ICPC 2019 徐州 M

这题标程是直接找，我写的方法是对当前的点到根节点之间的路径上二分找当前点可以做重心的区间，复杂度O(nlognlogn)

#include <bits/stdc++.h>
using namespace std;
const int N = 2 * 1e5 + 10;
vector < int > edge[N];
int sz[N], f[N][21], dep[N];
vector < int > ans[N];
void dfs1(int u, int fa) {
    sz[u] = 1; dep[u] = dep[fa] + 1;
    f[u][0] = fa;
    for (int i = 1; i <= 20; i++)
        f[u][i] = f[f[u][i - 1]][i - 1];
    for (int i = 0; i < edge[u].size(); i++) {
        int v = edge[u][i];
        if (v == fa)    continue;
        dfs1(v, u);
        sz[u] += sz[v];    
    }
}

bool check1(int u, int len, int maxn) {
    int t = u;
    for (int i = 20; i >= 0; i--)
        if ((1 << i) & len)
            t = f[t][i];
    return sz[t] <= 2 * sz[u];
}

bool check2(int u, int len, int maxn) {
    int t = u;
    for (int i = 20; i >= 0; i--)
        if ((1 << i) & len)
            t = f[t][i];
    return 2 * maxn <= sz[t];
}

void dfs(int u, int fa) {
    if (u == 3)
        fa = fa + 1 - 1;
    int maxn = 0;
    for (int i = 0; i < edge[u].size(); i++)
        if (edge[u][i] != fa)
            maxn = max(maxn, sz[edge[u][i]]);
    int l = 0, r = dep[u] - 1;
    while (l < r) {
        int mid = (l + r + 1) / 2;
        if (check1(u, mid, maxn))
            l = mid;
        else    r = mid - 1;
    }
    int L = 0, R = dep[u] - 1;
    while (L < R) {
        int mid = (L + R) / 2;
        if (check2(u, mid, maxn))
            R = mid;
        else    L = mid + 1;
    }
    //printf("%d %d
", L, r);
    int s = u, t = u;
    for (int i = 20; i >= 0; i--)
        if ((1 << i) & L)
            s = f[s][i];
    for (int i = 20; i >= 0; i--)
        if ((1 << i) & r)
            t = f[t][i];
    //printf("%d %d
", s, t);
    swap(L, r); swap(s, t);
    if (r >= L) {
        if (r == L)
            if (2 * maxn <= sz[s] && sz[s] <= 2 * sz[u])
                ans[s].push_back(u);
    }
    else {
        while (t != f[s][0]) {
            ans[t].push_back(u);
            t = f[t][0];
        } 
    }
    for (int i = 0; i < edge[u].size(); i++)
        if (edge[u][i] != fa)
            dfs(edge[u][i], u);
}

int main() {
    int N;
    scanf("%d", &N);
    for (int i = 1; i < N; i++) {
        int a, b;
        scanf("%d %d", &a, &b);
        edge[a].push_back(b);
        edge[b].push_back(a);
    }
    dfs1(1, 0);
    dfs(1, 0);
    for (int i = 1; i <= N; i++, puts("")) {
        if (ans[i].size() == 2) {
            if (ans[i][0] < ans[i][1])
                printf("%d %d", ans[i][0], ans[i][1]);
            else    printf("%d %d", ans[i][1], ans[i][0]);
        }
        else
            printf("%d", ans[i][0]);
        //for (int j = 0; j < ans[i].size(); j++)
        //    printf("%d ", ans[i][j]);
    }
    return 0;
}