OI常见模板汇总
单源最短路：
堆优化的Dijkstra：
#include <bits/stdc++.h> using namespace std; #define rep(i, a, b) for (register int i = (a); i <= (b); i++) const int inf = 0x3f3f3f3f, maxn = 1e5 + 5; int n, m, S, num_edge = 0; int dis[maxn], vis[maxn], head[maxn]; priority_queue< pair<int, int> > q; struct node { int to, nxt, dis; }edge[maxn << 1]; void origin() { memset(dis, inf, sizeof(dis)); memset(head, -1, sizeof(head)); } int read() { int x = 0, flag = 0; char ch = ' '; while (ch != '-' && (ch < '0' || ch > '9')) ch = getchar(); if (ch == '-') { flag = 1; ch = getchar(); } while (ch >= '0' && ch <= '9') { x = (x << 1) + (x << 3) + ch - '0'; ch = getchar(); } return flag ? -x : x; } void addedge(int from, int to, int dis) { edge[++num_edge].nxt = head[from]; edge[num_edge].to = to; edge[num_edge].dis = dis; head[from] = num_edge; } void write(int x) { if (x < 0) { putchar('-'); x = -x; } if (x > 9) write(x / 10); putchar(x % 10 + '0'); } void dijkstra(int S) { dis[S] = 0; q.push(make_pair(0, S)); while (!q.empty()) { int u = q.top().second; q.pop(); if (vis[u]) continue; vis[u] = 1; for (register int i = head[u]; ~i; i = edge[i].nxt) { int v = edge[i].to; if (dis[v] > dis[u] + edge[i].dis) { dis[v] = dis[u] + edge[i].dis; q.push(make_pair(-dis[v], v)); } } } } int main() { origin(); n = read(), m = read(), S = read(); rep(i, 1, m) { int u, v, w; u = read(), v = read(), w = read(); addedge(u, v, w); } dijkstra(S); rep(i, 1, n) { write(dis[i]); printf(" "); } }
队列优化的Bellman-Ford：
#include <bits/stdc++.h> using namespace std; #define rep(i, a, b) for (register int i = (a); i <= (b); i++) const int inf = 0x3f3f3f3f, maxn = 1e5 + 5; int n, m, S, num_edge = 0; int dis[maxn], vis[maxn], head[maxn]; queue<int> q; struct node { int to, nxt, dis; }edge[maxn << 1]; void origin() { memset(dis, inf, sizeof(dis)); memset(head, -1, sizeof(head)); } int read() { int x = 0, flag = 0; char ch = ' '; while (ch != '-' && (ch < '0' || ch > '9')) ch = getchar(); if (ch == '-') { flag = 1; ch = getchar(); } while (ch >= '0' && ch <= '9') { x = (x << 1) + (x << 3) + ch - '0'; ch = getchar(); } return flag ? -x : x; } void addedge(int from, int to, int dis) { edge[++num_edge].nxt = head[from]; edge[num_edge].to = to; edge[num_edge].dis = dis; head[from] = num_edge; } void Bellman_Ford(int S) { dis[S] = 0, vis[S] = 1; q.push(S); while (!q.empty()) { int u = q.front(); q.pop(); vis[u] = 0; for (register int i = head[u]; ~i; i = edge[i].nxt) { int v = edge[i].to; if (dis[v] > dis[u] + edge[i].dis) { dis[v] = dis[u] + edge[i].dis; if (!vis[v]) { q.push(v); vis[v] = 1; } } } } } void write(int x) { if (x < 0) { putchar('-'); x = -x; } if (x > 9) write(x / 10); putchar(x % 10 + '0'); } int main() { origin(); n = read(), m = read(), S = read(); rep(i, 1, m) { int u, v, w; u = read(), v = read(), w = read(); addedge(u, v, w); } Bellman_Ford(S); rep(i, 1, n) { write(dis[i]); printf(" "); } return 0; }
任意两点间最短路径（Floyd）：
