[JLOI2014]松鼠的新家 (树剖)
题目
解析
非常裸的一道树剖题
链上修改+单点查询的板子
记录一下所经过的点\(now[i]\),每次更新\(now[i-1]到now[i]\)
我们链上更新时上一次到的终点,是这一次一次更新的起点,又因为在\(a_n\)处可以不放糖,所以我们每次链上更新完成后,在上条链的终点位置处糖数\(-1\)。
然后套板子直接做
代码
#include <bits/stdc++.h>
using namespace std;
const int N = 2e6 + 10;
int n, m, num, cnt;
int head[N], size[N], f[N], top[N], son[N], dep[N], now[N], id[N];
class node {
public :
int v, nx;
} e[N];
class tree {
public :
int sum, lazy;
int len;
} t[N];
#define lson rt << 1
#define rson rt << 1 | 1
template<class T>inline void read(T &x) {
x = 0; int f = 0; char ch = getchar();
while (!isdigit(ch)) f |= (ch == '-'), ch = getchar();
while (isdigit(ch)) x = x * 10 + ch - '0', ch = getchar();
x = f ? -x : x;
return ;
}
inline void add(int u, int v) {
e[++num].nx = head[u], e[num].v = v, head[u] = num;
}
void dfs1(int u, int fa) {
size[u] = 1;
for (int i = head[u]; ~i; i = e[i].nx) {
int v = e[i].v;
if (v != fa) {
dep[v] = dep[u] + 1;
f[v] = u;
dfs1(v, u);
size[u] += size[v];
if (size[v] > size[son[u]]) son[u] = v;
}
}
}
void dfs2(int u, int t) {
id[u] = ++cnt;
top[u] = t;
if (son[u]) dfs2(son[u], t);
for (int i = head[u]; ~i; i = e[i].nx) {
int v = e[i].v;
if (v != f[u] && v != son[u]) dfs2(v, v); //WRONG
}
}
inline void pushup(int rt) {
t[rt].sum = t[lson].sum + t[rson].sum;
}
void build(int l, int r, int rt) {
t[rt].len = r - l + 1;
if (l == r) return;
int m = (l + r) >> 1;
build(l, m, lson);
build(m + 1, r, rson);
}
inline void pushdown(int rt) {
if (t[rt].lazy) {
t[lson].lazy += t[rt].lazy;
t[rson].lazy += t[rt].lazy;
t[lson].sum += t[rt].lazy * t[lson].len;
t[rson].sum += t[rt].lazy * t[rson].len;
t[rt].lazy = 0;
}
}
void update(int L, int R, int c, int l, int r, int rt) {
if (L <= l && r <= R) {
t[rt].sum += (t[rt].len * c);
t[rt].lazy += c;
return;
}
pushdown(rt);
int m = (l + r) >> 1;
if (L <= m) update(L, R, c, l, m, lson);
if (R > m) update(L, R, c, m + 1, r, rson);
pushup(rt);
}
int query(int L, int R, int l, int r, int rt) {
if (L <= l && r <= R) return t[rt].sum;
pushdown(rt);
int m = (l + r) >> 1, ans = 0;
if (L <= m) ans += query(L, R, l, m, lson);
if (R > m) ans += query(L, R, m + 1, r, rson);
return ans;
}
void update_chain(int x, int y, int z) {
int fx = top[x], fy = top[y];
while (fx != fy) {
if (dep[fx] < dep[fy]) swap(fx, fy), swap(x, y);
update(id[fx], id[x], z, 1, cnt, 1);
x = f[fx], fx = top[x];
}
if (id[x] > id[y]) swap(x, y);
update(id[x], id[y], z, 1, cnt, 1);
}
int main() {
memset(head, -1, sizeof(head));
read(n);
for (int i = 1, x; i <= n; ++i) read(x), now[i] = x;
for (int i = 1, x, y; i < n; ++i) read(x), read(y), add(x, y), add(y, x);
f[1] = 0, dep[1] = 0;
dfs1(1, 0);
dfs2(1, 1);
build(1, n, 1);
for (int i = 2; i <= n; ++i) update_chain(now[i - 1], now[i], 1), update_chain(now[i], now[i], -1);
for (int i = 1; i <= n; ++i) printf("%d\n", query(id[i], id[i], 1, n, 1));
return 0;
}
如果哪里有错误或不易理解,还请不吝赐教