ACM/ICPC 之 最短路-SPFA+正逆邻接表(POJ1511(ZOJ2008))

求单源最短路到其余各点，然后返回源点的总最短路长，以构造邻接表的方法不同分为两种解法。

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POJ1511(ZOJ2008)-Invitation Cards

　　改变构造邻接表的方法后，分为两种解法

解法一：

 //POJ1511-ZOJ2008
 //Time：7766Ms    Memory：99112K
 //求从1处到各点后再返回1处的最短总路长
 //需要构造邻接表和逆邻接表
 //构造方法1：vector构造邻接表
 //SPFA+邻接表
 #include<iostream>
 #include<cstring>
 #include<cstdio>
 #include<vector>
 #include<queue>
 using namespace std;

 #define MAX 1000005
 #define INF 0x3f3f3f3f

 struct Edge {
     int u, w;
     Edge(int uu, int ww) :u(uu), w(ww) {}
 };

 vector<Edge> e1[MAX], e2[MAX];    //邻接表-逆邻接表

 int n, m;
 int d[MAX];
 long long sum;
 bool v[MAX];

 void SPFA(int x, vector<Edge> e[MAX])
 {
     memset(d, INF, sizeof(d));
     memset(v, false, sizeof(v));
     queue<int> q;
     q.push(x);
     d[x] = ;
     while (!q.empty()){
         int cur = q.front();
         q.pop();
         v[cur] = false;
         for (int i = ; i < e[cur].size(); i++)
         {
             int u = e[cur][i].u;
             if (d[u] > d[cur] + e[cur][i].w)
             {
                 d[u] = d[cur] + e[cur][i].w;
                 if (!v[u]) { q.push(u); v[u] = true; }
             }
         }
     }
     for (int i = ; i <= n; i++)
         sum += d[i];
 }

 int main()
 {
     int T;
     scanf("%d", &T);
     while (T--) {
         sum = ;
         memset(e1, , sizeof(e1));
         memset(e2, , sizeof(e2));
         scanf("%d%d", &n, &m);
         while (m--) {
             int u, v, w;
             scanf("%d%d%d", &u, &v, &w);
             e1[u].push_back(Edge(v, w));    //正向
             e2[v].push_back(Edge(u, w));    //逆向
         }

         SPFA(, e1);
         SPFA(, e2);
         printf("%lld\n", sum);
     }

     return ;
 }

解法二：

 //POJ1511-ZOJ2008
 //Time:2000Ms    Memory:36424K
 //求从1处到各点后再返回1处的最短总路长
 //需要构造邻接表和逆邻接表
 //构造方法2：偏序关系构造邻接表
 //SPFA+邻接表
 #include<iostream>
 #include<cstring>
 #include<cstdio>
 #include<vector>
 #include<queue>
 using namespace std;

 #define MAX 1000005
 #define INF 0x3f3f3f3f

 struct Edge {
     int u, w, next;
     Edge() {}
     Edge(int uu, int ww, int nn) :u(uu), w(ww), next(nn) {}
 }e1[MAX], e2[MAX];    //邻接表-逆邻接表

 int h1[MAX], h2[MAX];    //正表表头-逆表表头
 int n, m;
 int d[MAX];
 long long sum;
 bool v[MAX];

 void SPFA(int x, Edge e[MAX], int h[MAX])
 {
     memset(d, INF, sizeof(d));
     memset(v, false, sizeof(v));
     queue<int> q;
     q.push(x);
     d[x] = ;
     while (!q.empty()){
         int cur = q.front();
         q.pop();
         v[cur] = false;
         for (int i = h[cur]; i != -; i = e[i].next)
         {
             int u = e[i].u;
             int w = e[i].w;
             if (d[u] > d[cur] + w)
             {
                 d[u] = d[cur] + w;
                 if (!v[u]) { q.push(u); v[u] = true; }
             }
         }
     }
     for (int i = ; i <= n; i++)
         sum += d[i];
 }

 int main()
 {
     int T;
     scanf("%d", &T);
     while (T--) {
         sum = ;
         memset(e1, , sizeof(e1));
         memset(e2, , sizeof(e2));
         memset(h1, -, sizeof(h1));
         memset(h2, -, sizeof(h2));
         scanf("%d%d", &n, &m);
         for (int i = ; i < m; i++) {
             int u, v, w;
             scanf("%d%d%d", &u, &v, &w);
             e1[i] = Edge(v, w, h1[u]);
             e2[i] = Edge(u, w, h2[v]);
             h1[u] = h2[v] = i;
         }

         SPFA(, e1, h1);
         SPFA(, e2, h2);
         printf("%lld\n", sum);
     }

     return ;
 }