assert(x != 0);
return power(*this, getMod() - 2);
}
constexpr MLong &operator*=(MLong rhs) & {
x = mul(x, rhs.x, getMod());
return *this;
}
constexpr MLong &operator+=(MLong rhs) & {
x = norm(x + rhs.x);
return *this;
}
constexpr MLong &operator-=(MLong rhs) & {
x = norm(x - rhs.x);
return *this;
}
constexpr MLong &operator/=(MLong rhs) & {
return *this *= rhs.inv();
}
friend constexpr MLong operator*(MLong lhs, MLong rhs) {
MLong res = lhs;
res *= rhs;
return res;
}
friend constexpr MLong operator+(MLong lhs, MLong rhs) {
MLong res = lhs;
res += rhs;
return res;
}
friend constexpr MLong operator-(MLong lhs, MLong rhs) {
MLong res = lhs;
res -= rhs;
return res;
}
friend constexpr MLong operator/(MLong lhs, MLong rhs) {
MLong res = lhs;
res /= rhs;
return res;
}
friend constexpr std::istream &operator>>(std::istream &is, MLong &a) {
i64 v;
is >> v;
a = MLong(v);
return is;
}
friend constexpr std::ostream &operator<<(std::ostream &os, const MLong &a) {
return os << a.val();
}
friend constexpr bool operator==(MLong lhs, MLong rhs) {
return lhs.val() == rhs.val();
}
friend constexpr bool operator!=(MLong lhs, MLong rhs) {
return lhs.val() != rhs.val();
}
};
template<>
i64 MLong<0LL>::Mod = i64(1E18) + 9;
template<int P>
struct MInt {
int x;
constexpr MInt() : x{} {}
constexpr MInt(i64 x) : x{norm(x % getMod())} {}
static int Mod;
constexpr static int getMod() {
if (P > 0) {
return P;
} else {
return Mod;
}
}
constexpr static void setMod(int Mod_) {
Mod = Mod_;
}
constexpr int norm(int x) const {
if (x < 0) {
x += getMod();
}
if (x >= getMod()) {
x -= getMod();
}
return x;
}
constexpr int val() const {
return x;
}
explicit constexpr operator int() const {
return x;
}
constexpr MInt operator-() const {
MInt res;
res.x = norm(getMod() - x);
return res;
}
constexpr MInt inv() const {
assert(x != 0);
return power(*this, getMod() - 2);
}
constexpr MInt &operator*=(MInt rhs) & {
x = 1LL * x * rhs.x % getMod();
return *this;
}
constexpr MInt &operator+=(MInt rhs) & {
x = norm(x + rhs.x);
return *this;
}
constexpr MInt &operator-=(MInt rhs) & {
x = norm(x - rhs.x);
return *this;
}
constexpr MInt &operator/=(MInt rhs) & {
return *this *= rhs.inv();
}
friend constexpr MInt operator*(MInt lhs, MInt rhs) {
MInt res = lhs;
res *= rhs;
return res;
}
friend constexpr MInt operator+(MInt lhs, MInt rhs) {
MInt res = lhs;
res += rhs;
return res;
}
friend constexpr MInt operator-(MInt lhs, MInt rhs) {
MInt res = lhs;
res -= rhs;
return res;
}
friend constexpr MInt operator/(MInt lhs, MInt rhs) {
MInt res = lhs;
res /= rhs;
return res;
}
friend constexpr std::istream &operator>>(std::istream &is, MInt &a) {
i64 v;
is >> v;
a = MInt(v);
return is;
}
friend constexpr std::ostream &operator<<(std::ostream &os, const MInt &a) {
return os << a.val();
}
friend constexpr bool operator==(MInt lhs, MInt rhs) {
return lhs.val() == rhs.val();
}
friend constexpr bool operator!=(MInt lhs, MInt rhs) {
return lhs.val() != rhs.val();
}
};
template<>
int MInt<0>::Mod = 998244353;
template<int V, int P>
constexpr MInt<P> CInv = MInt<P>(V).inv();
constexpr int P = 1000000007;
using Z = MInt<P>;
动态取模类（ModIntBase）
/** 动态取模类（ModIntBase）
* 2024-08-14: https://ac.nowcoder.com/acm/contest/view-submission?submissionId=70980889&returnHomeType=1&uid=329687984
**/
// TODO: Dynamic ModInt
template<typename T>
constexpr T power(T a, u64 b) {
T res {1};
for (; b != 0; b /= 2, a *= a) {
if (b % 2 == 1) {
res *= a;
}
}
return res;
}
template<u32 P>
constexpr u32 mulMod(u32 a, u32 b) {
return 1ULL * a * b % P;
}
template<u64 P>
constexpr u64 mulMod(u64 a, u64 b) {
u64 res = a * b - u64(1.L * a * b / P - 0.5L) * P;
res %= P;
return res;
}
template<typename U, U P>
requires std::unsigned_integral<U>
struct ModIntBase {
public:
constexpr ModIntBase() : x {0} {}
template<typename T>
requires std::integral<T>
constexpr ModIntBase(T x_) : x {norm(x_ % T {P})} {}
constexpr static U norm(U x) {
if ((x >> (8 * sizeof(U) - 1) & 1) == 1) {
x += P;
}
if (x >= P) {
x -= P;
}
return x;
}
constexpr U val() const {
return x;
}
constexpr ModIntBase operator-() const {
ModIntBase res;
res.x = norm(P - x);
return res;
}
constexpr ModIntBase inv() const {
return power(*this, P - 2);
}
constexpr ModIntBase &operator*=(const ModIntBase &rhs) & {
x = mulMod<P>(x, rhs.val());
return *this;
}
constexpr ModIntBase &operator+=(const ModIntBase &rhs) & {
x = norm(x + rhs.x);
return *this;
}
constexpr ModIntBase &operator-=(const ModIntBase &rhs) & {
x = norm(x - rhs.x);
return *this;
}
constexpr ModIntBase &operator/=(const ModIntBase &rhs) & {
return *this *= rhs.inv();
}
friend constexpr ModIntBase operator*(ModIntBase lhs, const ModIntBase &rhs) {
lhs *= rhs;
return lhs;
}
friend constexpr ModIntBase operator+(ModIntBase lhs, const ModIntBase &rhs) {
lhs += rhs;
return lhs;
}
friend constexpr ModIntBase operator-(ModIntBase lhs, const ModIntBase &rhs) {
lhs -= rhs;
return lhs;
}
friend constexpr ModIntBase operator/(ModIntBase lhs, const ModIntBase &rhs) {
lhs /= rhs;
return lhs;
}
friend constexpr std::ostream &operator<<(std::ostream &os, const ModIntBase &a) {
return os << a.val();
}
friend constexpr bool operator==(ModIntBase lhs, ModIntBase rhs) {
return lhs.val() == rhs.val();
}
friend constexpr bool operator!=(ModIntBase lhs, ModIntBase rhs) {
return lhs.val() != rhs.val();
}
friend constexpr bool operator<(ModIntBase lhs, ModIntBase rhs) {
return lhs.val() < rhs.val();
}
private:
U x;
};
template<u32 P>
using ModInt = ModIntBase<u32, P>;
template<u64 P>
using ModInt64 = ModIntBase<u64, P>;
constexpr u32 P = 998244353;
using Z = ModInt<P>;
状压RMQ（RMQ）
/** 状压RMQ（RMQ）
* 2023-03-02: https://atcoder.jp/contests/joi2022ho/submissions/39351739
* 2023-09-04: https://qoj.ac/submission/163598
* 2024-08-07: https://atcoder.jp/contests/abc365/submissions/56438692
