【luogu P3469 [POI2008]BLO-Blockade】 题解

题目链接：https://www.luogu.org/problemnew/show/P3469

#include <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>
#define ll long long
using namespace std;
const int maxn = 500000 + 10;
ll n, m, ans[maxn];
ll dfn[maxn], low[maxn], tim, size[maxn];
bool iscut[maxn];
struct edge{
	ll from, to, next;
}e[maxn<<2];
ll head[maxn], cnt;
void add(ll u, ll v)
{
	e[++cnt].from = u;
	e[cnt].next = head[u];
	e[cnt].to = v;
	head[u] = cnt;
}
void tarjan(ll x, ll fa)
{
	ll child = 0, sum = 0;
	dfn[x] = low[x] = ++tim;
	size[x] = 1;
	for(ll i = head[x]; i != -1; i = e[i].next)
	{
		ll v = e[i].to;
		if(!dfn[v])
		{
			tarjan(v,fa);
			size[x] += size[v];
			low[x] = min(low[x], low[v]);
			if(low[v] >= dfn[x]) 
			{
				ans[x] += size[v]*(n - size[v]);
				sum += size[v];
				child++;
				if(x != fa)
				iscut[x] = 1;
			}
			if(x == fa) child++;
		}
		low[x] = min(low[x], dfn[v]);
	}
	if(x == fa && child >= 2) iscut[fa] = 1;
	if(!iscut[x]) ans[x] = 2*(n-1);
	else ans[x] += (n-sum-1)*(sum+1)+n-1;
}
int main()
{
	memset(head, -1, sizeof(head));
	scanf("%lld%lld",&n,&m);
	for(ll i = 1; i <= m; i++)
	{
		ll u, v;
		scanf("%lld%lld",&u,&v);
		add(u,v),add(v,u);
	}
	tarjan(1,1);
	for(ll i = 1; i <= n; i++)
	printf("%lld\n",ans[i]);
	return 0;
}