#include <bits/stdc++.h> using namespace std; #define rep(i, a, b) for (register int i = (a); i <= (b); i++) const int inf = 0x3f3f3f3f, maxn = 1e3 + 5; int n, m; int dis[maxn][maxn]; int MIN(int a, int b) {return a < b ? a : b;} void origin() {memset(dis, inf, sizeof(dis));} int read() { int x = 0, flag = 0; char ch = ' '; while (ch != '-' && (ch < '0' || ch > '9')) ch = getchar(); if (ch == '-') { flag = 1; ch = getchar(); } while (ch >= '0' && ch <= '9') { x = (x << 1) + (x << 3) + ch - '0'; ch = getchar(); } return flag ? -x : x; } void write(int x) { if (x < 0) { putchar('-'); x = -x; } if (x > 9) write(x / 10); putchar(x % 10 + '0'); } int main() { origin(); n = read(), m = read(); rep(i, 1, m) { int u, v, w; u = read(), v = read(), w = read(); dis[u][v] = MIN(dis[u][v], w); } rep(k, 1, n) rep(i, 1, n) rep(j, 1, n) dis[i][j] = MIN(dis[i][j], dis[i][k] + dis[k][j]); rep(i, 1, n) rep(j, 1, n) { write(dis[i][j]); printf(" "); } return 0; }
最小生成树
Kruskal：
#include <bits/stdc++.h> using namespace std; #define rep(i, a, b) for (register int i = (a); i <= (b); i++) const int maxn = 5e3 + 5, maxm = 2e5 + 5; int n, m, ans = 0; int fa[maxn]; struct rec{ int to, dis, from; }edge[maxm]; bool operator <(const rec &a, const rec &b) { return a.dis < b.dis; } int read() { int x = 0, flag = 0; char ch = ' '; while (ch != '-' && (ch < '0' || ch > '9')) ch = getchar(); if (ch == '-') { flag = 1; ch = getchar(); } while (ch >= '0' && ch <= '9') { x = (x << 1) + (x << 3) + ch - '0'; ch = getchar(); } return flag ? -x : x; } int find(int x) {return fa[x] == x ? x : fa[x] = find(fa[x]);} void write(int x) { if (x < 0) { putchar('-'); x = -x; } if (x > 9) write(x / 10); putchar(x % 10 + '0'); } int main() { n = read(), m = read(); rep(i, 1, m) edge[i].from = read(), edge[i].to = read(), edge[i].dis = read(); sort(edge + 1, edge + m + 1); rep(i, 1, n) fa[i] = i; rep(i, 1, m) { int x = find(edge[i].from), y = find(edge[i].to); if (x == y) continue; fa[x] = y; ans += edge[i].dis; } write(ans); return 0; }
堆优化的Prim ：
#include <bits/stdc++.h> using namespace std; #define rep(i, a, b) for (register int i = (a); i <= (b); i++) const int inf = 0x3f3f3f3f, maxn = 5e3 + 5, maxm = 4e5 + 5; int n, m, ans = 0, num_edge = 0; int dis[maxn], vis[maxn], head[maxn]; priority_queue< pair<int, int> > q; struct node { int to, nxt, dis; }edge[maxm]; void origin() { memset(dis, inf, sizeof(dis)); memset(head, -1, sizeof(head)); } int read() { int x = 0, flag = 0; char ch = ' '; while (ch != '-' && (ch < '0' || ch > '9')) ch = getchar(); if (ch == '-') { flag = 1; ch = getchar(); } while (ch >= '0' && ch <= '9') { x = (x << 1) + (x << 3) + ch - '0'; ch = getchar(); } return flag ? -x : x; } void addedge(int from, int to, int dis) { edge[++num_edge].nxt = head[from]; edge[num_edge].to = to; edge[num_edge].dis = dis; head[from] = num_edge; } void prim() { dis[1] = 0; q.push(make_pair(0, 1)); while (!q.empty()) { int u = q.top().second; q.pop(); if (vis[u]) continue; vis[u] = 1; for (register int i = head[u]; ~i; i = edge[i].nxt) { int v = edge[i].to; if (!vis[v] && dis[v] > edge[i].dis) { dis[v] = edge[i].dis; q.push(make_pair(-dis[v], v)); } } } } void write(int x) { if (x < 0) { putchar('-'); x = -x; } if (x > 9) write(x / 10); putchar(x % 10 + '0'); } int main() { origin(); n = read(), m = read(); rep(i, 1, m) { int u, v, w; u = read(), v = read(), w = read(); addedge(u, v, w); addedge(v, u, w); } prim(); rep(i, 2, n) ans += dis[i]; write(ans); return 0; }