**/
template<class T,
class Cmp = std::less<T>>
struct RMQ {
const Cmp cmp = Cmp();
static constexpr unsigned B = 64;
using u64 = unsigned long long;
int n;
std::vector<std::vector<T>> a;
std::vector<T> pre, suf, ini;
std::vector<u64> stk;
RMQ() {}
RMQ(const std::vector<T> &v) {
init(v);
}
void init(const std::vector<T> &v) {
n = v.size();
pre = suf = ini = v;
stk.resize(n);
if (!n) {
return;
}
const int M = (n - 1) / B + 1;
const int lg = std::__lg(M);
a.assign(lg + 1, std::vector<T>(M));
for (int i = 0; i < M; i++) {
a[0][i] = v[i * B];
for (int j = 1; j < B && i * B + j < n; j++) {
a[0][i] = std::min(a[0][i], v[i * B + j], cmp);
}
}
for (int i = 1; i < n; i++) {
if (i % B) {
pre[i] = std::min(pre[i], pre[i - 1], cmp);
}
}
for (int i = n - 2; i >= 0; i--) {
if (i % B != B - 1) {
suf[i] = std::min(suf[i], suf[i + 1], cmp);
}
}
for (int j = 0; j < lg; j++) {
for (int i = 0; i + (2 << j) <= M; i++) {
a[j + 1][i] = std::min(a[j][i], a[j][i + (1 << j)], cmp);
}
}
for (int i = 0; i < M; i++) {
const int l = i * B;
const int r = std::min(1U * n, l + B);
u64 s = 0;
for (int j = l; j < r; j++) {
while (s && cmp(v[j], v[std::__lg(s) + l])) {
s ^= 1ULL << std::__lg(s);
}
s |= 1ULL << (j - l);
stk[j] = s;
}
}
}
T operator()(int l, int r) {
if (l / B != (r - 1) / B) {
T ans = std::min(suf[l], pre[r - 1], cmp);
l = l / B + 1;
r = r / B;
if (l < r) {
int k = std::__lg(r - l);
ans = std::min({ans, a[k][l], a[k][r - (1 << k)]}, cmp);
}
return ans;
} else {
int x = B * (l / B);
return ini[__builtin_ctzll(stk[r - 1] >> (l - x)) + l];
}
}
};
Splay
长度过长，点击查看
```cpp /** Splay * 2023-02-15: https://atcoder.jp/contests/joi2023ho/submissions/38901674 **/ struct Node { Node *l = nullptr; Node *r = nullptr; int cnt = 0; i64 sum = 0; };Node *add(Node *t, int l, int r, int p, int v) {
Node *x = new Node;
if (t) {
*x = *t;
}
x->cnt += 1;
x->sum += v;
if (r - l == 1) {
return x;
}
int m = (l + r) / 2;
if (p < m) {
x->l = add(x->l, l, m, p, v);
} else {
x->r = add(x->r, m, r, p, v);
}
return x;
}
int find(Node *tl, Node *tr, int l, int r, int x) {
if (r <= x) {
return -1;
}
if (l >= x) {
int cnt = (tr ? tr->cnt : 0) - (tl ? tl->cnt : 0);
if (cnt == 0) {
return -1;
}
if (r - l == 1) {
return l;
}
}
int m = (l + r) / 2;
int res = find(tl ? tl->l : tl, tr ? tr->l : tr, l, m, x);
if (res == -1) {
res = find(tl ? tl->r : tl, tr ? tr->r : tr, m, r, x);
}
return res;
}
std::pair<int, i64> get(Node *t, int l, int r, int x, int y) {
if (l >= y || r <= x || !t) {
return {0, 0LL};
}
if (l >= x && r <= y) {
return {t->cnt, t->sum};
}
int m = (l + r) / 2;
auto [cl, sl] = get(t->l, l, m, x, y);
auto [cr, sr] = get(t->r, m, r, x, y);
return {cl + cr, sl + sr};
}
struct Tree {
int add = 0;
int val = 0;
int id = 0;
Tree *ch[2] = {};
Tree *p = nullptr;
};
int pos(Tree *t) {
return t->p->ch[1] == t;
}
void add(Tree *t, int v) {
t->val += v;
t->add += v;
}
void push(Tree *t) {
if (t->ch[0]) {
add(t->ch[0], t->add);
}
if (t->ch[1]) {
add(t->ch[1], t->add);
}
t->add = 0;
}
void rotate(Tree *t) {
Tree *q = t->p;
int x = !pos(t);
q->ch[!x] = t->ch[x];
if (t->ch[x]) t->ch[x]->p = q;
t->p = q->p;
if (q->p) q->p->ch[pos(q)] = t;
t->ch[x] = q;
q->p = t;
}
void splay(Tree *t) {
std::vector<Tree *> s;
for (Tree *i = t; i->p; i = i->p) s.push_back(i->p);
while (!s.empty()) {
push(s.back());
s.pop_back();
}
push(t);
while (t->p) {
if (t->p->p) {
if (pos(t) == pos(t->p)) rotate(t->p);
else rotate(t);
}
rotate(t);
}
}
void insert(Tree *&t, Tree *x, Tree *p = nullptr) {
if (!t) {
t = x;
x->p = p;
return;
}
push(t);
if (x->val < t->val) {
insert(t->ch[0], x, t);
} else {
insert(t->ch[1], x, t);
}
}
void dfs(Tree *t) {
if (!t) {
return;
}
push(t);
dfs(t->ch[0]);
std::cerr << t->val << " ";
dfs(t->ch[1]);
}
std::pair<Tree *, Tree *> split(Tree *t, int x) {
if (!t) {
return {t, t};
}
Tree *v = nullptr;
Tree *j = t;
for (Tree *i = t; i; ) {
push(i);
j = i;
if (i->val >= x) {
v = i;
i = i->ch[0];
} else {
i = i->ch[1];
}
}
splay(j);
if (!v) {
return {j, nullptr};
}
splay(v);
Tree *u = v->ch[0];
if (u) {
v->ch[0] = u->p = nullptr;
}
// std::cerr << "split " << x << "\n";
// dfs(u);
// std::cerr << "\n";
// dfs(v);
// std::cerr << "\n";
return {u, v};
}
Tree *merge(Tree *l, Tree *r) {
if (!l) {
return r;
}
if (!r) {
return l;
}
Tree *i = l;
while (i->ch[1]) {
i = i->ch[1];
}
splay(i);
i->ch[1] = r;
r->p = i;
return i;
}
```cpp
/** Splay
* 2024-03-30: https://codeforces.com/contest/1942/submission/254202464
**/
struct Matrix : std::array<std::array<i64, 4>, 4> {
Matrix(i64 v = 0) {
for (int i = 0; i < 4; i++) {
for (int j = 0; j < 4; j++) {
(*this)[i][j] = (i == j ? v : inf);
}
}
}
};
Matrix operator*(const Matrix &a, const Matrix &b) {
Matrix c(inf);
for (int i = 0; i < 3; i++) {
for (int j = 0; j < 3; j++) {
for (int k = 0; k < 4; k++) {
c[i][k] = std::min(c[i][k], a[i][j] + b[j][k]);
}
}
c[i][3] = std::min(c[i][3], a[i][3]);
}
c[3][3] = 0;
return c;
}
struct Node {
Node *ch[2], *p;
i64 sumg = 0;
i64 sumh = 0;
i64 sumb = 0;
i64 g = 0;
i64 h = 0;
i64 b = 0;
Matrix mat;
Matrix prd;
std::array<i64, 4> ans{};
Node() : ch{nullptr, nullptr}, p(nullptr) {}
void update() {
mat = Matrix(inf);
mat[0][0] = b + h - g + sumg;
mat[1][1] = mat[1][2] = mat[1][3] = h + sumh;
mat[2][0] = mat[2][1] = mat[2][2] = mat[2][3] = b + h + sumb;
mat[3][3] = 0;
}
};
void push(Node *t) {
}
void pull(Node *t) {
t->prd = (t->ch[0] ? t->ch[0]->prd : Matrix()) * t->mat * (t->ch[1] ? t->ch[1]->prd : Matrix());
}
bool isroot(Node *t) {
return t->p == nullptr || (t->p->ch[0] != t && t->p->ch[1] != t);
}
int pos(Node *t) {
return t->p->ch[1] == t;
}
void pushAll(Node *t) {
if (!isroot(t)) {
pushAll(t->p);
}
push(t);
}
void rotate(Node *t) {
Node *q = t->p;
int x = !pos(t);
q->ch[!x] = t->ch[x];
if (t->ch[x]) {
