HDU-4725 The Shortest Path in Nya Graph 最短路

　　题目链接：http://acm.hdu.edu.cn/showproblem.php?pid=4725

　　如果直接建图复杂度过大，但是考虑到每层之间的有效边很少，只要在每层增加两个虚拟节点n+i和2*n+i。n+i节点向 i 层的所有连边，权值为0。i 层的所有点向2*n+i节点连边，权值为0。然后每层直接建立边就可以了，即2*n+i-1向n+i连边，权值为c，2*n+i向n+i-1连边，权值为c。3*n个点，最多有有9*n条边。。

 //STATUS:C++_AC_730MS_14340KB
 #include <functional>
 #include <algorithm>
 #include <iostream>
 //#include <ext/rope>
 #include <fstream>
 #include <sstream>
 #include <iomanip>
 #include <numeric>
 #include <cstring>
 #include <cassert>
 #include <cstdio>
 #include <string>
 #include <vector>
 #include <bitset>
 #include <queue>
 #include <stack>
 #include <cmath>
 #include <ctime>
 #include <list>
 #include <set>
 #include <map>
 using namespace std;
 //#pragma comment(linker,"/STACK:102400000,102400000")
 //using namespace __gnu_cxx;
 //define
 #define pii pair<int,int>
 #define mem(a,b) memset(a,b,sizeof(a))
 #define lson l,mid,rt<<1
 #define rson mid+1,r,rt<<1|1
 #define PI acos(-1.0)
 //typedef
 typedef __int64 LL;
 typedef unsigned __int64 ULL;
 //const
 const int N=;
 const int INF=0x3f3f3f3f;
 const int MOD=,STA=;
 const LL LNF=1LL<<;
 const double EPS=1e-;
 const double OO=1e60;
 const int dx[]={-,,,};
 const int dy[]={,,,-};
 const int day[]={,,,,,,,,,,,,};
 //Daily Use ...
 inline int sign(double x){return (x>EPS)-(x<-EPS);}
 template<class T> T gcd(T a,T b){return b?gcd(b,a%b):a;}
 template<class T> T lcm(T a,T b){return a/gcd(a,b)*b;}
 template<class T> inline T lcm(T a,T b,T d){return a/d*b;}
 template<class T> inline T Min(T a,T b){return a<b?a:b;}
 template<class T> inline T Max(T a,T b){return a>b?a:b;}
 template<class T> inline T Min(T a,T b,T c){return min(min(a, b),c);}
 template<class T> inline T Max(T a,T b,T c){return max(max(a, b),c);}
 template<class T> inline T Min(T a,T b,T c,T d){return min(min(a, b),min(c,d));}
 template<class T> inline T Max(T a,T b,T c,T d){return max(max(a, b),max(c,d));}
 //End

 struct Edge{
     int u,v,w;
 }e[*N];
 int first[N],next[*N];
 LL d[N];
 int S,T,n,m,c,mt;

 void adde(int a,int b,int c)
 {
     e[mt].u=a,e[mt].v=b;e[mt].w=c;
     next[mt]=first[a],first[a]=mt++;
 }
 #define pli pair<LL,int>
 LL dijkstra(int s)
 {
     int i,j,u,v,x;
     pli t;
     priority_queue<pli,vector<pli>,greater<pli> > q;
     for(i=;i<=*n;i++)d[i]=LNF;
     d[s]=;
     q.push(make_pair(d[s],s));
     while(!q.empty()){
         t=q.top();q.pop();
         u=t.second;
         if(t.first!=d[u])continue;
         for(i=first[u];i!=-;i=next[i]){
             if(d[u]+e[i].w<d[e[i].v]){
                 d[e[i].v]=d[u]+e[i].w;
                 q.push(make_pair(d[e[i].v],e[i].v));
             }
         }
     }
     return d[T];
 }

 int main(){
 //   freopen("in.txt","r",stdin);
     int Ca,i,j,k,a,b,w,ca=;
     scanf("%d",&Ca);
     while(Ca--)
     {
         scanf("%d%d%d",&n,&m,&c);
         S=,T=n;
         mem(first,-);mt=;
         for(i=;i<=n;i++){
             scanf("%d",&a);
             adde(n+a,i,);
             adde(i,(n<<)+a,);
         }
         for(i=;i<=n;i++){
             adde((n<<)+i-,n+i,c);
             adde((n<<)+i,n+i-,c);
         }
         for(i=;i<m;i++){
             scanf("%d%d%d",&a,&b,&w);
             adde(a,b,w);
             adde(b,a,w);
         }
         dijkstra(S);
         if(d[T]==LNF)d[T]=-;

         printf("Case #%d: %I64d\n",ca++,d[T]);
     }
     return ;
 }