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 + 10;

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 * 2];

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 = 0; i<n; i++) {
        dis[i] = 2e10;
    }
    memset(done, false, sizeof(done));
    priority_queue<Heap> pq;
    dis[0] = 0;
    pq.push(Heap(0, 0));
    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 != -1) {
            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 = 0; ans_c = 0;
    for (int i = 0; i<n; i++) {
        ans_d += dis[i];
    }
    for (int i = 1; i<n; i++) {
        ans_c += pre[i];
    }
}

void init() {
    memset(head, -1, sizeof(head));
    memset(pre, -1, sizeof(pre));
    tot = 0;
}

int main() {
    //    freopen("data_in.txt","r",stdin);
    int tc;
    scanf("%d", &tc);
    while (tc--) {
        scanf("%d%d", &n, &m);
        init();
        for (int i = 0; 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
", ans_d, ans_c);
    }
    return 0;
}