有向图和无向图判断最小环

有向图:

  • 有向图比较简单,就直接跑一边floyd
    #include <bits/stdc++.h>
    using namespace std;
    #define N 101
    #define INF 0x7ffffff
    int mpt[N][N];
    int m,n;
    void floyd(){
      for(int k=1;k<=n;k++){
          for(int i=1;i<=n;i++)
              for(int j=1;j<=n;j++)
                  if(mpt[i][j]>mpt[i][k]+mpt[k][j])
                      mpt[i][j]=mpt[i][k]+mpt[k][j];
      }
    }
    void init(){
      for(int i=0;i<N;i++)
          for(int j=0;j<N;j++){
              mpt[i][j]=INF;
          }
    }
    int main(){
      int t;
      scanf("%d",&t);
      while(t--){
          scanf("%d%d",&n,&m);
          init();
          int s,e,v;
          for(int i=1;i<=m;i++){
              scanf("%d%d%d",&s,&e,&v);
              if(v<mpt[s][e]){
                  mpt[s][e]=v;
              }
          }
          floyd();
          int min=INF;
          for(int i=1;i<=n;i++){
              if(min>mpt[i][i])
                  min=mpt[i][i];
          }
          if(min<INF)
              printf("%d\n",min);
          else
              printf("-1\n");
      }
      return 0;
    }

无向图

#include <bits/stdc++.h>
using namespace std;
#define ll long long
const int _inf = 0x7fffffff;
const int inf = _inf/3;    //程序可能出现3个inf相加
const int maxn = 105;
int graph[maxn][maxn], pre[maxn][maxn], dis[maxn][maxn];
int cnt, path[maxn], sum;
int n, m;
void init()  {
    for(int i = 1; i <= n; ++i) {
        for(int j = 1; j <= n; ++j){
            pre[i][j] = i;
            graph[i][j] = dis[i][j] = inf;
        }
        graph[i][i] = dis[i][i] = 0;
    }
}
void Folyd()
{
    int mins = inf;
    for(int k = 1; k <= n; ++k){
        for(int i = 1; i < k; ++i)
        for(int j = i+1; j < k; ++j){
            int tmp = dis[i][j] + graph[k][i] + graph[j][k];
            if(mins > tmp){
                mins = tmp;
                cnt = 0; sum = 1;
                int t = i;
                while(t != j){
                    path[cnt++] = t;
                    t = pre[j][t];
                }
                path[cnt++] = j;
                path[cnt++] = k;
            }
            else if(tmp == mins) ++sum;
        }
        for(int i = 1; i <= n; ++i)
        for(int j = 1; j <= n; ++j){
            if(dis[i][j] > dis[i][k]+dis[k][j]){
                dis[i][j] = dis[i][k]+dis[k][j];
                pre[i][j] = pre[k][j];
            }
        }
    }
    if(mins == inf) puts("No solution.");
    else{
        for(int i = cnt-1; i > 0; --i) printf("%d ", path[i]);//输出最小的环的路径
        printf("%d\n", path[0]);
    }
}
int main()
{
    int u, v, w;
    while(~scanf("%d %d", &n, &m))
    {
        init();
        for(int i = 1; i <= m; ++i){
            scanf("%d %d %d", &u, &v, &w);
            if(w < graph[u][v]){
                graph[u][v] = graph[v][u] = w;
                dis[u][v] = dis[v][u] = w;
            }
        }
        Folyd();
    }
    return 0;
}
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11-05 07:29
贵州大学 Java
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