Kruskal の最小スパニング ツリー アルゴリズム - C++ の貪欲なアルゴリズム

After sorting:

Weight  Src    Dest
21       27    26
22       28    22
22       26    25
24       20    21
24       22    25
26       28    26
27       22    23
27       27    28
28       20    27
28       21    22
29       23    24
30       25    24
31       21    27
34       23    25

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
struct Edge {
   int src, dest, weight;
};
struct Graph {
   int V, E;
   struct Edge* edge;
};
struct Graph* createGraph(int V, int E){
   struct Graph* graph = (struct Graph*)(malloc(sizeof(struct Graph)));
   graph->V = V;
   graph->E = E;
   graph->edge = (struct Edge*)malloc(sizeof( struct Edge)*E);
   return graph;
}
struct subset {
   int parent;
   int rank;
};
int find(struct subset subsets[], int i){
   if (subsets[i].parent != i)
      subsets[i].parent
   = find(subsets, subsets[i].parent);
   return subsets[i].parent;
}
void Union(struct subset subsets[], int x, int y){
   int xroot = find(subsets, x);
   int yroot = find(subsets, y);
   if (subsets[xroot].rank < subsets[yroot].rank)
      subsets[xroot].parent = yroot;
   else if (subsets[xroot].rank > subsets[yroot].rank)
      subsets[yroot].parent = xroot;
   else{
      subsets[yroot].parent = xroot;
      subsets[xroot].rank++;
   }
}
int myComp(const void* a, const void* b){
   struct Edge* a1 = (struct Edge*)a;
   struct Edge* b1 = (struct Edge*)b;
   return a1->weight > b1->weight;
}
void KruskalMST(struct Graph* graph){
   int V = graph->V;
   struct Edge
   result[V];
   int e = 0;
   int i = 0;
   qsort(graph->edge, graph->E, sizeof(graph->edge[0]), myComp);
   struct subset* subsets
   = (struct subset*)malloc(V * sizeof(struct subset));
   for (int v = 0; v < V; ++v) {
      subsets[v].parent = v;
      subsets[v].rank = 0;
   }
   while (e < V - 1 && i < graph->E) {
      struct Edge next_edge = graph->edge[i++];
      int x = find(subsets, next_edge.src);
      int y = find(subsets, next_edge.dest);
      if (x != y) {
         result[e++] = next_edge;
         Union(subsets, x, y);
      }
   }
   printf("Following are the edges in the constructed MST\n");
   int minimumCost = 0;
   for (i = 0; i < e; ++i){
      printf("%d -- %d == %d\n", result[i].src,
      result[i].dest, result[i].weight);
      minimumCost += result[i].weight;
   }
   printf("Minimum Cost Spanning tree : %d",minimumCost);
   return;
}
int main(){
   /* Let us create the following weighted graph
   30
   0--------1
   | \       |
   26| 25\ |15
   | \ |
   22--------23
   24 */
   int V = 24;
   int E = 25;
   struct Graph* graph = createGraph(V, E);
   graph->edge[0].src = 20;
   graph->edge[0].dest = 21;
   graph->edge[0].weight = 30;
   graph->edge[1].src = 20;
   graph->edge[1].dest = 22;
   graph->edge[1].weight = 26;
   graph->edge[2].src = 20;
   graph->edge[2].dest = 23;
   graph->edge[2].weight = 25;
   graph->edge[3].src = 21;
   graph->edge[3].dest = 23;
   graph->edge[3].weight = 35;
   graph->edge[4].src = 22;
   graph->edge[4].dest = 23;
   graph->edge[4].weight = 24;
   KruskalMST(graph);
   return 0;
}

Following are the edges in the constructed MST
22 -- 23 == 24
20 -- 23 == 25
20 -- 21 == 30
Minimum Cost Spanning tree : 79