E - Currency Exchange——最短路_spfa()算法_e - currency exchange最短路-优快云博客

本文介绍了使用SPFA算法解决带有环的最短路径问题，并结合前向星存储结构进行高效实现。通过具体实例展示了如何判断负权环的存在，以及算法在实际问题中的应用。

Think:
1知识点：最短路_spfa()算法+前向星
2反思：判断环是否存在

以下为Accepted代码

#include <cstdio>
#include <cstring>
#include <algorithm>
#include <queue>

using namespace std;

const int inf = 0x3f3f3f3f;
const int N = 104;
const int M = 104;

int n, cnt, head[N], cont[N], vis[N];
double val, dis[N];

struct Edge{
    int v, next;
    double rate, comm, w;
}edge[M*2];

void add_edge(int u, int v, double r, double c);
bool spfa(int x);

int main(){
    int m, x, i, u, v;
    double r1, r2, c1, c2;
    while(~scanf("%d %d %d %lf", &n, &m, &x, &val)){
        cnt = 0;
        memset(head, -1, sizeof(head));
        for(i = 1; i <= m; i++){
            scanf("%d %d %lf %lf %lf %lf", &u, &v, &r1, &c1, &r2, &c2);
            add_edge(u, v, r1, c1);
            add_edge(v, u, r2, c2);
        }
        if(spfa(x))
            printf("YES\n");
        else
            printf("NO\n");
    }
    return 0;
}
void add_edge(int u, int v, double r, double c){
    edge[cnt].v = v;
    edge[cnt].w = 0;
    edge[cnt].rate = r;
    edge[cnt].comm = c;
    edge[cnt].next = head[u];
    head[u] = cnt++;
}
bool spfa(int x){
    queue <int> q;
    memset(dis, 0, sizeof(dis));
    memset(vis, 0, sizeof(vis));
    dis[x] = val, vis[x] = 1;
    q.push(x);
    cont[x]++;
    while(!q.empty()){
        int u = q.front();
        q.pop();
        vis[u] = 0;
        for(int i = head[u]; ~i; i = edge[i].next){
            int v = edge[i].v;
            edge[i].w = (dis[u]-edge[i].comm)*edge[i].rate - dis[u];
            if(dis[v] < dis[u] + edge[i].w){
                dis[v] = dis[u] + edge[i].w;
                if(!vis[v]){
                    vis[v] = 1;
                    q.push(v);
                    cont[v]++;
                }
                if(cont[v] >= n)/*判断是否存在环*/
                    return true;
            }
        }
    }
    return false;
}