最近公共祖先（LCA）：
树上倍增法：
#include <bits/stdc++.h> using namespace std; #define rep(i, a, b) for (register int i = (a); i <= (b); i++) #define per(i, a, b) for (register int i = (a); i >= (b); i--) const int maxn = 5e5 + 5; int n, m, t, S, num_edge = 0; int dep[maxn], head[maxn], fa[maxn][20]; queue<int> q; struct node { int to, nxt; }edge[maxn << 1]; void origin() {memset(head, -1, sizeof(head));} int read() { int x = 0, flag = 0; char ch = ' '; while (ch != '-' && (ch < '0' || ch > '9')) ch = getchar(); if (ch == '-') { flag = 1; ch = getchar(); } while (ch >= '0' && ch <= '9') { x = (x << 1) + (x << 3) + ch - '0'; ch = getchar(); } return flag ? -x : x; } void addedge(int from, int to) { edge[++num_edge].nxt = head[from]; edge[num_edge].to = to; head[from] = num_edge; } void bfs(int S) { q.push(S); dep[S] = 1; while (!q.empty()) { int u = q.front(); q.pop(); for (register int i = head[u]; ~i; i = edge[i].nxt) { int v = edge[i].to; if (dep[v]) continue; dep[v] = dep[u] + 1; fa[v][0] = u; rep(j, 1, t) fa[v][j] = fa[fa[v][j - 1]][j - 1]; q.push(v); } } } int lca(int u, int v) { if (dep[u] > dep[v]) u ^= v ^= u ^= v; per(i, t, 0) if (dep[fa[v][i]] >= dep[u]) v = fa[v][i]; if (u == v) return u; per(i, t, 0) { if (fa[u][i] != fa[v][i]) { u = fa[u][i]; v = fa[v][i]; } } return fa[u][0]; } void write(int x) { if (x < 0) { putchar('-'); x = -x; } if (x > 9) write(x / 10); putchar(x % 10 + '0'); } int main() { origin(); n = read(), m = read(), S = read(); t = (int)(log(n) / log(2)) + 1; rep(i, 1, n - 1) { int u, v; u = read(), v = read(); addedge(u, v); addedge(v, u); } bfs(S); rep(i, 1, m) { int u, v; u = read(), v = read(); write(lca(u, v)); printf("\n"); } return 0; }
高精度运算：
#include <bits/stdc++.h> using namespace std; #define rep(i, a, b) for (register int i = a; i <= b; i++) #define per(i, a, b) for (register int i = a; i >= b; i--) const int power = 4, base = 1e4, maxn = 1e4 + 5; char a[maxn], b[maxn]; struct num { int a[maxn]; num() {memset(a, 0, sizeof(a));} int& operator [](int x) {return a[x];} num(char *s) { memset(a, 0, sizeof(a)); int len = strlen(s); a[0] = (len + power - 1) / power; for (register int w, i = 0, t = 0; i < len; w = (w << 1) + (w << 3), i++) { if (!(i % power)) { w = 1; t++; } a[t] += w * (s[i] - '0'); } } void add(int k) {if (k || a[0]) a[++a[0]] = k;} void rever() {reverse(a + 1, a + a[0] + 1);} void write() { printf("%d", a[a[0]]); per(i, a[0] - 1, 1) printf("%0*d", power, a[i]); } }p, q, ans; int operator <(num &p, num &q) { if (p[0] < q[0]) return 1; if (p[0] > p[0]) return 0; for (int i = p[0]; i > 0; i--) if (p[i] != q[i]) return p[i] < q[i]; return 0; } num operator +(num &p, num &q) { num a; a[0] = max(p[0], q[0]); rep (i, 1, a[0]) { a[i] += p[i] + q[i]; a[i + 1] = a[i] / base; a[i] %= base; } while (a[a[0] + 1]) a[0]++; return a; } num operator -(num &p, num &q) { num a = p; rep(i, 1, a[0]) { a[i] -= q[i]; if (a[i] < 0) { a[i] += base; a[i + 1]--; } } while (a[0] && !a[a[0]]) a[0]--; return a; } num operator *(num &p, num &q) { num a; a[0] = p[0] + q[0] - 1; rep(i, 1, p[0]) rep(j, 1, q[0]) { a[i + j - 1] += p[i] * q[j]; a[i + j] += a[i + j - 1] / base; a[i + j - 1] %= base; } if (a[a[0] + 1]) a[0]++; return a; } num operator /(num &p, num &q) { num a, b; per(i, p[0], 1) { b.add(p[i]); b.rever(); while (!