Codeforces 1009 F

F - Dominant Indices

思路：树上启发式合并

先跑轻子树，然后清除轻子树的信息

最后跑重子树，不清除信息

然后再跑一遍轻子树，重新加回轻子树的信息

由于一个节点到根节点最多有logn个轻边，所以复杂度为nlogn

代码：

#include<bits/stdc++.h>
using namespace std;
#define fi first
#define se second
#define pi acos(-1.0)
#define LL long long
//#define mp make_pair
#define pb push_back
#define ls rt<<1, l, m
#define rs rt<<1|1, m+1, r
#define ULL unsigned LL
#define pll pair<LL, LL>
#define pii pair<int, int>
#define piii pair<pii, int>
#define mem(a, b) memset(a, b, sizeof(a))
#define fio ios::sync_with_stdio(false);cin.tie(0);cout.tie(0);
#define fopen freopen("in.txt", "r", stdin);freopen("out.txt", "w", stout);
//head

const int N = 1e6 + 5;
vector<int>g[N];
map<int, int>mp;
int deep[N], sz[N], bs[N], ans[N], mx = 0;
void dfs(int o, int u) {
    deep[u] = deep[o] + 1;
    sz[u] = 1;
    for (int v : g[u]) {
        if(v != o) {
            dfs(u, v);
            sz[u] += sz[v];
            if(sz[v] > sz[bs[u]]) bs[u] = v;
        }
    }
}
void ADD(int o,int u) {
    mp[deep[u]]++;
    if(mp[deep[u]] > mp[mx] || mp[deep[u]] == mp[mx] && deep[u] < mx) mx = deep[u];
    for (int v : g[u]) {
        if(v != o) {
            ADD(u, v);
        }
    }
}
void DFS(int o, int u) {
    for (int v : g[u]) {
        if(v != o && v != bs[u]) {
            DFS(u, v);
            mp.clear();
            mx = 0;
        }
    }
    if(bs[u])DFS(u, bs[u]);
    for (int v : g[u]) {
        if(v != o && v != bs[u]) {
            ADD(u, v);
        }
    }
    mp[deep[u]]++;
    if(mp[deep[u]] > mp[mx] || mp[deep[u]] == mp[mx] && deep[u] < mx) mx = deep[u];
    ans[u] = mx - deep[u];
}
int main() {
    int n, u, v;
    scanf("%d", &n);
    for (int i = 1; i < n; i++) {
        scanf("%d %d", &u, &v);
        g[u].pb(v);
        g[v].pb(u);
    }
    dfs(0, 1);
    DFS(0, 1);
    for (int i = 1; i <= n; i++) printf("%d%c", ans[i], '
');
    return 0;
}