详解次小生成树以及相关的C++求解方法

 #include <stdio.h> 
  #include <stdlib.h> 
  #include <string.h> 
   
  #define MAX 100000 
   
  int father[210];  // 并查集 
  int visit[210]; // 记录最小生成树用到的边的下标 
  int windex; // 记录最小生成树用到边的数量 
   
  typedef struct node { 
    int st, ed, w; 
  } node; 
   
  /** 
   * 预处理并查集数组 
   */ 
  void preProcess() 
  { 
    int i, len = sizeof(father) / sizeof(father[0]); 
   
    for (i = 0; i < len; i ++) { 
      father[i] = i; 
    } 
   
  } 
   
  /** 
   * kruskal使用贪心算法，将边按权值从小到大排序 
   */ 
  int cmp(const void *p, const void *q) 
  { 
    const node *a = p; 
    const node *b = q; 
   
    return a->w - b->w; 
  } 
   
  /** 
   * 并查集寻找起始结点，路径压缩优化 
   */ 
  int findParent(int x) 
  { 
    int parent; 
   
    if (x == father[x]) { 
      return x; 
    } 
   
    parent = findParent(father[x]); 
    father[x] = parent; 
     
    return parent; 
  } 
   
  /** 
   * 求最小生成树 
   */ 
  int minTree(node *points, int m, int n) 
  { 
    preProcess(); 
   
    int i, count, flag, pa, pb; 
   
    for (i = count = flag = windex = 0; i < m; i ++) { 
      pa = findParent(points[i].st); 
      pb = findParent(points[i].ed); 
       
      if (pa != pb) { 
        visit[windex ++] = i; 
        father[pa] = pb; 
        count ++; 
      } 
   
      if (count == n - 1) { 
        flag = 1; 
        break; 
      } 
    } 
   
    return flag; 
  } 
   
  /** 
   * 求次小生成树 
   */ 
  int secMinTree(node *points, int m, int n) 
  { 
    int i, j, min, tmp, pa, pb, count, flag; 
   
    for (i = 0, min = MAX; i < windex; i ++) { 
      preProcess(); 
   
      // 求次小生成树 
      for (j = count = tmp = flag = 0; j < m; j ++) { 
        if (j != visit[i]) { 
          pa = findParent(points[j].st); 
          pb = findParent(points[j].ed); 
   
          if (pa != pb) { 
            count ++; 
            tmp += points[j].w; 
            father[pa] = pb; 
          } 
   
          if (count == n - 1) { 
            flag = 1; 
            break; 
          } 
        } 
      } 
   
      if (flag && tmp < min)  min = tmp; 
    } 
   
    min = (min == MAX) ? -1 : min; 
   
    return min;  
  } 
   
   
  int main(void) 
  { 
    int i, t, n, m, flag, min; 
    node *points; 
   
    scanf("%d", &t); 
   
    while (t --) { 
      scanf("%d %d", &n, &m); 
   
      points = (node *)malloc(sizeof(node) * m);  
   
      for (i = 0; i < m; i ++) { 
        scanf("%d %d %d", &points[i].st, &points[i].ed, &points[i].w); 
      } 
   
      qsort(points, m, sizeof(points[0]), cmp); 
       
      flag = minTree(points, m, n); 
   
      if (flag == 0) {  // 无法生成最小生成树 
        printf("-1\n"); 
        continue; 
      } else { 
        min = secMinTree(points, m, n); 
        printf("%d\n", min); 
      } 
   
   
      free(points); 
    } 
   
    return 0; 
  }