Kruskal's algorithm.cpp

// C++ program for Kruskal's algorithm
// to find Minimum Spanning Tree of a
// given connected, undirected and weighted
// graph
#include <bits/stdc++.h>
using namespace std;

// a structure to represent a
// weighted edge in graph
class Edge {
public:
	int src, dest, weight;
};

// a structure to represent a connected,
// undirected and weighted graph
class Graph {
public:
	
	// 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.
	Edge* edge;
};

// Creates a graph with V vertices and E edges
Graph* createGraph(int V, int E)
{
	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
class subset {
public:
	int parent;
	int rank;
};

// A utility function to find set of an element i
// (uses path compression technique)
int find(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(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)
{
	Edge* a1 = (Edge*)a;
	Edge* b1 = (Edge*)b;
	return a1->weight > b1->weight;
}

// The main function to construct MST using Kruskal's
// algorithm
void KruskalMST(Graph* graph)
{
	int V = graph->V;
	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
	subset* subsets = new subset[(V * sizeof(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
		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
	cout << "Following are the edges in the constructed "
			"MST\n";
	int minimumCost = 0;
	for (i = 0; i < e; ++i)
	{
		cout << result[i].src << " -- " << result[i].dest
			<< " == " << result[i].weight << endl;
		minimumCost = minimumCost + result[i].weight;
	}
	// return;
	cout << "Minimum Cost Spanning Tree: " << minimumCost
		<< endl;
}

// Driver code
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
	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;


	// Function call
	KruskalMST(graph);

	return 0;
}