PAT All Roads Lead to Rome 单源最短路

思路：单源最短路末班就好了，字符串映射成数字处理。

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AC代码

//#define LOCAL
#include <stdio.h>
#include <string.h>
#include <algorithm>
#include <queue>
#include <map>
#include <vector>
#include <string>
using namespace std;
#define inf 0x3f3f3f3f
const int maxn = 200;
map<string, int> ha;
int id, st, ed;
int n, k;
int hap[maxn];
char names[maxn][50];

int getId(string s) {
    if(!ha.count(s)) {
        ha[s] = id++;
    }
    return ha[s];
}

struct Edge {
    int from, to, dist;
    Edge(int u, int v, int d):from(u),to(v),dist(d) {}
};
vector<Edge> edges;
vector<int> G[maxn];
bool done[maxn];
int d[maxn], hp[maxn], pt[maxn], routes[maxn]; //Best
int p[maxn];

void init() {
    ha.clear();
    id = 0;
    for(int i = 0; i < maxn; i++) G[i].clear();
    edges.clear();
}

void addEdge(int from, int to, int dist) {
    edges.push_back(Edge(from, to, dist));
    int m = edges.size();
    G[from].push_back(m-1);
}

struct HeapNode{
    int d, u;
    HeapNode(int d, int u):d(d), u(u){
    }
    bool operator < (const HeapNode& rhs) const {
        return d > rhs.d;
    }
};

//距离小，开心多，平均大
void dijkstra(int s) {
    memset(done, 0, sizeof(done));
    priority_queue<HeapNode> Q;
    for(int i = 0; i < n; i++) {
        d[i] = inf;
        hp[i] = -inf;
        pt[i] = inf;
    }
    d[s] = hp[s] = pt[s] = 0;
    routes[s] = 1;
    Q.push(HeapNode(0, s));
    while(!Q.empty()) {
        HeapNode x = Q.top(); Q.pop();
        int u = x.u;
        if(done[u]) continue;
        done[u] = true;
        for(int i = 0; i < G[u].size(); i++) {
            Edge& e = edges[G[u][i]];
            bool update = false;
            if(d[e.to] > d[u] + e.dist) {
                routes[e.to] = routes[u];
                update = true;
            } else if(d[e.to] == d[u] + e.dist) {
                routes[e.to] += routes[u];
                if(hp[e.to] < hp[u] + hap[e.to]) {
                    update = true;
                } else if(hp[e.to] == hp[u] + hap[e.to]) {
                    if(pt[e.to] > pt[u] + 1) {
                        update = true;
                    }
                }
            }
            if(update) {
                d[e.to] = d[u] + e.dist;
                p[e.to] = u;
                hp[e.to] = hp[u] + hap[e.to];
                pt[e.to] = pt[u] + 1;
                Q.push(HeapNode(d[e.to], e.to));
            }
        }
    }
}

void print(int u) {
    if(u == 0) {
        printf("%s", names[0]);
        return;
    } else {
        print(p[u]);
        printf("->%s", names[u]);
    }
}

int main() {
#ifdef LOCAL
    freopen("data.in", "r", stdin);
    freopen("data.out", "w", stdout);
#endif
    while(scanf("%d%d%s", &n, &k, names[0]) == 3) {
        init();
        st = getId(names[0]);
        int happy;
        for(int i = 1; i < n; i++) {
            scanf("%s %d", names[i], &happy);
            int u = getId(names[i]);
            hap[u] = happy;
        }
        ed = getId("ROM");
        char x[50], y[50];
        int u, v, cost;
        for(int i = 0; i < k; i++) {
            scanf("%s%s%d", x, y, &cost);
            u = getId(x), v = getId(y);
            //printf("%d %d\n", u, v);
            addEdge(u, v, cost);
            addEdge(v, u, cost);
        }
        dijkstra(0);
        printf("%d %d %d %d\n", routes[ed], d[ed], hp[ed], (int)(hp[ed]/pt[ed]));
        print(ed);
        printf("\n");
    }
    return 0;
}

如有不当之处欢迎指出！