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。。

  1 //STATUS:C++_AC_730MS_14340KB
  2 #include <functional>
  3 #include <algorithm>
  4 #include <iostream>
  5 //#include <ext/rope>
  6 #include <fstream>
  7 #include <sstream>
  8 #include <iomanip>
  9 #include <numeric>
 10 #include <cstring>
 11 #include <cassert>
 12 #include <cstdio>
 13 #include <string>
 14 #include <vector>
 15 #include <bitset>
 16 #include <queue>
 17 #include <stack>
 18 #include <cmath>
 19 #include <ctime>
 20 #include <list>
 21 #include <set>
 22 #include <map>
 23 using namespace std;
 24 //#pragma comment(linker,"/STACK:102400000,102400000")
 25 //using namespace __gnu_cxx;
 26 //define
 27 #define pii pair<int,int>
 28 #define mem(a,b) memset(a,b,sizeof(a))
 29 #define lson l,mid,rt<<1
 30 #define rson mid+1,r,rt<<1|1
 31 #define PI acos(-1.0)
 32 //typedef
 33 typedef __int64 LL;
 34 typedef unsigned __int64 ULL;
 35 //const
 36 const int N=300010;
 37 const int INF=0x3f3f3f3f;
 38 const int MOD=1000000007,STA=8000010;
 39 const LL LNF=1LL<<60;
 40 const double EPS=1e-8;
 41 const double OO=1e60;
 42 const int dx[4]={-1,0,1,0};
 43 const int dy[4]={0,1,0,-1};
 44 const int day[13]={0,31,28,31,30,31,30,31,31,30,31,30,31};
 45 //Daily Use ...
 46 inline int sign(double x){return (x>EPS)-(x<-EPS);}
 47 template<class T> T gcd(T a,T b){return b?gcd(b,a%b):a;}
 48 template<class T> T lcm(T a,T b){return a/gcd(a,b)*b;}
 49 template<class T> inline T lcm(T a,T b,T d){return a/d*b;}
 50 template<class T> inline T Min(T a,T b){return a<b?a:b;}
 51 template<class T> inline T Max(T a,T b){return a>b?a:b;}
 52 template<class T> inline T Min(T a,T b,T c){return min(min(a, b),c);}
 53 template<class T> inline T Max(T a,T b,T c){return max(max(a, b),c);}
 54 template<class T> inline T Min(T a,T b,T c,T d){return min(min(a, b),min(c,d));}
 55 template<class T> inline T Max(T a,T b,T c,T d){return max(max(a, b),max(c,d));}
 56 //End
 57 
 58 struct Edge{
 59     int u,v,w;
 60 }e[3*N];
 61 int first[N],next[3*N];
 62 LL d[N];
 63 int S,T,n,m,c,mt;
 64 
 65 void adde(int a,int b,int c)
 66 {
 67     e[mt].u=a,e[mt].v=b;e[mt].w=c;
 68     next[mt]=first[a],first[a]=mt++;
 69 }
 70 #define pli pair<LL,int>
 71 LL dijkstra(int s)
 72 {
 73     int i,j,u,v,x;
 74     pli t;
 75     priority_queue<pli,vector<pli>,greater<pli> > q;
 76     for(i=1;i<=3*n;i++)d[i]=LNF;
 77     d[s]=0;
 78     q.push(make_pair(d[s],s));
 79     while(!q.empty()){
 80         t=q.top();q.pop();
 81         u=t.second;
 82         if(t.first!=d[u])continue;
 83         for(i=first[u];i!=-1;i=next[i]){
 84             if(d[u]+e[i].w<d[e[i].v]){
 85                 d[e[i].v]=d[u]+e[i].w;
 86                 q.push(make_pair(d[e[i].v],e[i].v));
 87             }
 88         }
 89     }
 90     return d[T];
 91 }
 92 
 93 int main(){
 94 //   freopen("in.txt","r",stdin);
 95     int Ca,i,j,k,a,b,w,ca=1;
 96     scanf("%d",&Ca);
 97     while(Ca--)
 98     {
 99         scanf("%d%d%d",&n,&m,&c);
100         S=1,T=n;
101         mem(first,-1);mt=0;
102         for(i=1;i<=n;i++){
103             scanf("%d",&a);
104             adde(n+a,i,0);
105             adde(i,(n<<1)+a,0);
106         }
107         for(i=2;i<=n;i++){
108             adde((n<<1)+i-1,n+i,c);
109             adde((n<<1)+i,n+i-1,c);
110         }
111         for(i=0;i<m;i++){
112             scanf("%d%d%d",&a,&b,&w);
113             adde(a,b,w);
114             adde(b,a,w);
115         }
116         dijkstra(S);
117         if(d[T]==LNF)d[T]=-1;
118 
119         printf("Case #%d: %I64d
",ca++,d[T]);
120     }
121     return 0;
122 }