Dominant Indices 【CodeForces - 1009F】【Dsu on Tree】

题目链接

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  题意：有N个点的树，现在我们查询以每个点作为子树的根，它的子树中每个深度包含的结点数目最多的深度是哪个深度，如果有多个深度的话，取最小的深度。

  思路：由于是对于子树来进行询问的，这种时候最适合用Dsu on Tree来做了，直接维护最大深度结点个数以及对应的深度即可。

#include <iostream>
#include <cstdio>
#include <cmath>
#include <string>
#include <cstring>
#include <algorithm>
#include <limits>
#include <vector>
#include <stack>
#include <queue>
#include <set>
#include <map>
#include <bitset>
#include <unordered_map>
#include <unordered_set>
#define lowbit(x) ( x&(-x) )
#define pi 3.141592653589793
#define e 2.718281828459045
#define INF 0x3f3f3f3f
#define HalF (l + r)>>1
#define lsn rt<<1
#define rsn rt<<1|1
#define Lson lsn, l, mid
#define Rson rsn, mid+1, r
#define QL Lson, ql, qr
#define QR Rson, ql, qr
#define myself rt, l, r
using namespace std;
typedef unsigned long long ull;
typedef unsigned int uit;
typedef long long ll;
const int maxN = 1e6 + 7;
int N, Q, head[maxN], cnt;
struct Eddge
{
    int nex, to;
    Eddge(int a=-1, int b=0):nex(a), to(b) {}
}edge[maxN << 1];
inline void addEddge(int u, int v)
{
    edge[cnt] = Eddge(head[u], v);
    head[u] = cnt++;
}
inline void _add(int u, int v) { addEddge(u, v); addEddge(v, u); }
int siz[maxN], dfn[maxN], tot, rid[maxN], Wson[maxN], deep[maxN];
void pre_dfs(int u, int fa)
{
    siz[u] = 1; dfn[u] = ++tot; rid[tot] = u; deep[u] = deep[fa] + 1;
    int maxx = 0;
    for(int i=head[u], v; ~i; i=edge[i].nex)
    {
        v = edge[i].to;
        if(v == fa) continue;
        pre_dfs(v, u);
        siz[u] += siz[v];
        if(siz[v] > maxx)
        {
            maxx = siz[v];
            Wson[u] = v;
        }
    }
}
int mx, ss, ans[maxN], deep_siz[maxN] = {0};
void dfs(int u, int fa, bool keep)
{
    for(int i=head[u], v; ~i; i=edge[i].nex)
    {
        v = edge[i].to;
        if(v == fa || v == Wson[u]) continue;
        dfs(v, u, false);
    }
    if(Wson[u])
    {
        dfs(Wson[u], u, true);
    }
    for(int i=head[u], v, id; ~i; i=edge[i].nex)
    {
        v = edge[i].to;
        if(v == fa || v == Wson[u]) continue;
        for(int j=dfn[v]; j<dfn[v] + siz[v]; j++)
        {
            id = rid[j];
            deep_siz[deep[id]]++;
            if(deep_siz[deep[id]] > mx)
            {
                mx = deep_siz[deep[id]];
                ss = deep[id];
            }
            else if(deep_siz[deep[id]] == mx && ss > deep[id]) ss = deep[id];
        }
    }
    deep_siz[deep[u]]++;
    if(deep_siz[deep[u]] > mx)
    {
        mx = deep_siz[deep[u]];
        ss = deep[u];
    }
    else if(deep_siz[deep[u]] == mx && ss > deep[u]) ss = deep[u];
    ans[u] = ss - deep[u];
    if(!keep)
    {
        mx = 0; ss = 0;
        for(int i=dfn[u], v; i<dfn[u] + siz[u]; i++)
        {
            v = rid[i];
            deep_siz[deep[v]] = 0;
        }
    }
}
inline void init()
{
    cnt = tot = mx = ss = 0;
    for(int i=1; i<=N; i++) head[i] = -1;
}
int main()
{
    scanf("%d", &N);
    init();
    for(int i=1, u, v; i<N; i++)
    {
        scanf("%d%d", &u, &v);
        _add(u, v);
    }
    deep[0] = 0;
    pre_dfs(1, 0);
    dfs(1, 0, false);
    for(int i=1; i<=N; i++) printf("%d\n", ans[i]);
    return 0;
}