(b < q)) { b = b - q; a[i]++; } b.rever(); } a[0] = p[0]; while (a[0] && !a[a[0]]) a[0]--; return a; } int main() { scanf("%s", a), scanf("%s", b); reverse(a, a + strlen(a)); reverse(b, b + strlen(b)); p = num(a), q = num(b); ans = p + q; ans.write(); if (p < q) { putchar('-'); ans = q - p; ans.write(); } else { ans = p - q; ans.write(); } ans = p * q; ans.write(); ans = p / q; ans.write(); return 0; }
线段树：
#include <bits/stdc++.h> using namespace std; #define ls rt << 1 #define rs rt << 1 | 1 #define rep(i, a, b) for (register int i = (a); i <= (b); i++) const int maxn = 1e5 + 5; int n, m; int a[maxn]; struct segment_tree { int l, r, sum, lazy; #define l(x) T[x].l #define r(x) T[x].r #define sum(x) T[x].sum #define lazy(x) T[x].lazy #define length(x) (r(x) - l(x) + 1) }T[maxn << 2]; int read() { int x = 0, flag = 0; char ch = ' '; while (ch != '-' && (ch < '0' || ch > '9')) ch = getchar(); if (ch == '-') { flag = 1; ch = getchar(); } while (ch >= '0' && ch <= '9') { x = (x << 1) + (x << 3) + ch - '0'; ch = getchar(); } return flag ? -x : x; } void build(int rt, int l, int r) { l(rt) = l, r(rt) = r; if (l == r) { sum(rt) = a[l]; return; } int mid = (l + r) >> 1; build(ls, l, mid); build(rs, mid + 1, r); sum(rt) = sum(ls) + sum(rs); } void spread(int rt) { if (lazy(rt)) { sum(ls) += lazy(rt) * length(ls); sum(rs) += lazy(rt) * length(rs); lazy(ls) += lazy(rt); lazy(rs) += lazy(rt); lazy(rt) = 0; } } void change(int rt, int l ,int r, int k) { if (l <= l(rt) && r(rt) <= r) { sum(rt) += k * length(rt); lazy(rt) += k; return; } int mid = (l(rt) + r(rt)) >> 1; if (l <= mid) change(ls, l, r, k); if (r > mid) change(rs, l, r, k); spread(rt); sum(rt) = sum(ls) + sum(rs); } int query(int rt, int l, int r) { if (l <= l(rt) && r(rt) <= r) return sum(rt); spread(rt); int mid = (l(rt) + r(rt)) >> 1; int ans = 0; if (l <= mid) ans += query(ls, l, r); if (r > mid) ans += query(rs, l, r); return ans; } void write(int x) { if (x < 0) { putchar('-'); x = -x; } if (x > 9) write(x / 10); putchar(x % 10 + '0'); } int main() { n = read(), m = read(); rep(i, 1, n) a[i] = read(); build(1, 1, n); while (m--) { int opt, x, y, k; opt = read(), x = read(), y = read(); if (opt == 1) { k = read(); change(1, x, y, k); } else { write(query(1, x, y)); printf("\n"); } } return 0; }
区间动规：
rep(len, 2, n) rep(l, 1, n - len + 1) { int r = l + len - 1 rep(k, l, r - 1) dp[l][r] = min(dp[l][r], dp[l][k] + dp[k + 1][r] + val[l][r]); } write(dp[1][n]);
数位动规：
顺序版：
