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\n",ca++,d[T]);

120     }

121     return 0;

122 }