Kruskal’s Minimum Spanning Tree Algorithm

Pseudocode

KRUSKAL(G):
 A = ∅
 foreach v ∈ G.V:
   MAKE-SET(v)
 foreach (u, v) ordered by weight(u, v), increasing:
    if FIND-SET(u) ≠ FIND-SET(v):
       A = A ∪ {(u, v)}
       UNION(u, v)
 return A

MAIN CODE

struct Edge
{
    int src, dest, weight;
};
 
struct Graph
{
    int V, E; 
    struct Edge* edge;
};
  
struct subset
{
    int parent;
    int rank;
};
 
int find(struct subset subsets[], int i)
{
    // find root and make root as parent of i (path compression)
    if (subsets[i].parent != i)
        subsets[i].parent = find(subsets, subsets[i].parent);
 
    return subsets[i].parent;
}
 
// (uses union by rank)
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)
    {
        
        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);
        }
    }
    return;
}