Algorithme De Kruskal (document en anglais)

// Kruskal's algortihm to find Minimum Spanning Tree of a given connected,

// undirected and weighted graph

#include <stdio.h>

#include <stdlib.h>

#include <string.h>

// a structure to represent a weighted edge in graph

struct Edge

{

int src, dest, weight;

};

// a structure to represent a connected, undirected and weighted graph

struct Graph

{

// V-> Number of vertices, E-> Number of edges

int V, E;

// graph is represented as an array of edges. Since the graph is

// undirected, the edge from src to dest is also edge from dest

// to src. Both are counted as 1 edge here.

struct Edge* edge;

};

// Creates a graph with V vertices and E edges

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( graph->E * sizeof( struct Edge ) );

return graph;

}

// A structure to represent a subset for union-find

struct subset

{

int parent;

int rank;

};

// A utility function to find set of an element i

// (uses path compression technique)

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;

}

// A function that does union of two sets of x and y

// (uses union by rank)

void Union(struct subset subsets[], int x, int y)

{

int xroot = find(subsets, x);

int yroot = find(subsets, y);

// Attach smaller rank tree under root of high rank tree

// (Union by Rank)

if (subsets[xroot].rank < subsets[yroot].rank)

subsets[xroot].parent = yroot;

else if (subsets[xroot].rank > subsets[yroot].rank)

subsets[yroot].parent = xroot;

// If ranks are same, then make one as root and increment

// its rank by one

else

{

subsets[yroot].parent = xroot;

subsets[xroot].rank++;

}

}

// Compare two edges according to their weights.

// Used in qsort() for sorting an array of edges

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;

}

// The main function to construct MST using Kruskal's algorithm

void KruskalMST(struct Graph* graph)

{

int V = graph->V;

struct Edge result[V]; // Tnis will store the resultant MST

int e =

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