t->ch[x]->p = q;
}
t->p = q->p;
if (!isroot(q)) {
q->p->ch[pos(q)] = t;
}
t->ch[x] = q;
q->p = t;
pull(q);
}
void splay(Node *t) {
pushAll(t);
while (!isroot(t)) {
if (!isroot(t->p)) {
if (pos(t) == pos(t->p)) {
rotate(t->p);
} else {
rotate(t);
}
}
rotate(t);
}
pull(t);
}
std::array<i64, 4> get(Node *t) {
std::array<i64, 4> ans;
ans.fill(inf);
ans[3] = 0;
for (int i = 0; i < 3; i++) {
for (int j = 0; j < 4; j++) {
ans[i] = std::min(ans[i], t->prd[i][j]);
}
}
return ans;
}
void access(Node *t) {
std::array<i64, 4> old{};
for (Node *i = t, *q = nullptr; i; q = i, i = i->p) {
splay(i);
if (i->ch[1]) {
auto res = get(i->ch[1]);
i->sumg += res[0];
i->sumh += std::min({res[1], res[2], res[3]});
i->sumb += std::min({res[0], res[1], res[2], res[3]});
}
i->ch[1] = q;
i->sumg -= old[0];
i->sumh -= std::min({old[1], old[2], old[3]});
i->sumb -= std::min({old[0], old[1], old[2], old[3]});
old = get(i);
i->update();
pull(i);
}
splay(t);
}
/** Splay
* 2024-06-24: https://cf.dianhsu.com/gym/105229/submission/267199687?version=1.5
**/
constexpr int D = 27;
struct Info {
int up[D][2] {};
int down[D][2] {};
int t = 0;
i64 ans = 0;
};
Info operator+(const Info &a, const Info &b) {
Info c;
c.t = a.t ^ b.t;
c.ans = a.ans + b.ans;
for (int i = 0; i < D; i++) {
for (int j = 0; j < 2; j++) {
c.ans += (1LL << i) * a.down[i][j] * b.up[i][j ^ 1];
c.up[i][j] += a.up[i][j] + b.up[i][j ^ (a.t >> i & 1)];
c.down[i][j] += b.down[i][j] + a.down[i][j ^ (b.t >> i & 1)];
}
}
return c;
}
struct Node {
Node *ch[2], *p;
Info val;
Info tot;
int cnt[D][2];
i64 pair[D][2];
i64 sum;
Node() : ch{nullptr, nullptr}, p(nullptr), cnt {}, pair {}, sum {} {}
};
void pull(Node *t) {
t->tot = (t->ch[0] ? t->ch[0]->tot : Info {}) + t->val + (t->ch[1] ? t->ch[1]->tot : Info {});
}
bool isroot(Node *t) {
return t->p == nullptr || (t->p->ch[0] != t && t->p->ch[1] != t);
}
int pos(Node *t) {
return t->p->ch[1] == t;
}
void rotate(Node *t) {
Node *q = t->p;
int x = !pos(t);
q->ch[!x] = t->ch[x];
if (t->ch[x]) {
t->ch[x]->p = q;
}
t->p = q->p;
if (!isroot(q)) {
q->p->ch[pos(q)] = t;
}
t->ch[x] = q;
q->p = t;
pull(q);
}
void update(Node *t) {
t->val.ans = t->val.t + t->sum;
for (int i = 0; i < D; i++) {
t->val.ans += (1LL << i) * t->pair[i][t->val.t >> i & 1];
for (int j = 0; j < 2; j++) {
t->val.up[i][j] = t->cnt[i][j ^ (t->val.t >> i & 1)];
t->val.down[i][j] = t->cnt[i][j ^ (t->val.t >> i & 1)];
}
t->val.up[i][t->val.t >> i & 1]++;
t->val.down[i][t->val.t >> i & 1]++;
}
pull(t);
}
void splay(Node *t) {
while (!isroot(t)) {
if (!isroot(t->p)) {
if (pos(t) == pos(t->p)) {
rotate(t->p);
} else {
rotate(t);
}
}
rotate(t);
}
pull(t);
}
void add(Node *t, Info s) {
for (int i = 0; i < D; i++) {
for (int x = 0; x < 2; x++) {
t->pair[i][x] += s.up[i][1 ^ x];
for (int j = 0; j < 2; j++) {
t->pair[i][x] += t->cnt[i][j] * s.up[i][j ^ 1 ^ x];
}
}
for (int j = 0; j < 2; j++) {
t->cnt[i][j] += s.up[i][j];
}
}
t->sum += s.ans;
}
void del(Node *t, Info s) {
t->sum -= s.ans;
for (int i = 0; i < D; i++) {
for (int j = 0; j < 2; j++) {
t->cnt[i][j] -= s.up[i][j];
}
for (int x = 0; x < 2; x++) {
for (int j = 0; j < 2; j++) {
t->pair[i][x] -= t->cnt[i][j] * s.up[i][j ^ 1 ^ x];
}
t->pair[i][x] -= s.up[i][1 ^ x];
}
}
}
void access(Node *t, int v) {
Info lst;
for (Node *i = t, *q = nullptr; i; q = i, i = i->p) {
splay(i);
if (i->ch[1]) {
add(i, i->ch[1]->tot);
}
i->ch[1] = q;
if (q) {
del(i, lst);
} else {
i->val.t = v;
}
lst = i->tot;
update(i);
}
splay(t);
}
其他平衡树
/** 其他平衡树
* 2023-08-04: https://ac.nowcoder.com/acm/contest/view-submission?submissionId=63246177
**/
struct Node {
Node *l = nullptr;
Node *r = nullptr;
int sum = 0;
int sumodd = 0;
Node(Node *t) {
if (t) {
*this = *t;
}
}
};
Node *add(Node *t, int l, int r, int x, int v) {
t = new Node(t);
t->sum += v;
t->sumodd += (x % 2) * v;
if (r - l == 1) {
return t;
}
int m = (l + r) / 2;
if (x < m) {
t->l = add(t->l, l, m, x, v);
} else {
t->r = add(t->r, m, r, x, v);
}
return t;
}
int query1(Node *t1, Node *t2, int l, int r, int k) {
if (r - l == 1) {
return l;
}
int m = (l + r) / 2;
int odd = (t1 && t1->r ? t1->r->sumodd : 0) - (t2 && t2->r ? t2->r->sumodd : 0);
int cnt = (t1 && t1->r ? t1->r->sum : 0) - (t2 && t2->r ? t2->r->sum : 0);
if (odd > 0 || cnt > k) {
return query1(t1 ? t1->r : t1, t2 ? t2->r : t2, m, r, k);
} else {
return query1(t1 ? t1->l : t1, t2 ? t2->l : t2, l, m, k - cnt);
}
}
std::array<int, 3> query2(Node *t1, Node *t2, int l, int r, int k) {
if (r - l == 1) {
int cnt = (t1 ? t1->sumodd : 0) - (t2 ? t2->sumodd : 0);
return {l, cnt, k};
}
int m = (l + r) / 2;
int cnt = (t1 && t1->r ? t1->r->sumodd : 0) - (t2 && t2->r ? t2->r->sumodd : 0);
if (cnt > k) {
return query2(t1 ? t1->r : t1, t2 ? t2->r : t2, m, r, k);
} else {
return query2(t1 ? t1->l : t1, t2 ? t2->l : t2, l, m, k - cnt);
}
}
/** 其他平衡树
* 2023-08-26: https://codeforces.com/contest/1864/submission/220558951
**/
struct Node {
Node *l = nullptr;
Node *r = nullptr;
int cnt = 0;
};
Node *add(Node *t, int l, int r, int x) {
if (t) {
t = new Node(*t);
} else {
t = new Node;
}
t->cnt += 1;
if (r - l == 1) {
return t;
}
int m = (l + r) / 2;
if (x < m) {
t->l = add(t->l, l, m, x);
} else {
t->r = add(t->r, m, r, x);
}
return t;
}
int query(Node *t1, Node *t2, int l, int r, int x) {
int cnt = (t2 ? t2->cnt : 0) - (t1 ? t1->cnt : 0);
if (cnt == 0 || l >= x) {
return -1;
}
if (r - l == 1) {
return l;
}
int m = (l + r) / 2;
int res = query(t1 ? t1->r : t1, t2 ? t2->r : t2, m, r, x);
if (res == -1) {
res = query(t1 ? t1->l : t1, t2 ? t2->l : t2, l, m, x);
}
return res;
}
/** 其他平衡树
* 2023-04-03: https://codeforces.com/contest/38/submission/200537139
**/
struct Info {
int imp = 0;
int id = 0;
};
Info operator+(Info a, Info b) {
return {std::max(a.imp, b.imp), 0};
}
struct Node {
int w = rng();
Info info;
Info sum;