//大部分时候DP数组并不需要开这么多维. void origin() {memset(dp, -1, sizeof(dp));} int dfs(int pos, int pre, int limit, int lead, int sum, ???) { int ans = 0; if (pos > len) return sum; if (!limit && !lead && dp[pos][pre][limit][lead][sum]??? != -1) return dp[pos][pre][limit][lead][sum]???; int res = limit ? num[len - pos + 1] : 9; rep(i, 0, res) { if (!i && lead) ans += dfs(pos + 1, 0, (i == res) && limit, 1, ???); else if (i && lead) ans += dfs(pos + 1, i, (i == res) && limit, 0, ???); else if(/*根据题意而设的判断*/) ans += dfs(pos + 1, ???, (i == res) && limit, ???); } if (!limit && !lead) dp[pos][pre][limit][lead][sum]??? = ans; return ans; } int work(int x) { origin(); len = 0; while(x) { num[++len] = x % 10; x /= 10; } return dfs(1, 0, 1, 1, 0, ???); } int main() { l = read(), r = read(); write(work(r) - work(l - 1)); return 0; }
逆序版：
//大部分时候DP数组并不需要开这么多维. void origin() {memset(dp, -1, sizeof(dp));} int dfs(int pos, int pre, int limit, int lead, int sum, ???) { int ans = 0; if (!pos) return sum; if (!limit && !lead && dp[pos][pre][limit][lead][sum]??? != -1) return dp[pos][pre][limit][lead][sum]???; int res = limit ? num[pos] : 9; rep(i, 0, res) { if (!i && lead) ans += dfs(pos - 1, 0, (i == res) && limit, 1, ???); else if (i && lead) ans += dfs(pos - 1, i, (i == res) && limit, 0, ???); else if(/*根据题意而设的判断*/) ans += dfs(pos - 1, ???, (i == res) && limit, ???); } if (!limit && !lead) dp[pos][pre][limit][lead][sum]??? = ans; return ans; } int work(int x) { origin(); len = 0; while(x) { num[++len] = x % 10; x /= 10; } return dfs(len, 0, 1, 1, 0, ???); } int main() { l = read(), r = read(); write(work(r) - work(l - 1)); return 0; }
网络最大流：
#include <bits/stdc++.h> using namespace std; #define rep(i, a, b) for (register int i = (a); i <= (b); i++) const int inf = 0x3f3f3f3f, maxn = 1e4 + 5, maxm = 1e6 + 5; int n, m, S, T, ans = 0, num_edge = -1; int cur[maxn], dep[maxn], head[maxn]; queue<int> q; struct node { int to, dis, nxt; }edge[maxm]; void origin() {memset(head, -1, sizeof(head));} int read() { int x = 0, flag = 0; char ch = ' '; while (ch != '-' && (ch < '0' || ch > '9')) ch = getchar(); if (ch == '-') { flag = 1; ch = getchar(); } while (ch >= '0' && ch <= '9') { x = (x << 1) + (x << 3) + ch - '0'; ch = getchar(); } return flag ? -x : x; } void addedge(int from, int to, int dis) { edge[++num_edge].nxt = head[from]; edge[num_edge].to = to; edge[num_edge].dis = dis; head[from] = num_edge; } int bfs(int S, int T) { memset(dep, 0, sizeof(dep)); while (!q.empty()) q.pop(); memcpy(cur, head, sizeof(cur)); dep[S] = 1; q.push(S); while (!q.empty()) { int u = q.front(); q.pop(); for (int i = head[u]; ~i; i = edge[i].nxt) { int v = edge[i].to; if (!dep[v] && edge[i].dis) { dep[v] = dep[u] + 1; q.push(v); } } } if (dep[T]) return 1; return 0; } int dfs(int u, int flow) { if (u == T || !flow) return flow; int d, used = 0; for (int i = cur[u]; ~i; i = edge[i].nxt) { cur[u] = i; int v = edge[i].to; if (dep[v] == dep[u] + 1 && (d = dfs(v, min(flow, edge[i].dis)))) { used += d; flow -= d; edge[i].dis -= d; edge[i ^ 1].dis += d; if (!flow) break; } } if (!used) dep[u] = -2; return used; } int dinic() { int ans = 0; while (bfs(S, T)) ans += dfs(S, inf); return ans; } void write(int x) { if (x < 0) { putchar('-'); x = -x; } if (x > 9) write(x / 10); putchar(x % 10 + '0'); } int main() { origin(); n = read(), m = read(), S = read(), T = read(); rep(i, 1, m) { int u, v, w; u = read(), v = read(), w = read(); addedge(u, v, w); addedge(v, u, 0); } ans = dinic(); write(ans); return 0; }
