Problem Description
It's now the year 21XX,when the earth will explode soon.The evil U.S. decided to invade the Mars to save their lives.
But the childlike Marsmen never keeps any army,because war never take place on the Mars.So it's very convenient for the U.S. to act the action.
Luckily,the Marsmen find out the evil plan before the invadation,so they formed a defense system.The system provides enchantment for some citys,and the enchantment generator for city A maybe set in city B,and to make things worse,both city B and C and more will provide echantment for city A.
The satelite of U.S. has got the map of the Mars.And they knows that when they enter a city,they can destory all echantment generator in this city at once,and they can enter a city only if they has destoryed all enchantment generator for this city,but troops can stay at the outside of the city and can enter it at the moment its echantment is destoryed.Of course the U.S. army will face no resistance because the Mars keep no army,so troops can invade in many way at the same time.
Now the U.S. will invade the Mars,give you the map,your task is to calculate the minimium time to enter the capital of the Mars.
But the childlike Marsmen never keeps any army,because war never take place on the Mars.So it's very convenient for the U.S. to act the action.
Luckily,the Marsmen find out the evil plan before the invadation,so they formed a defense system.The system provides enchantment for some citys,and the enchantment generator for city A maybe set in city B,and to make things worse,both city B and C and more will provide echantment for city A.
The satelite of U.S. has got the map of the Mars.And they knows that when they enter a city,they can destory all echantment generator in this city at once,and they can enter a city only if they has destoryed all enchantment generator for this city,but troops can stay at the outside of the city and can enter it at the moment its echantment is destoryed.Of course the U.S. army will face no resistance because the Mars keep no army,so troops can invade in many way at the same time.
Now the U.S. will invade the Mars,give you the map,your task is to calculate the minimium time to enter the capital of the Mars.
Input
The first line contains an integer T,which is the number of test cases.
For each testcase:
The first line contains two integers N and M,1<=N<=3000,1<=M<=70000,the cities is numbered from 1 to N and the U.S. landed on city 1 while the capital of the Mars is city N.
The next M lines describes M paths on the Mars.Each line contains three integers ai,bi and wi,indicates there is a unidirectional path form ai to bi lasts wi minutes(1<=wi<=10^8).
The next N lines describes N citys,the 1+M+i line starts with a integer li,followed with li integers, which is the number of cities has a echantment generator protects city i.
It's guaranteed that the city N will be always reachable.
For each testcase:
The first line contains two integers N and M,1<=N<=3000,1<=M<=70000,the cities is numbered from 1 to N and the U.S. landed on city 1 while the capital of the Mars is city N.
The next M lines describes M paths on the Mars.Each line contains three integers ai,bi and wi,indicates there is a unidirectional path form ai to bi lasts wi minutes(1<=wi<=10^8).
The next N lines describes N citys,the 1+M+i line starts with a integer li,followed with li integers, which is the number of cities has a echantment generator protects city i.
It's guaranteed that the city N will be always reachable.
Output
For each case,print a line with a number indicating the minimium time needed to enter the capital of the Mars.
Sample Input
1
6 6
1 2 1
1 4 3
2 3 1
2 5 2
4 6 2
5 3 2
0
0
0
1 3
0
2 3 5
6 6
1 2 1
1 4 3
2 3 1
2 5 2
4 6 2
5 3 2
0
0
0
1 3
0
2 3 5
Sample Output
5
We can follow these ways to achieve the fastest speed:
1->2->3,1->2->5,1->4->6.
Hint
The Map is like this:We can follow these ways to achieve the fastest speed:
1->2->3,1->2->5,1->4->6.
**************************************************************************************************************************
dijskstra（）&&优先队列
***************************************************************************************************************************
1 /* 2 用优先队列，每一次把度数为0的点和最短路径的点计入队列 3 最终还是用dijkstra() 4 */ 5 #include<iostream> 6 #include<cstdio> 7 #include<cstring> 8 #include<string> 9 #include<algorithm> 10 #include<map> 11 #include<queue> 12 #include<stack> 13 #include<cmath> 14 #include<vector> 15 #define inf 0x3f3f3f3f 16 #define Inf 0x3FFFFFFFFFFFFFFFLL 17 #define eps 1e-9 18 #define pi acos(-1.0) 19 using namespace std; 20 typedef long long ll; 21 const int maxn=3000+10; 22 const int maxm=70000+10; 23 struct Edge 24 { 25 int v,w,next; 26 }; 27 struct HeapNode 28 { 29 int d,u; 30 bool operator < (const HeapNode &a) const 31 { 32 return d>a.d; 33 } 34 }; 35 Edge edges[maxm<<1]; 36 int head[maxn],pro[maxn],nEdge,n,m; 37 bool vis[maxn]; 38 ll d[maxn],dt[maxn]; 39 vector<int>lim[maxn]; 40 void AddEdge(int u,int v,int w) 41 { 42 nEdge++; 43 edges[nEdge].v=v; 44 edges[nEdge].w=w; 45 edges[nEdge].next=head[u]; 46 head[u]=nEdge; 47 } 48 void Init() 49 { 50 for(int i=0;i<=n;++i) lim[i].clear(); 51 memset(head,0xff,sizeof(head)); 52 memset(dt,0,sizeof(dt)); 53 memset(pro,0,sizeof(pro)); 54 memset(vis,0,sizeof(vis)); 55 nEdge=-1; 56 } 57 void dijkstra() 58 { 59 for(int i=1;i<=n;++i) d[i]=Inf; 60 d[1]=0; 61 priority_queue<HeapNode>q; 62 HeapNode hp; 63 hp.d=0;hp.u=1; 64 q.push(hp); 65 int u,v,sz; 66 while(!q.empty()) 67 { 68 hp=q.top();q.pop(); 69 u=hp.u; 70 if(vis[u]) continue; 71 vis[u]=true; 72 sz=lim[u].size(); 73 for(int i=0;i<sz;++i) 74 { 75 v=lim[u][i]; 76 pro[v]--; 77 dt[v]=max(dt[v],d[u]); 78 if(pro[v]==0&&d[v]!=Inf) 79 { 80 d[v]=max(dt[v],d[v]); 81 hp.u=v;hp.d=d[v]; 82 q.push(hp); 83 } 84 } 85 for(int k=head[u];k!=-1;k=edges[k].next) 86 { 87 v=edges[k].v; 88 if(d[v]>d[u]+edges[k].w) 89 { 90 d[v]=max(d[u]+edges[k].w,dt[v]); 91 hp.u=v;hp.d=d[v]; 92 if(pro[v]==0) q.push(hp); 93 } 94 } 95 } 96 } 97 int main() 98 { 99 int t; 100 scanf("%d",&t); 101 while(t--) 102 { 103 scanf("%d%d",&n,&m); 104 Init(); 105 int u,v,w; 106 for(int i=0;i<m;++i) 107 { 108 scanf("%d%d%d",&u,&v,&w); 109 AddEdge(u,v,w); 110 } 111 for(int i=1;i<=n;++i) 112 { 113 scanf("%d",&u); 114 pro[i]=u; 115 while(u--) 116 { 117 scanf("%d",&v); 118 lim[v].push_back(i); 119 } 120 } 121 dijkstra(); 122 printf("%I64d ",d[n]); 123 } 124 return 0; 125 }