int siz = 1;
Node *l = nullptr;
Node *r = nullptr;
};
void pull(Node *t) {
t->sum = t->info;
t->siz = 1;
if (t->l) {
t->sum = t->l->sum + t->sum;
t->siz += t->l->siz;
}
if (t->r) {
t->sum = t->sum + t->r->sum;
t->siz += t->r->siz;
}
}
std::pair<Node *, Node *> splitAt(Node *t, int p) {
if (!t) {
return {t, t};
}
if (p <= (t->l ? t->l->siz : 0)) {
auto [l, r] = splitAt(t->l, p);
t->l = r;
pull(t);
return {l, t};
} else {
auto [l, r] = splitAt(t->r, p - 1 - (t->l ? t->l->siz : 0));
t->r = l;
pull(t);
return {t, r};
}
}
void insertAt(Node *&t, int p, Node *x) {
if (!t) {
t = x;
return;
}
if (x->w < t->w) {
auto [l, r] = splitAt(t, p);
t = x;
t->l = l;
t->r = r;
pull(t);
return;
}
if (p <= (t->l ? t->l->siz : 0)) {
insertAt(t->l, p, x);
} else {
insertAt(t->r, p - 1 - (t->l ? t->l->siz : 0), x);
}
pull(t);
}
Node *merge(Node *a, Node *b) {
if (!a) {
return b;
}
if (!b) {
return a;
}
if (a->w < b->w) {
a->r = merge(a->r, b);
pull(a);
return a;
} else {
b->l = merge(a, b->l);
pull(b);
return b;
}
}
int query(Node *t, int v) {
if (!t) {
return 0;
}
if (t->sum.imp < v) {
return t->siz;
}
int res = query(t->r, v);
if (res != (t->r ? t->r->siz : 0)) {
return res;
}
if (t->info.imp > v) {
return res;
}
return res + 1 + query(t->l, v);
}
void dfs(Node *t) {
if (!t) {
return;
}
dfs(t->l);
std::cout << t->info.id << " ";
dfs(t->r);
}
/** 其他平衡树
* 2023-07-31: https://ac.nowcoder.com/acm/contest/view-submission?submissionId=63162242
**/
struct Node {
Node *l = nullptr;
Node *r = nullptr;
int cnt = 0;
int cntnew = 0;
};
Node *add(int l, int r, int x, int isnew) {
Node *t = new Node;
t->cnt = 1;
t->cntnew = isnew;
if (r - l == 1) {
return t;
}
int m = (l + r) / 2;
if (x < m) {
t->l = add(l, m, x, isnew);
} else {
t->r = add(m, r, x, isnew);
}
return t;
}
struct Info {
Node *t = nullptr;
int psum = 0;
bool rev = false;
};
void pull(Node *t) {
t->cnt = (t->l ? t->l->cnt : 0) + (t->r ? t->r->cnt : 0);
t->cntnew = (t->l ? t->l->cntnew : 0) + (t->r ? t->r->cntnew : 0);
}
std::pair<Node *, Node *> split(Node *t, int l, int r, int x, bool rev) {
if (!t) {
return {t, t};
}
if (x == 0) {
return {nullptr, t};
}
if (x == t->cnt) {
return {t, nullptr};
}
if (r - l == 1) {
Node *t2 = new Node;
t2->cnt = t->cnt - x;
t->cnt = x;
return {t, t2};
}
Node *t2 = new Node;
int m = (l + r) / 2;
if (!rev) {
if (t->l && x <= t->l->cnt) {
std::tie(t->l, t2->l) = split(t->l, l, m, x, rev);
t2->r = t->r;
t->r = nullptr;
} else {
std::tie(t->r, t2->r) = split(t->r, m, r, x - (t->l ? t->l->cnt : 0), rev);
}
} else {
if (t->r && x <= t->r->cnt) {
std::tie(t->r, t2->r) = split(t->r, m, r, x, rev);
t2->l = t->l;
t->l = nullptr;
} else {
std::tie(t->l, t2->l) = split(t->l, l, m, x - (t->r ? t->r->cnt : 0), rev);
}
}
pull(t);
pull(t2);
return {t, t2};
}
Node *merge(Node *t1, Node *t2, int l, int r) {
if (!t1) {
return t2;
}
if (!t2) {
return t1;
}
if (r - l == 1) {
t1->cnt += t2->cnt;
t1->cntnew += t2->cntnew;
delete t2;
return t1;
}
int m = (l + r) / 2;
t1->l = merge(t1->l, t2->l, l, m);
t1->r = merge(t1->r, t2->r, m, r);
delete t2;
pull(t1);
return t1;
}
分数四则运算（Frac）
/** 分数四则运算（Frac）
* 2024-07-30: https://qoj.ac/submission/498911
**/
template<class T>
struct Frac {
T num;
T den;
Frac(T num_, T den_) : num(num_), den(den_) {
if (den < 0) {
den = -den;
num = -num;
}
}
Frac() : Frac(0, 1) {}
Frac(T num_) : Frac(num_, 1) {}
explicit operator double() const {
return 1. * num / den;
}
Frac &operator+=(const Frac &rhs) {
num = num * rhs.den + rhs.num * den;
den *= rhs.den;
return *this;
}
Frac &operator-=(const Frac &rhs) {
num = num * rhs.den - rhs.num * den;
den *= rhs.den;
return *this;
}
Frac &operator*=(const Frac &rhs) {
num *= rhs.num;
den *= rhs.den;
return *this;
}
Frac &operator/=(const Frac &rhs) {
num *= rhs.den;
den *= rhs.num;
if (den < 0) {
num = -num;
den = -den;
}
return *this;
}
friend Frac operator+(Frac lhs, const Frac &rhs) {
return lhs += rhs;
}
friend Frac operator-(Frac lhs, const Frac &rhs) {
return lhs -= rhs;
}
friend Frac operator*(Frac lhs, const Frac &rhs) {
return lhs *= rhs;
}
friend Frac operator/(Frac lhs, const Frac &rhs) {
return lhs /= rhs;
}
friend Frac operator-(const Frac &a) {
return Frac(-a.num, a.den);
}
friend bool operator==(const Frac &lhs, const Frac &rhs) {
return lhs.num * rhs.den == rhs.num * lhs.den;
}
friend bool operator!=(const Frac &lhs, const Frac &rhs) {
return lhs.num * rhs.den != rhs.num * lhs.den;
}
friend bool operator<(const Frac &lhs, const Frac &rhs) {
return lhs.num * rhs.den < rhs.num * lhs.den;
}
friend bool operator>(const Frac &lhs, const Frac &rhs) {
return lhs.num * rhs.den > rhs.num * lhs.den;
}
friend bool operator<=(const Frac &lhs, const Frac &rhs) {
return lhs.num * rhs.den <= rhs.num * lhs.den;
}
friend bool operator>=(const Frac &lhs, const Frac &rhs) {
return lhs.num * rhs.den >= rhs.num * lhs.den;
}
friend std::ostream &operator<<(std::ostream &os, Frac x) {
T g = std::gcd(x.num, x.den);
if (x.den == g) {
return os << x.num / g;
} else {
return os << x.num / g << "/" << x.den / g;
}
}
};
线性基（Basis）
/** 线性基（Basis）
* 2023-12-03: https://codeforces.com/contest/1902/submission/235594491
**/
struct Basis {
int a[20] {};
int t[20] {};
Basis() {
std::fill(t, t + 20, -1);
}
void add(int x, int y = 1E9) {
for (int i = 0; i < 20; i++) {
if (x >> i & 1) {
if (y > t[i]) {
std::swap(a[i], x);
std::swap(t[i], y);
}
x ^= a[i];
}
}
}
bool query(int x, int y = 0) {
for (int i = 0; i < 20; i++) {
if ((x >> i & 1) && t[i] >= y) {
x ^= a[i];
}
}
return x == 0;
}
};
高精度（BigInt）
/** 高精度（BigInt）
* 2023-09-11: https://qoj.ac/submission/176420
**/
constexpr int N = 1000;
struct BigInt {
int a[N];
BigInt(int x = 0) : a{} {
for (int i = 0; x; i++) {
a[i] = x % 10;
x /= 10;
}
}
BigInt &operator*=(int x) {
for (int i = 0; i < N; i++) {
a[i] *= x;
}
