spfa

最短路径

把处理的加入队列，下次也是从队列取出来处理，直到队列空了。感觉跟我第一次错迪杰斯特拉一样，但是这个好理解也简单。

漏了两个处理：1是记录已经在队列的就不要入了。2是记录进入队列次数，超过n就是负数。

#include <iostream>
#include <cstring>
#include <algorithm>
#include <queue>
#include <vector>

using namespace std;
int INF=0x3f3f3f3f;

int main()
{
    ios::sync_with_stdio(false);
    cin.tie(0);
    int n,m,a,b,c;
    cin >> n>> m;
    vector<vector<pair<int,int>>> ev(n+1);
    for (int i = 0; i < m; i ++ ){
        cin >> a >> b >> c;
        ev[a].push_back({b,c});
    }
    
    queue<int> Q;
    vector<int> dist(n+1,INF);
    dist[1] = 0;
    Q.push(1);
    int now,e,v;
    while(!Q.empty()){
        now = Q.front();
        Q.pop();
        for(auto x:ev[now]){
            e = x.first;
            v = x.second;
            if(dist[e]<=dist[now]+v){
                dist[e] = dist[e];
            }
            else{
                dist[e] = dist[now] + v;
                Q.push(e);
            }
        }
    }
    if(dist[n]>INF/2){
        cout << "impossible";
    }else{
        cout << dist[n];
    }
    return 0;
}

判断负权回路

#include <iostream>
#include <cstring>
#include <algorithm>
#include <vector>
#include <queue>
using namespace std;

int main()
{
    ios::sync_with_stdio(false);
    cin.tie(0);
    int n,m,a,b,c;
    cin >> n >> m;
    int INF=0x3f3f3f3f;
    vector<int> dist(n+1,INF);
    vector<vector<pair<int,int>>> ev(n+1);
    vector<int> innum(n+1,1);//由于全部入队，都是1，记录入队次数，大于n就是有负权
    queue<int> Q;
    vector<bool> inflag(n+1,true);//都是1,记录入队情况
    for (int i = 0; i < m; i ++ ){
        cin >> a >> b >> c;
        ev[a].push_back({b,c});
    }
    for (int i = 1; i <= n; i ++ ){
        Q.push(i);//先全部入队
    }
    dist[1] = 0;
    while(!Q.empty()){
        int now = Q.front();
        Q.pop();
        inflag[now] = false;
        for(auto x: ev[now]){
            int e = x.first;
            int v = x.second;
            if(dist[e]>dist[now]+v){
                dist[e] = dist[now] + v;
                if(!inflag[now]){
                    Q.push(e);
                    innum[e]++;
                }
                if(innum[e]>n){
                    cout << "Yes";
                    return 0;
                }
            }
        }
    }
    cout << "No";
}