pat 1087

注意INIFINTE 定义成32767已经不够了，有可能出现大于INIFINTE的distance，以后定义成0x7fffffff （7个f）
相同最短路径的个数等于父路径个数或父路径个数加一，而不是++

#include<stdio.h>
#include<vector>
#include<string.h>
#define SIZE 205
#define INIFINTE 0x7fffffff
using namespace std;

struct map{
    int index;
    int dist;
};

int dist[SIZE], name[SIZE], hh[18279], numofcost[SIZE], parent[SIZE],happiness[SIZE],numofcity[SIZE],flag[SIZE],h[SIZE];
vector<struct map> graph[SIZE];

int hashname(char str[]){
    return (str[0]-'A') * 26 * 26 + (str[1] - 'A') * 26 + str[2] - 'A';
}
char s[4];
char *rehash(int n){
    s[0] = n / (26 * 26) + 'A';
    n = n % (26 * 26);
    s[1] = n / 26 + 'A';
    n = n % 26;
    s[2] = n + 'A';
    s[3] = '\0';
    return s;
}

void Dij(int s,int n){
    int i;
    for (i = 0; i < n; i++){
        dist[i] = INIFINTE;
        flag[i] = 0;
        h[i] = -1;
    }
    dist[s] = 0;
    h[s] = 0;
    numofcost[s] = 1;
    int j,u,dis;
    for (i = 0; i < n; i++){
        dis = INIFINTE;
        u = -1;
        for (j = 0; j < n;j++)
            if (!flag[j])
                if (dist[j] < dis){
                    u = j;
                    dis = dist[j];
                }
        if (u == -1)
            break;
        flag[u] = 1;
        int size = graph[u].size();
        for (j = 0; j < size; j++){
            struct map s = graph[u][j];
            if (dist[s.index] > dist[u] + s.dist){
                dist[s.index] = dist[u] + s.dist;
                parent[s.index] = u;
                numofcity[s.index] = numofcity[u] + 1;
                h[s.index] = h[u] + happiness[s.index];
                numofcost[s.index] = numofcost[u];
            }
            else if (dist[s.index] == dist[u] + s.dist){
                if (h[s.index] == h[u] + happiness[s.index]){
                    if (numofcity[s.index] >= numofcity[u] + 1){
                        parent[s.index] = u;
                        numofcity[s.index] = numofcity[u] + 1;
                    }
                }
                else if (h[s.index] < h[u] + happiness[s.index]){
                    parent[s.index] = u;
                    numofcity[s.index] = numofcity[u] + 1;
                    h[s.index] = h[u] + happiness[s.index];
                }
                numofcost[s.index] += numofcost[u];
            }
        }
    }
}

void PrintPath(int s, int d){
    int i;
    if (s == d)
        printf("%s", rehash(name[s]));
    else {
        PrintPath(s, parent[d]);
        printf("->%s", rehash(name[d]));
    }
}
int main(){
    freopen("1.in", "r", stdin);
    int NumOfCity, NumOfRoad, start;
    char startch[4];
    memset(hh, -1, sizeof(hh));
    scanf("%d%d%s", &NumOfCity, &NumOfRoad, &startch);
    start = hashname(startch);
    happiness[0] = 0;
    name[0] = start;
    hh[start] = 0;
    int i;
    char str[4],ch[4];
    for (i = 1; i < NumOfCity; i++){
        scanf("%s%d", &str, &happiness[i]);
        name[i] = hashname(str);
        hh[name[i]] = i;
    }
    struct map node;
    int s, d;
    for (i = 0; i < NumOfRoad; i++){
        scanf("%s%s%d", &str, &ch, &node.dist);
        s = hashname(str);
        d = hashname(ch);
        node.index = hh[d];
        graph[hh[s]].push_back(node);
        node.index = hh[s];
        graph[hh[d]].push_back(node);
    }
    Dij(0,NumOfCity);
    int aim;
    aim = hh[hashname("ROM")];
    printf("%d %d %d ", numofcost[aim], dist[aim], h[aim]);
    printf("%d\n", h[aim] / numofcity[aim]);
    PrintPath(0, aim);
    putchar('\n');
    return 0;
}