for (int i = 0; i < N - 1; i++) {
a[i + 1] += a[i] / 10;
a[i] %= 10;
}
return *this;
}
BigInt &operator/=(int x) {
for (int i = N - 1; i >= 0; i--) {
if (i) {
a[i - 1] += a[i] % x * 10;
}
a[i] /= x;
}
return *this;
}
BigInt &operator+=(const BigInt &x) {
for (int i = 0; i < N; i++) {
a[i] += x.a[i];
if (a[i] >= 10) {
a[i + 1] += 1;
a[i] -= 10;
}
}
return *this;
}
};
std::ostream &operator<<(std::ostream &o, const BigInt &a) {
int t = N - 1;
while (a.a[t] == 0) {
t--;
}
for (int i = t; i >= 0; i--) {
o << a.a[i];
}
return o;
}
Link-Cut Tree
/** Link-Cut Tree【久远】
* 2020-09-01: https://codeforces.com/gym/102129/submission/91552908
**/
namespace SegT {
int tag[8 * N];
int64_t wsum[8 * N], sum[8 * N];
void add(int p, int l, int r, int v) {
sum[p] += v * (r - l);
wsum[p] += 1ll * v * (r - l) * (l + r + 1) / 2;
tag[p] += v;
}
void push(int p, int l, int r) {
int m = (l + r) / 2;
add(2 * p, l, m, tag[p]);
add(2 * p + 1, m, r, tag[p]);
tag[p] = 0;
}
void pull(int p) {
sum[p] = sum[2 * p] + sum[2 * p + 1];
wsum[p] = wsum[2 * p] + wsum[2 * p + 1];
}
void rangeAdd(int p, int l, int r, int x, int y, int v) {
if (l >= y || r <= x)
return;
if (l >= x && r <= y)
return add(p, l, r, v);
push(p, l, r);
int m = (l + r) / 2;
rangeAdd(2 * p, l, m, x, y, v);
rangeAdd(2 * p + 1, m, r, x, y, v);
pull(p);
}
int64_t query(int p, int l, int r, int x) {
if (l >= x)
return sum[p] * x;
if (r <= x)
return wsum[p];
int m = (l + r) / 2;
push(p, l, r);
return query(2 * p, l, m, x) + query(2 * p + 1, m, r, x);
}
int get(int p, int l, int r, int x) {
if (r - l == 1)
return sum[p];
int m = (l + r) / 2;
push(p, l, r);
if (x < m) {
return get(2 * p, l, m, x);
} else {
return get(2 * p + 1, m, r, x);
}
}
}
namespace LCT {
int ch[2 * N][2], p[2 * N], endp[2 * N], mn[2 * N], mx[2 * N];
bool isroot(int t) {
return ch[p[t]][0] != t && ch[p[t]][1] != t;
}
bool pos(int t) {
return ch[p[t]][1] == t;
}
void pull(int t) {
mn[t] = std::max(0, ch[t][0] ? mn[ch[t][0]] : SAM::len[SAM::link[t]]);
mx[t] = ch[t][1] ? mx[ch[t][1]] : SAM::len[t];
}
void rotate(int t) {
int k = !pos(t);
int q = p[t];
ch[q][!k] = ch[t][k];
if (ch[t][k])
p[ch[t][k]] = q;
p[t] = p[q];
if (isroot(q)) {
endp[t] = endp[q];
} else {
ch[p[q]][pos(q)] = t;
}
ch[t][k] = q;
p[q] = t;
pull(q);
}
void splay(int t) {
while (!isroot(t)) {
int q = p[t];
if (!isroot(q))
rotate(pos(t) == pos(q) ? q : t);
rotate(t);
}
pull(t);
}
void access(int t, int len) {
for (int i = t, u = 0; i; u = i, i = p[i]) {
splay(i);
if (ch[i][1])
endp[ch[i][1]] = endp[i];
ch[i][1] = 0;
pull(i);
if (u)
SegT::rangeAdd(1, 0, n, endp[i] - mx[i], endp[i] - mn[i], -1);
ch[i][1] = u;
pull(i);
}
splay(t);
endp[t] = len;
SegT::rangeAdd(1, 0, n, len - mx[t], len - mn[t], 1);
}
void cut(int t) {
splay(t);
if (ch[t][0]) {
endp[ch[t][0]] = endp[t];
p[ch[t][0]] = p[t];
p[t] = 0;
ch[t][0] = 0;
pull(t);
} else {
p[t] = 0;
}
}
void link(int t, int x) {
p[t] = x;
}
}
struct Node {
Node *ch[2], *p;
bool rev;
int siz = 1;
Node() : ch{nullptr, nullptr}, p(nullptr), rev(false) {}
};
void reverse(Node *t) {
if (t) {
std::swap(t->ch[0], t->ch[1]);
t->rev ^= 1;
}
}
void push(Node *t) {
if (t->rev) {
reverse(t->ch[0]);
reverse(t->ch[1]);
t->rev = false;
}
}
void pull(Node *t) {
t->siz = (t->ch[0] ? t->ch[0]->siz : 0) + 1 + (t->ch[1] ? t->ch[1]->siz : 0);
}
bool isroot(Node *t) {
return t->p == nullptr || (t->p->ch[0] != t && t->p->ch[1] != t);
}
int pos(Node *t) {
return t->p->ch[1] == t;
}
void pushAll(Node *t) {
if (!isroot(t)) {
pushAll(t->p);
}
push(t);
}
void rotate(Node *t) {
Node *q = t->p;
int x = !pos(t);
q->ch[!x] = t->ch[x];
if (t->ch[x]) {
t->ch[x]->p = q;
}
t->p = q->p;
if (!isroot(q)) {
q->p->ch[pos(q)] = t;
}
t->ch[x] = q;
q->p = t;
pull(q);
}
void splay(Node *t) {
pushAll(t);
while (!isroot(t)) {
if (!isroot(t->p)) {
if (pos(t) == pos(t->p)) {
rotate(t->p);
} else {
rotate(t);
}
}
rotate(t);
}
pull(t);
}
void access(Node *t) {
for (Node *i = t, *q = nullptr; i; q = i, i = i->p) {
splay(i);
i->ch[1] = q;
pull(i);
}
splay(t);
}
void makeroot(Node *t) {
access(t);
reverse(t);
}
void link(Node *x, Node *y) {
makeroot(x);
x->p = y;
}
void split(Node *x, Node *y) {
makeroot(x);
access(y);
}
void cut(Node *x, Node *y) {
split(x, y);
x->p = y->ch[0] = nullptr;
pull(y);
}
int dist(Node *x, Node *y) {
split(x, y);
return y->siz - 1;
}
五、字符串
点击展开本章节
马拉车（Manacher）
/** 马拉车（Manacher, with string）
* 2024-04-06: https://qoj.ac/submission/380047
* 2024-04-09: https://qoj.ac/submission/384389 【模板】
**/
std::vector<int> manacher(std::string s) {
std::string t = "#";
for (auto c : s) {
t += c;
t += '#';
}
int n = t.size();
std::vector<int> r(n);
for (int i = 0, j = 0; i < n; i++) {
if (2 * j - i >= 0 && j + r[j] > i) {
r[i] = std::min(r[2 * j - i], j + r[j] - i);
}
while (i - r[i] >= 0 && i + r[i] < n && t[i - r[i]] == t[i + r[i]]) {
r[i] += 1;
}
if (i + r[i] > j + r[j]) {
j = i;
}
}
return r;
}
Z函数
/** Z函数
* 2023-08-11: https://ac.nowcoder.com/acm/contest/view-submission?submissionId=63378373
* 2024-04-09: https://qoj.ac/submission/384405 【模板】
**/
std::vector<int> Z(std::string s) {
int n = s.size();
std::vector<int> z(n + 1);
z[0] = n;
for (int i = 1, j = 1; i < n; i++) {
z[i] = std::max(0, std::min(j + z[j] - i, z[i - j]));
while (i + z[i] < n && s[z[i]] == s[i + z[i]]) {
z[i]++;
}
if (i + z[i] > j + z[j]) {
j = i;
}
}
return z;
}
后缀数组
后缀数组（SuffixArray 旧版）
/** 后缀数组（SuffixArray 旧版）
* 2023-03-14: https://atcoder.jp/contests/discovery2016-qual/submissions/39727257
* 2023-09-05: https://qoj.ac/submission/164483
* 2024-04-09: https://qoj.ac/submission/384415 【模板】
**/
struct SuffixArray {
int n;
std::vector<int> sa, rk, lc;
SuffixArray(const std::string &s) {
n = s.length();
sa.resize(n);
lc.resize(n - 1);
rk.resize(n);
std::iota(sa.begin(), sa.end(), 0);
