题解 | #[USACO 2011 Jan G]Roads and Planes#

#include <bits/stdc++.h>

using namespace std;

const int N = 150010, INF = 0x3f3f3f3f;

typedef pair<int,int> PII;

int T,R,P,S;
int a,b,c;
int e[N],w[N],ne[N],h[N],idx;
vector<int> block[N];
queue<int> q;
int bcnt;
int id[N],d[N],din[N];
bool str[N];

void add(int a,int b,int c)
{
	e[idx]=b,w[idx]=c,ne[idx]=h[a],h[a]=idx++;
}

void dfs(int u,int bid)
{
	id[u]=bid;
	block[bid].push_back(u);
	
	for(int i=h[u];i!=-1;i=ne[i])
	{
		int j=e[i];
		if(!id[j])
		{
			dfs(j,bid);
		}
	}
}

void Dijstra(int bid)
{
	priority_queue<PII,vector<PII> ,greater<PII> > heap;
	
	for(auto u: block[bid]) heap.push({d[u],u});
	
	while(heap.size())
	{
		auto t=heap.top();
		heap.pop();
		
		int ver=t.second;
		
		if(str[ver]) continue;
		str[ver]=true;
		
		for(int i=h[ver];i!=-1;i=ne[i])
		{
			int j=e[i];
			if(id[j]!=id[ver]&&--din[id[j]]==0) q.push(id[j]);
			
			if(d[j]>d[ver]+w[i])
			{
				d[j]=d[ver]+w[i];
				if(id[ver]==id[j]) heap.push({d[j],j});
			}
		}
	}
}

void topsort()
{
	memset(d,0x3f,sizeof d);
	memset(str,false,sizeof str);
	d[S]=0;
	
	for(int i=1;i<=bcnt;i++)
	{
		if(!din[i])
		{
			q.push(i);
		}
	}
	
	
	while(q.size())
	{
		auto t=q.front();
		q.pop();
		
		Dijstra(t);
	}
}

int main()
{
	cin>>T>>R>>P>>S;
	memset(h,-1,sizeof h);
	
	while(R--)
	{
		cin>>a>>b>>c;
		add(a,b,c);
		add(b,a,c);
	}
	
	for(int i=1;i<=T;i++)
	{
		if(!id[i])
		{
			dfs(i,++bcnt);
		}
	}
	
	while(P--)
	{
		cin>>a>>b>>c;
		din[id[b]]++;
		add(a,b,c);
	}
	
	topsort();
	
	for(int i=1;i<=T;i++)
	{
		if(d[i]>INF/2) cout<<"NO PATH\n";
		else cout<<d[i]<<'\n';
	}
	
	return 0;
}