ZOJ 3946 Highway Project 贪心+最短路

题目链接：

http://www.icpc.moe/onlinejudge/showProblem.do?problemCode=3946

题解：

用dijkstra跑单元最短路径，如果对于顶点v，存在一系列边(ui，v)使得dis[v]最小(dis[v]表示0到v的距离)。这些边能且只能选一条，那么我们自然应该选cost最小的那个边了。

 #include<iostream>
 #include<cstdio>
 #include<cstring>
 #include<vector>
 #include<algorithm>
 #include<queue>
 using namespace std;

 typedef long long LL;
 const int maxn = 1e5 + ;

 struct Edge {
     int ne, u, v, c, d;
     Edge(int ne, int u, int v, int d, int c) :ne(ne), u(u), v(v), d(d), c(c) {}
     Edge() {}
 }egs[maxn * ];

 struct Heap {
     int u, d, c;
     Heap(int u, int d) :u(u), d(d) {}
     Heap() {}
     bool operator < (const Heap& tmp) const {
         return d>tmp.d;
     }
 };

 struct Node {
     int u, v, w;
     bool operator < (const Node& tmp) const {
         return w<tmp.w;
     }
 }nds[maxn];

 int head[maxn], tot;

 void addEdge(int u, int v, int d, int c) {
     egs[tot] = Edge(head[u], u, v, d, c);
     head[u] = tot++;
 }

 int n, m;
 LL ans_d, ans_c;

 LL dis[maxn];
 //pre[u]记录u和前驱节点的那条边的cost
 int pre[maxn];
 bool done[maxn];

 void dij() {
     for (int i = ; i<n; i++) {
         dis[i] = 2e10;
     }
     memset(done, false, sizeof(done));
     priority_queue<Heap> pq;
     dis[] = ;
     pq.push(Heap(, ));
     while (!pq.empty()) {
         Heap x = pq.top(); pq.pop();
         int u = x.u;
         if (done[u]) continue;
         done[u] = true;
         int p = head[u];
         while (p != -) {
             Edge &e = egs[p];
             if (dis[e.v]>dis[u] + e.d) {
                 dis[e.v] = dis[u] + e.d;
                 pre[e.v] = e.c;
                 pq.push(Heap(e.v, dis[e.v]));
             }
             else if (dis[e.v] == dis[u] + e.d) {
                 //这里贪心选cost最小的边
                 if (pre[e.v]>e.c)
                     pre[e.v] = e.c;
             }
             p = e.ne;
         }
     }
     ans_d = ; ans_c = ;
     for (int i = ; i<n; i++) {
         ans_d += dis[i];
     }
     for (int i = ; i<n; i++) {
         ans_c += pre[i];
     }
 }

 void init() {
     memset(head, -, sizeof(head));
     memset(pre, -, sizeof(pre));
     tot = ;
 }

 int main() {
     //    freopen("data_in.txt","r",stdin);
     int tc;
     scanf("%d", &tc);
     while (tc--) {
         scanf("%d%d", &n, &m);
         init();
         for (int i = ; i<m; i++) {
             int u, v, d, c;
             scanf("%d%d%d%d", &u, &v, &d, &c);
             addEdge(u, v, d, c);
             addEdge(v, u, d, c);
         }
         dij();
         printf("%lld %lld\n", ans_d, ans_c);
     }
     return ;
 }