std::sort(sa.begin(), sa.end(), [&](int a, int b) {return s[a] < s[b];});
rk[sa[0]] = 0;
for (int i = 1; i < n; ++i)
rk[sa[i]] = rk[sa[i - 1]] + (s[sa[i]] != s[sa[i - 1]]);
int k = 1;
std::vector<int> tmp, cnt(n);
tmp.reserve(n);
while (rk[sa[n - 1]] < n - 1) {
tmp.clear();
for (int i = 0; i < k; ++i)
tmp.push_back(n - k + i);
for (auto i : sa)
if (i >= k)
tmp.push_back(i - k);
std::fill(cnt.begin(), cnt.end(), 0);
for (int i = 0; i < n; ++i)
++cnt[rk[i]];
for (int i = 1; i < n; ++i)
cnt[i] += cnt[i - 1];
for (int i = n - 1; i >= 0; --i)
sa[--cnt[rk[tmp[i]]]] = tmp[i];
std::swap(rk, tmp);
rk[sa[0]] = 0;
for (int i = 1; i < n; ++i)
rk[sa[i]] = rk[sa[i - 1]] + (tmp[sa[i - 1]] < tmp[sa[i]] || sa[i - 1] + k == n || tmp[sa[i - 1] + k] < tmp[sa[i] + k]);
k *= 2;
}
for (int i = 0, j = 0; i < n; ++i) {
if (rk[i] == 0) {
j = 0;
} else {
for (j -= j > 0; i + j < n && sa[rk[i] - 1] + j < n && s[i + j] == s[sa[rk[i] - 1] + j]; )
++j;
lc[rk[i] - 1] = j;
}
}
}
};
后缀数组（SA及其应用 新版）
/** 后缀数组（SA及其应用 新版）
* 2023-09-24: https://qoj.ac/submission/187270
* 2024-04-07: https://qoj.ac/submission/381482
**/
struct SA {
int n;
std::vector<int> sa, rk, lc;
SA(std::string s) {
n = s.size();
sa.resize(n);
lc.resize(n - 1);
rk.resize(n);
std::iota(sa.begin(), sa.end(), 0);
std::sort(sa.begin(), sa.end(),
[&](int a, int b) {
return s[a] < s[b];
});
rk[sa[0]] = 0;
for (int i = 1; i < n; i++) {
rk[sa[i]] = rk[sa[i - 1]] + (s[sa[i]] != s[sa[i - 1]]);
}
int k = 1;
std::vector<int> tmp, cnt(n);
tmp.reserve(n);
while (rk[sa[n - 1]] < n - 1) {
tmp.clear();
for (int i = 0; i < k; i++) {
tmp.push_back(n - k + i);
}
for (auto i : sa) {
if (i >= k) {
tmp.push_back(i - k);
}
}
std::fill(cnt.begin(), cnt.end(), 0);
for (int i = 0; i < n; i++) {
cnt[rk[i]]++;
}
for (int i = 1; i < n; i++) {
cnt[i] += cnt[i - 1];
}
for (int i = n - 1; i >= 0; i--) {
sa[--cnt[rk[tmp[i]]]] = tmp[i];
}
std::swap(rk, tmp);
rk[sa[0]] = 0;
for (int i = 1; i < n; i++) {
rk[sa[i]] = rk[sa[i - 1]] + (tmp[sa[i - 1]] < tmp[sa[i]] || sa[i - 1] + k == n || tmp[sa[i - 1] + k] < tmp[sa[i] + k]);
}
k *= 2;
}
for (int i = 0, j = 0; i < n; i++) {
if (rk[i] == 0) {
j = 0;
} else {
for (j -= j > 0; i + j < n && sa[rk[i] - 1] + j < n && s[i + j] == s[sa[rk[i] - 1] + j]; ) {
j++;
}
lc[rk[i] - 1] = j;
}
}
}
};
void solve() {
constexpr int K = 21;
std::vector st(K, std::vector<int>(l - 1));
st[0] = lc;
for (int j = 0; j < K - 1; j++) {
for (int i = 0; i + (2 << j) <= l - 1; i++) {
st[j + 1][i] = std::min(st[j][i], st[j][i + (1 << j)]);
}
}
auto rmq = [&](int l, int r) {
int k = std::__lg(r - l);
return std::min(st[k][l], st[k][r - (1 << k)]);
};
auto lcp = [&](int i, int j) {
if (i == j || i == n || j == n) {
return std::min(n - i, n - j);
}
int a = rk[i];
int b = rk[j];
if (a > b) {
std::swap(a, b);
}
return std::min({n - i, n - j, rmq(a, b)});
};
auto lcs = [&](int i, int j) {
if (i == j || i == 0 || j == 0) {
return std::min(i, j);
}
int a = rk[n + n - i];
int b = rk[n + n - j];
if (a > b) {
std::swap(a, b);
}
return std::min({i, j, rmq(a, b)});
};
}
后缀自动机
后缀自动机（SuffixAutomaton 旧版）
/** 后缀自动机（SuffixAutomaton 旧版）
* 2022-08-17: https://ac.nowcoder.com/acm/contest/view-submission?submissionId=53409023&returnHomeType=1&uid=329687984
**/
struct SuffixAutomaton {
static constexpr int ALPHABET_SIZE = 26, N = 5e5;
struct Node {
int len;
int link;
int next[ALPHABET_SIZE];
Node() : len(0), link(0), next{} {}
} t[2 * N];
int cntNodes;
SuffixAutomaton() {
cntNodes = 1;
std::fill(t[0].next, t[0].next + ALPHABET_SIZE, 1);
t[0].len = -1;
}
int extend(int p, int c) {
if (t[p].next[c]) {
int q = t[p].next[c];
if (t[q].len == t[p].len + 1)
return q;
int r = ++cntNodes;
t[r].len = t[p].len + 1;
t[r].link = t[q].link;
std::copy(t[q].next, t[q].next + ALPHABET_SIZE, t[r].next);
t[q].link = r;
while (t[p].next[c] == q) {
t[p].next[c] = r;
p = t[p].link;
}
return r;
}
int cur = ++cntNodes;
t[cur].len = t[p].len + 1;
while (!t[p].next[c]) {
t[p].next[c] = cur;
p = t[p].link;
}
t[cur].link = extend(p, c);
return cur;
}
};
后缀自动机（SAM 新版）
/** 后缀自动机（SAM 新版）
* 2023-05-27: https://cf.dianhsu.com/gym/104353/submission/207318083
* 2023-09-25: https://qoj.ac/submission/188106
* 2024-04-09: https://qoj.ac/submission/384423 【模板】
* 2024-04-09: https://qoj.ac/submission/384429 【模板】
**/
struct SAM {
static constexpr int ALPHABET_SIZE = 26;
struct Node {
int len;
int link;
std::array<int, ALPHABET_SIZE> next;
Node() : len{}, link{}, next{} {}
};
std::vector<Node> t;
SAM() {
init();
}
void init() {
t.assign(2, Node());
t[0].next.fill(1);
t[0].len = -1;
}
int newNode() {
t.emplace_back();
return t.size() - 1;
}
int extend(int p, int c) {
if (t[p].next[c]) {
int q = t[p].next[c];
if (t[q].len == t[p].len + 1) {
return q;
}
int r = newNode();
t[r].len = t[p].len + 1;
t[r].link = t[q].link;
t[r].next = t[q].next;
t[q].link = r;
while (t[p].next[c] == q) {
t[p].next[c] = r;
p = t[p].link;
}
return r;
}
int cur = newNode();
t[cur].len = t[p].len + 1;
while (!t[p].next[c]) {
t[p].next[c] = cur;
p = t[p].link;
}
t[cur].link = extend(p, c);
return cur;
}
int extend(int p, char c, char offset = 'a') {
return extend(p, c - offset);
}
int next(int p, int x) {
return t[p].next[x];
}
int next(int p, char c, char offset = 'a') {
return next(p, c - 'a');
}
int link(int p) {
return t[p].link;
}
int len(int p) {
return t[p].len;
}
int size() {
return t.size();
}
};
回文自动机（PAM）
/** 回文自动机（PAM）
* 2023-05-19: https://ac.nowcoder.com/acm/contest/view-submission?submissionId=62237107&returnHomeType=1&uid=329687984
* 2024-04-09: https://qoj.ac/submission/384435 【模板】
**/
struct PAM {
static constexpr int ALPHABET_SIZE = 26;
struct Node {
int len;
int link;
int cnt;
std::array<int, ALPHABET_SIZE> next;
Node() : len{}, link{}, cnt{}, next{} {}
};
std::vector<Node> t;
int suff;
std::string s;
PAM() {
init();
}
void init() {