二叉搜索树 & 平衡树：
splay：
#include <bits/stdc++.h> using namespace std; const int maxn = 1e5 + 5; int n, rt, tot = 0; int fa[maxn], cnt[maxn], val[maxn], size[maxn], ch[maxn][3]; int get(int x) {return x == ch[fa[x]][1];} void maintain(int x) {size[x] = size[ch[x][0]] + size[ch[x][1]] + cnt[x];} void clear(int x) {fa[x] = cnt[x] = val[x] = size[x] = ch[x][0] = ch[x][1] = 0;} int pre() { int cnr = ch[rt][0]; if (!cnr) return -1; while (ch[cnr][1]) cnr = ch[cnr][1]; return cnr; } int nxt() { int cnr = ch[rt][1]; if (!cnr) return -1; while (ch[cnr][0]) cnr = ch[cnr][0]; return cnr; } void rotate(int x) { int y = fa[x], z = fa[y], chk = get(x); ch[y][chk] = ch[x][chk ^ 1]; fa[ch[x][chk ^ 1]] = y; ch[x][chk ^ 1] = y; fa[y] = x; fa[x] = z; if (z) ch[z][y == ch[z][1]] = x; maintain(y); maintain(x); } void splay(int x) { for (register int f = fa[x]; f = fa[x], f; rotate(x)) if (fa[f]) rotate(get(x) == get(f) ? f : x); rt = x; } int kth(int k) { int cnr = rt; while (1) { if (ch[cnr][0] && k <= size[ch[cnr][0]]) cnr = ch[cnr][0]; else { k -= cnt[cnr] + size[ch[cnr][0]]; if (k <= 0) return val[cnr]; cnr = ch[cnr][1]; } } } int rk(int k) { int res = 0, cnr = rt; while (1) { if (k < val[cnr]) cnr = ch[cnr][0]; else { res += size[ch[cnr][0]]; if (k == val[cnr]) { splay(cnr); return res + 1; } res += cnt[cnr]; cnr = ch[cnr][1]; } } } void insert(int k) { if (!rt) { val[++tot] = k; cnt[tot]++; rt = tot; maintain(rt); return; } int f = 0, cnr = rt; while (1) { if (k == val[cnr]) { cnt[cnr]++; maintain(cnr); maintain(f); splay(cnr); break; } f = cnr; cnr = ch[cnr][val[cnr] < k]; if (!cnr) { val[++tot] = k; cnt[tot]++; fa[tot] = f; ch[f][val[f] < k] = tot; maintain(tot); maintain(f); splay(tot); break; } } } void erase(int k) { rk(k); if (cnt[rt] > 1) { cnt[rt]--; maintain(rt); return; } if (!ch[rt][0] && !ch[rt][1]) { clear(rt); rt = 0; return; } if (!ch[rt][0]) { int cnr = rt; rt = ch[rt][1]; fa[rt] = 0; clear(cnr); return; } if (!ch[rt][1]) { int cnr = rt; rt = ch[rt][0]; fa[rt] = 0; clear(cnr); return; } int x = pre(), cnr = rt; splay(x); fa[ch[cnr][1]] = x; ch[x][1] = ch[cnr][1]; clear(cnr); maintain(rt); } int read() { int x = 0, flag = 0; char ch = ' '; while (ch != '-' && (ch < '0' || ch > '9')) ch = getchar(); if (ch == '-') { flag = 1; ch = getchar(); } while (ch >= '0' && ch <= '9') { x = (x << 1) + (x << 3) + (ch ^ '0'); ch = getchar(); } return flag ? -x : x; } void write(int x) { if (x < 0) { putchar('-'); x = -x; } if (x > 9) write(x / 10); putchar(x % 10 + '0'); } int main() { n = read(); while (n--) { int x, opt; opt = read(), x = read(); if (opt == 1) insert(x); else if (opt == 2) erase(x); else if (opt == 3) { write(rk(x)); printf("\n"); } else if (opt == 4) { write(kth(x)); printf("\n"); } else if (opt == 5) { insert(x); write(val[pre()]); printf("\n"); erase(x); } else { insert(x); write(val[nxt()]); printf("\n"); erase(x); } } return 0; }
对不起，这篇文章暂时鸽了。
