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

34 2 01 21 34 5 12 13 14 12 32 44 4 21 22 33 41 4

 

Sample Output

302730

 

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<cstdio>#include<cstring>#include<vector>#include<queue>#include<functional>#include<algorithm>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<int> 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<int,vector<int>,greater<int> > 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<t[q].size();i++){cnt[t[q][i]]--;if (!vis[t[q][i]]&&cnt[t[q][i]]<=k){p.push(t[q][i]);vis[t[q][i]]=1;}}}printf("%d\n",res);}return 0;}