t.assign(2, Node());
t[0].len = -1;
suff = 1;
s.clear();
}
int newNode() {
t.emplace_back();
return t.size() - 1;
}
bool add(char c) {
int pos = s.size();
s += c;
int let = c - 'a';
int cur = suff, curlen = 0;
while (true) {
curlen = t[cur].len;
if (pos - 1 - curlen >= 0 && s[pos - 1 - curlen] == s[pos]) {
break;
}
cur = t[cur].link;
}
if (t[cur].next[let]) {
suff = t[cur].next[let];
return false;
}
int num = newNode();
suff = num;
t[num].len = t[cur].len + 2;
t[cur].next[let] = num;
if (t[num].len == 1) {
t[num].link = 1;
t[num].cnt = 1;
return true;
}
while (true) {
cur = t[cur].link;
curlen = t[cur].len;
if (pos - 1 - curlen >= 0 && s[pos - 1 - curlen] == s[pos]) {
t[num].link = t[cur].next[let];
break;
}
}
t[num].cnt = 1 + t[t[num].link].cnt;
return true;
}
int next(int p, int x) {
return t[p].next[x];
}
int link(int p) {
return t[p].link;
}
int len(int p) {
return t[p].len;
}
int size() {
return t.size();
}
};
AC自动机
AC自动机（AC 旧版）
/** AC自动机（AC 旧版）
* 2021-07-07: https://codeforces.com/contest/710/submission/121661266
**/
constexpr int N = 3e5 + 30, A = 26;
struct Node {
int fail;
int sum;
int next[A];
Node() : fail(-1), sum(0) {
std::memset(next, -1, sizeof(next));
}
} node[N];
int cnt = 0;
int bin[N];
int nBin = 0;
int newNode() {
int p = nBin > 0 ? bin[--nBin] : cnt++;
node[p] = Node();
return p;
}
struct AC {
std::vector<int> x;
AC(AC &&a) : x(std::move(a.x)) {}
AC(std::vector<std::string> s, std::vector<int> w) {
x = {newNode(), newNode()};
std::fill(node[x[0]].next, node[x[0]].next + A, x[1]);
node[x[1]].fail = x[0];
for (int i = 0; i < int(s.size()); i++) {
int p = x[1];
for (int j = 0; j < int(s[i].length()); j++) {
int c = s[i][j] - 'a';
if (node[p].next[c] == -1) {
int u = newNode();
x.push_back(u);
node[p].next[c] = u;
}
p = node[p].next[c];
}
node[p].sum += w[i];
}
std::queue<int> que;
que.push(x[1]);
while (!que.empty()) {
int u = que.front();
que.pop();
node[u].sum += node[node[u].fail].sum;
for (int c = 0; c < A; c++) {
if (node[u].next[c] == -1) {
node[u].next[c] = node[node[u].fail].next[c];
} else {
node[node[u].next[c]].fail = node[node[u].fail].next[c];
que.push(node[u].next[c]);
}
}
}
}
~AC() {
for (auto p : x) {
bin[nBin++] = p;
}
}
i64 query(const std::string &s) const {
i64 ans = 0;
int p = x[1];
for (int i = 0; i < int(s.length()); i++) {
int c = s[i] - 'a';
p = node[p].next[c];
ans += node[p].sum;
}
return ans;
}
};
AC自动机（AhoCorasick, with vector 新版）
/** AC自动机（AhoCorasick, with vector 新版）
* 2023-04-07: https://codeforces.com/contest/1801/submission/201155712
**/
struct AhoCorasick {
static constexpr int ALPHABET = 26;
struct Node {
int len;
int link;
std::array<int, ALPHABET> next;
Node() : link{}, next{} {}
};
std::vector<Node> t;
AhoCorasick() {
init();
}
void init() {
t.assign(2, Node());
t[0].next.fill(1);
t[0].len = -1;
}
int newNode() {
t.emplace_back();
return t.size() - 1;
}
int add(const std::vector<int> &a) {
int p = 1;
for (auto x : a) {
if (t[p].next[x] == 0) {
t[p].next[x] = newNode();
t[t[p].next[x]].len = t[p].len + 1;
}
p = t[p].next[x];
}
return p;
}
int add(const std::string &a, char offset = 'a') {
std::vector<int> b(a.size());
for (int i = 0; i < a.size(); i++) {
b[i] = a[i] - offset;
}
return add(b);
}
void work() {
std::queue<int> q;
q.push(1);
while (!q.empty()) {
int x = q.front();
q.pop();
for (int i = 0; i < ALPHABET; i++) {
if (t[x].next[i] == 0) {
t[x].next[i] = t[t[x].link].next[i];
} else {
t[t[x].next[i]].link = t[t[x].link].next[i];
q.push(t[x].next[i]);
}
}
}
}
int next(int p, int x) {
return t[p].next[x];
}
int next(int p, char c, char offset = 'a') {
return next(p, c - 'a');
}
int link(int p) {
return t[p].link;
}
int len(int p) {
return t[p].len;
}
int size() {
return t.size();
}
};
AC自动机（AhoCorasick, with string 新版）
/** AC自动机（AhoCorasick, with string 新版）
* 2024-04-09: https://www.luogu.com.cn/record/155114676 【模板】
**/
struct AhoCorasick {
static constexpr int ALPHABET = 26;
struct Node {
int len;
int link;
std::array<int, ALPHABET> next;
Node() : len{0}, link{0}, next{} {}
};
std::vector<Node> t;
AhoCorasick() {
init();
}
void init() {
t.assign(2, Node());
t[0].next.fill(1);
t[0].len = -1;
}
int newNode() {
t.emplace_back();
return t.size() - 1;
}
int add(const std::string &a) {
int p = 1;
for (auto c : a) {
int x = c - 'a';
if (t[p].next[x] == 0) {
t[p].next[x] = newNode();
t[t[p].next[x]].len = t[p].len + 1;
}
p = t[p].next[x];
}
return p;
}
void work() {
std::queue<int> q;
q.push(1);
while (!q.empty()) {
int x = q.front();
q.pop();
for (int i = 0; i < ALPHABET; i++) {
if (t[x].next[i] == 0) {
t[x].next[i] = t[t[x].link].next[i];
} else {
t[t[x].next[i]].link = t[t[x].link].next[i];
q.push(t[x].next[i]);
}
}
}
}
int next(int p, int x) {
return t[p].next[x];
}
int link(int p) {
return t[p].link;
}
int len(int p) {
return t[p].len;
}
int size() {
return t.size();
}
};
字符串哈希（随机底模例题）
/** 字符串哈希（随机底模例题）
* 2022-06-09: https://codeforces.com/contest/1598/submission/160006998
**/
#include <bits/stdc++.h>
using i64 = long long;
bool isprime(int n) {
if (n <= 1) {
return false;
}
for (int i = 2; i * i <= n; i++) {
if (n % i == 0) {
return false;
}
}
return true;
}
int findPrime(int n) {
while (!isprime(n)) {
n++;
}
return n;
}
using Hash = std::array<int, 2>;
int main() {
std::ios::sync_with_stdio(false);
std::cin.tie(nullptr);
std::mt19937 rng(std::chrono::steady_clock::now().time_since_epoch().count());
const int P = findPrime(rng() % 900000000 + 100000000);
std::string s, x;
std::cin >> s >> x;
int n = s.length();
int m = x.length();
std::vector<int> h(n + 1), p(n + 1);
for (int i = 0; i < n; i++) {
h[i + 1] = (10LL * h[i] + s[i] - '0') % P;
}
p[0] = 1;
for (int i = 0; i < n; i++) {
p[i + 1] = 10LL * p[i] % P;
}
auto get = [&](int l, int r) {
return (h[r] + 1LL * (P - h[l]) * p[r - l]) % P;
};
