最小生成树+二分【洛谷P2330】

传送门：https://www.luogu.org/problemnew/show/P2330

终于做对了一个图论+二分的题，虽然比较简单吧，是个黄题...

直接prim求一下最小生成树，然后就二分一下分值就好啦！

#include <bits/stdc++.h>
using namespace std;
const int maxn = 330;
const int INF = 1e9+7;
int vis[maxn];
int n,m;
int cnt = 0;
struct node
{
	int to;
	int cost;
	bool operator<(const node &a)const
	{
		return cost>a.cost;
	}
};
vector<node> G[maxn];
int prim(int s,int x)
{
	int ans = 0;
	priority_queue<node> q;
	vis[s] = 1;
	for(int i=0;i<G[s].size();i++)
	{
		q.push(G[s][i]);
	}
	while(!q.empty())
	{
		node tmp = q.top();
		q.pop();
		if(vis[tmp.to]) continue;
		if(tmp.cost<=x)
		{
			cnt++;
			vis[tmp.to] = 1;
			ans += tmp.cost;
			for(int i=0;i<G[tmp.to].size();i++)
			{
				q.push(G[tmp.to][i]);
			}
		}
	}
	return ans;
}
bool check(int x)
{
	memset(vis,0,sizeof(vis));
	cnt = 0;
	prim(1,x);
	for(int i=1;i<=n;i++)
	{
		if(!vis[i])
		{
			return false;
		}
	}
	return true;
}
int main()
{
	ios::sync_with_stdio(false);
	cin.tie(0);
	cin>>n>>m;
	int l = INF,r = 0;
	for(int i=0;i<m;i++)
	{
		int x,y,z;
		cin>>x>>y>>z;
		G[x].push_back((node){y,z});
		G[y].push_back((node){x,z});
		l = min(l,z);
		r = max(r,z);
	}
	int ans = 0;
	int res = 0;
	while(l<=r)
	{
		int mid = (l+r)/2;
		if(check(mid))
		{
			res = cnt;
			ans = mid;
			r = mid-1;
		}
		else
		{
			l = mid+1;
		}
	}
	cout<<res<<" "<<ans<<endl;
	return 0;
}