PAT Grade A Zhenti 1003. Emergency

Topic link: https://www.patest.cn/contests/pat-a-practise/1003

The meaning of the question, give us n points, there are m roads, each point has a weight, each road has its own length and is a two-way road, let us find the distance from the starting point s to the end point e The number of shortest paths, and find the weights of all points and the largest one in these shortest paths.

After careful analysis, this problem should be a deformation problem of the shortest path (if students who are not proficient in the shortest path can go out and turn left to learn the shortest path: the portal ), it is very easy to first find the weight and the largest one, just need to It is easier to add a weight sum to the path length as a second comparison condition.

Then the key question is how to find the shortest path number. The method used by the editor here is to use a num array to record the number of shortest paths from s to the current point. When we update the shortest path, if the path from the previous point a to the current point b is shorter than the current path to b, Then num[b] = num[a], if the path from a to b is equal to the shortest path to the current b, then num[b] += num[a], after each update, clear the num of the previous point Zero to avoid repeated updates.

#include <queue>
#include <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>
using namespace std;  
const int INF = 0x3f3f3f3f;
const int maxn = 505;
int mp[maxn][maxn];
int num[maxn], dis[maxn], sum[maxn];
int val[maxn];  
int s, e, n;
struct Edge{
	int v, w, next;
}edge[maxn*maxn];
int head[maxn], tot;
void init() {
	to = 0;
	memset(head, -1, sizeof(head));
}
void addEdge(int u, int v, int w) {
	edge[tot].v = v;
	edge [tot] .w = w;
	edge[tot].next = head[u];
	head[u] = tot++;
}
void SPFA()  
{  
    queue<int> q;  
    q.push(s);  
    memset(num,0,sizeof(num));  
    memset(dis,INF,sizeof(dis));  
    memset(sum,0,sizeof(sum));
    dis[s] = 0;  
    sum[s] = val[s];  
    num[s] = 1;  
    int u,v,w;  
    while(!q.empty()) {  
        u = q.front();
        q.pop();  
        if(u == e) continue;
        for(int i=head[u]; i!=-1; i=edge[i].next) {
			v = edge [i] .v;
			w = edge[i].w;
            if(dis[v] > dis[u]+w) {  
                dis[v] = dis[u]+w;  
                sum [v] = sum [u] + val [v];  
                if(!num[v]) q.push(v);  
                num[v] = num[u];  
            }  
            else if(dis[v] == dis[u]+w) {  
                sum [v] = max (sum [u] + val [v], sum [v]);  
                if(!num[v]) q.push(v);  
                num[v] += num[u];  
            }  
        }  
        num [u] = 0;  
    }  
}  
  
intmain()  
{
    int m, u, v, w;  
    scanf("%d%d%d%d",&n, &m, &s, &e);
    init();
    for(int i = 0; i < n; ++i) {
    	scanf("%d",&val[i]);  
	}
    memset(mp,INF,sizeof(mp));
    while(m--) {  
        scanf("%d%d%d",&u, &v, &w);
		addEdge(u, v, w);
		addEdge(v, u, w);  
    }
    SPFA();  
    printf("%d %d\n",num[e], sum[e]);
    return 0;  
}