int px = 0;
for (auto c : x) {
px = (10LL * px + c - '0') % P;
}
for (int i = 0; i <= n - 2 * (m - 1); i++) {
if ((get(i, i + m - 1) + get(i + m - 1, i + 2 * m - 2)) % P == px) {
std::cout << i + 1 << " " << i + m - 1 << "\n";
std::cout << i + m << " " << i + 2 * m - 2 << "\n";
return 0;
}
}
std::vector<int> z(m + 1), f(n + 1);
z[0] = m;
for (int i = 1, j = -1; i < m; i++) {
if (j != -1) {
z[i] = std::max(0, std::min(j + z[j] - i, z[i - j]));
}
while (z[i] + i < m && x[z[i]] == x[z[i] + i]) {
z[i]++;
}
if (j == -1 || i + z[i] > j + z[j]) {
j = i;
}
}
for (int i = 0, j = -1; i < n; i++) {
if (j != -1) {
f[i] = std::max(0, std::min(j + f[j] - i, z[i - j]));
}
while (f[i] + i < n && f[i] < m && x[f[i]] == s[f[i] + i]) {
f[i]++;
}
if (j == -1 || i + f[i] > j + f[j]) {
j = i;
}
}
for (int i = 0; i + m <= n; i++) {
int l = std::min(m, f[i]);
for (auto j : { m - l, m - l - 1 }) {
if (j <= 0) {
continue;
}
if (j <= i && (get(i - j, i) + get(i, i + m)) % P == px) {
std::cout << i - j + 1 << " " << i << "\n";
std::cout << i + 1 << " " << i + m << "\n";
return 0;
}
if (i + m + j <= n && (get(i, i + m) + get(i + m, i + m + j)) % P == px) {
std::cout << i + 1 << " " << i + m << "\n";
std::cout << i + m + 1 << " " << i + m + j << "\n";
return 0;
}
}
}
return 0;
}
最长公共前缀 LCP（例题）
/** 最长公共前缀 LCP（例题）
* 2024-03-02: https://qoj.ac/submission/343378
**/
constexpr int L = 2E6 + 10;
int len[L];
int lnk[L];
int nxt[L][26];
int f[L];
int tot = 1;
std::vector<int> adj[L];
int extend(int p, int c) {
if (nxt[p][c]) {
int q = nxt[p][c];
if (len[q] == len[p] + 1) {
return q;
}
int r = ++tot;
len[r] = len[p] + 1;
lnk[r] = lnk[q];
std::copy(nxt[q], nxt[q] + 26, nxt[r]);
lnk[q] = r;
while (nxt[p][c] == q) {
nxt[p][c] = r;
p = lnk[p];
}
return r;
}
int cur = ++tot;
len[cur] = len[p] + 1;
while (!nxt[p][c]) {
nxt[p][c] = cur;
p = lnk[p];
}
lnk[cur] = extend(p, c);
return cur;
}
int main() {
std::ios::sync_with_stdio(false);
std::cin.tie(nullptr);
std::fill(nxt[0], nxt[0] + 26, 1);
len[0] = -1;
int N;
std::cin >> N;
std::vector<std::string> S(N);
for (int i = 0; i < N; i++) {
std::cin >> S[i];
int p = 1;
for (auto c : S[i]) {
p = extend(p, c - 'a');
if (f[p] != -1) {
if (f[p] == 0) {
f[p] = i + 1;
} else if (f[p] != i + 1) {
f[p] = -1;
}
}
}
}
for (int i = 1; i <= tot; i++) {
adj[lnk[i]].push_back(i);
}
}
字典树 Trie
/** 字典树 Trie
* 2023-09-26: https://qoj.ac/submission/188957
**/
constexpr i64 inf = 1E18;
constexpr int N = 1E6 + 10;
int trie[N][26];
int tot;
int newNode() {
tot++;
std::fill(trie[tot], trie[tot] + 26, 0);
val[tot] = inf;
return tot;
}
void solve() {
//* init
tot = 0;
newNode();
//* insert
for (int i = 0; i < N; i++) {
int p = 1;
int l = S[i].size();
for (int j = 0; j < l; j++) {
int x = S[i][j] - 'a';
if (!trie[p][x]) {
trie[p][x] = newNode();
}
p = trie[p][x];
//* 处理
//* val[p] = std::min(val[p], l + K + f[(K - (l - j - 1) % K) % K]);
}
}
//* query
for (int i = 0; i < L; i++) {
int p = 1;
for (int j = i; j < L; j++) {
int x = T[j] - 'a';
p = trie[p][x];
if (!p) {
continue;
}
//* 处理
//* dp[j + 1] = std::min(dp[j + 1], dp[i] + val[p]);
}
}
}
/** 字典树 Trie
* 2024-06-18: https://cf.dianhsu.com/gym/105222/submission/266217560?version=1.5
**/
int tot;
int trie[N][2];
int f[N];
int newNode() {
int x = ++tot;
trie[x][0] = trie[x][1] = 0;
f[x] = inf;
return x;
}
void add(int x, int i) {
int p = 1;
for (int j = 29; j >= 0; j--) {
int &q = trie[p][x >> j & 1];
if (q == 0) {
q = newNode();
}
p = q;
f[p] = std::min(f[p], i);
}
}
int query(int a, int b) {
int ans1 = inf, ans2 = inf;
int p = 1;
for (int i = 29; i >= 0; i--) {
int d = a >> i & 1;
int e = b >> i & 1;
if (e) {
ans1 = std::min(ans1, f[trie[p][d]]);
} else {
ans2 = std::min(ans2, f[trie[p][d ^ 1]]);
}
p = trie[p][e ^ d];
}
ans1 = std::min(ans1, f[p]);
ans2 = std::min(ans2, f[p]);
if (ans1 == inf || ans2 == inf) {
return -1;
}
return std::max({1, ans1, ans2});
}
/** 字典树 Trie
* 2024-06-03: https://codeforces.com/contest/1980/submission/263960334
**/
int trie[N][2];
int cnt[N][2];
int tot = 0;
int newNode() {
int x = ++tot;
trie[x][0] = trie[x][1] = 0;
cnt[x][0] = cnt[x][1] = 0;
return x;
}
void add(int x, int d, int t = 1) {
int p = 1;
cnt[p][d] += t;
for (int i = 29; i >= 0; i--) {
int u = x >> i & 1;
if (!trie[p][u]) {
trie[p][u] = newNode();
}
p = trie[p][u];
cnt[p][d] += t;
}
}
int query(int x, int d) {
int p = 1;
if (!cnt[p][d]) {
return 0;
}
int ans = 0;
for (int i = 29; i >= 0; i--) {
int u = x >> i & 1;
if (cnt[trie[p][u ^ 1]][d]) {
ans |= 1 << i;
p = trie[p][u ^ 1];
} else {
p = trie[p][u];
}
}
return ans;
}
/** 字典树 Trie
* 2024-06-18: https://cf.dianhsu.com/gym/105222/submission/266217560
* 2024-06-04: https://codeforces.com/contest/1980/submission/263960334
**/
constexpr int N = 1E7;
constexpr int inf = 1E9;
int tot;
int trie[N][2];
int f[N];
int newNode() {
int x = ++tot;
trie[x][0] = trie[x][1] = 0;
f[x] = inf;
return x;
}
void add(int x, int i) {
int p = 1;
for (int j = 29; j >= 0; j--) {
int &q = trie[p][x >> j & 1];
if (q == 0) {
q = newNode();
}
p = q;
f[p] = std::min(f[p], i);
}
}
int query(int a, int b) {
int ans1 = inf, ans2 = inf;
int p = 1;
for (int i = 29; i >= 0; i--) {
int d = a >> i & 1;
int e = b >> i & 1;
if (e) {
ans1 = std::min(ans1, f[trie[p][d]]);
} else {
ans2 = std::min(ans2, f[trie[p][d ^ 1]]);
}
p = trie[p][e ^ d];
}
ans1 = std::min(ans1, f[p]);
ans2 = std::min(ans2, f[p]);
if (ans1 == inf || ans2 == inf) {
return -1;
}
return std::max({1, ans1, ans2});
}
前缀函数（KMP）
/** 前缀函数（KMP）
* 2023-11-17: https://qoj.ac/submission/253754
* 2024-04-09: https://qoj.ac/submission/384408 【模板】
**/
std::vector<int> kmp(std::string s) {
int n = s.size();
std::vector<int> f(n + 1);
for (int i = 1, j = 0; i < n; i++) {
while (j && s[i] != s[j]) {
j = f[j];
}
j += (s[i] == s[j]);
f[i + 1] = j;
}
return f;
}
