Create kruskal.c

data_structures/graphs/kruskal.c

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+// C program for Kruskal's algorithm 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 = new Graph; 
+	graph->V = V; 
+	graph->E = E; 
+
+	graph->edge = new Edge[E]; 
+
+	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 = 0; // An index variable, used for result[] 
+	int i = 0; // An index variable, used for sorted edges 
+
+	// Step 1: Sort all the edges in non-decreasing 
+	// order of their weight. If we are not allowed to 
+	// change the given graph, we can create a copy of 
+	// array of edges 
+	qsort(graph->edge, graph->E, sizeof(graph->edge[0]), myComp); 
+
+	// Allocate memory for creating V ssubsets 
+	struct subset *subsets = 
+		(struct subset*) malloc( V * sizeof(struct subset) ); 
+
+	// Create V subsets with single elements 
+	for (int v = 0; v < V; ++v) 
+	{ 
+		subsets[v].parent = v; 
+		subsets[v].rank = 0; 
+	} 
+
+	// Number of edges to be taken is equal to V-1 
+	while (e < V - 1 && i < graph->E) 
+	{ 
+		// Step 2: Pick the smallest edge. And increment 
+		// the index for next iteration 
+		struct Edge next_edge = graph->edge[i++]; 
+
+		int x = find(subsets, next_edge.src); 
+		int y = find(subsets, next_edge.dest); 
+
+		// If including this edge does't cause cycle, 
+		// include it in result and increment the index 
+		// of result for next edge 
+		if (x != y) 
+		{ 
+			result[e++] = next_edge; 
+			Union(subsets, x, y); 
+		} 
+		// Else discard the next_edge 
+	} 
+
+	// print the contents of result[] to display the 
+	// built MST 
+	printf("Following are the edges in the constructed MST\n"); 
+	for (i = 0; i < e; ++i) 
+		printf("%d -- %d == %d\n", result[i].src, result[i].dest, 
+												result[i].weight); 
+	return; 
+} 
+
+// Driver program to test above functions 
+int main() 
+{ 
+	/* Let us create following weighted graph 
+			10 
+		0--------1 
+		| \	 | 
+	6| 5\ |15 
+		|	 \ | 
+		2--------3 
+			4	 */
+	int V = 4; // Number of vertices in graph 
+	int E = 5; // Number of edges in graph 
+	struct Graph* graph = createGraph(V, E); 
+
+
+	// add edge 0-1 
+	graph->edge[0].src = 0; 
+	graph->edge[0].dest = 1; 
+	graph->edge[0].weight = 10; 
+
+	// add edge 0-2 
+	graph->edge[1].src = 0; 
+	graph->edge[1].dest = 2; 
+	graph->edge[1].weight = 6; 
+
+	// add edge 0-3 
+	graph->edge[2].src = 0; 
+	graph->edge[2].dest = 3; 
+	graph->edge[2].weight = 5; 
+
+	// add edge 1-3 
+	graph->edge[3].src = 1; 
+	graph->edge[3].dest = 3; 
+	graph->edge[3].weight = 15; 
+
+	// add edge 2-3 
+	graph->edge[4].src = 2; 
+	graph->edge[4].dest = 3; 
+	graph->edge[4].weight = 4; 
+
+	KruskalMST(graph); 
+
+	return 0; 
+}