HDU 5638 Toposort

Problem Description

There is a directed acyclic graph with  n vertices and  m edges. You are allowed to delete exact  k edges in such way that the lexicographically minimal topological sort of the graph is minimum possible.

 

Input

There are multiple test cases. The first line of input contains an integer  T indicating the number of test cases. For each test case:

The first line contains three integers  n,  m and  k  (1≤n≤100000,0≤k≤m≤200000) -- the number of vertices, the number of edges and the number of edges to delete.

For the next  m lines, each line contains two integers  ui and  vi, which means there is a directed edge from  ui to  vi  (1≤ui,vi≤n).

You can assume the graph is always a dag. The sum of values of  n in all test cases doesn't exceed  106. The sum of values of  m in all test cases doesn't exceed  2×106.

 

Output

For each test case, output an integer  S=(∑i=1ni⋅pi) mod (109+7), where  p1,p2,...,pn is the lexicographically minimal topological sort of the graph.

 

Sample Input

3 4 2 0 1 2 1 3 4 5 1 2 1 3 1 4 1 2 3 2 4 4 4 2 1 2 2 3 3 4 1 4

 

Sample Output

30 27 30

 

有向图删除k条边使得拓扑序列字典序最小，可以直接用优先队列维护。

#include
#include
#include
#include
#include
#include
using namespace std;
typedef long long LL;
const int maxn=1e5+10;
const int mod=1e9+7;
int T,n,m,k,cnt[maxn],x,y,vis[maxn];
vector t[maxn];

int main()
{
	scanf("%d",&T);
	while (T--)
	{
		scanf("%d%d%d",&n,&m,&k);
		for (int i=1;i<=n;i++) t[i].clear(),cnt[i]=vis[i]=0;
		while (m--)
		{
			scanf("%d%d",&x,&y);
			t[x].push_back(y);
			cnt[y]++;
		}
		priority_queue,greater > p;
		for (int i=1;i<=n;i++) if (cnt[i]<=k) p.push(i),vis[i]=1;
		int res=0,i=1;
		while (!p.empty())
		{
			int q=p.top();	p.pop();
			if (cnt[q]>k) {vis[q]=0; continue;}
			(res+=(LL)q*i++%mod)%=mod;
			k-=cnt[q];
			for (int i=0;i