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Prim's Algorithm For Finding Minimum Spanning Trees In C

11.09.2007
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        The is a straight-forward implementation of Prim's Algorithm for finding the minimum spanning tree of a graph.

A detailed explanation is given <a href="http://compprog.wordpress.com/2007/11/09/minimal-spanning-trees-prims-algorithm/">here</a>.

#include <stdio.h>

/*
	The input file (weight.txt) look something like this
		4
		0 0 0 21
		0 0 8 17
		0 8 0 16
		21 17 16 0

	The first line contains n, the number of nodes.
	Next is an nxn matrix containg the distances between the nodes
	NOTE: The distance between a node and itself should be 0
*/

int n; /* The number of nodes in the graph */

int weight[100][100]; /* weight[i][j] is the distance between node i and node j;
			if there is no path between i and j, weight[i][j] should
			be 0 */

char inTree[100]; /* inTree[i] is 1 if the node i is already in the minimum
			spanning tree; 0 otherwise*/

int d[100]; /* d[i] is the distance between node i and the minimum spanning
		tree; this is initially infinity (100000); if i is already in
		the tree, then d[i] is undefined;
		this is just a temporary variable. It's not necessary but speeds
		up execution considerably (by a factor of n) */

int whoTo[100]; /* whoTo[i] holds the index of the node i would have to be
			linked to in order to get a distance of d[i] */

/* updateDistances(int target)
	should be called immediately after target is added to the tree;
	updates d so that the values are correct (goes through target's
	neighbours making sure that the distances between them and the tree
	are indeed minimum)
*/
void updateDistances(int target) {
	int i;
	for (i = 0; i < n; ++i)
		if ((weight[target][i] != 0) && (d[i] > weight[target][i])) {
			d[i] = weight[target][i];
			whoTo[i] = target;
		}
}

int main(int argc, char *argv[]) {
	FILE *f = fopen("dist.txt", "r");
	fscanf(f, "%d", &n);
	int i, j;
	for (i = 0; i < n; ++i)
		for (j = 0; j < n; ++j)
			fscanf(f, "%d", &weight[i][j]);
	fclose(f);

	/* Initialise d with infinity */
	for (i = 0; i < n; ++i)
		d[i] = 100000;

	/* Mark all nodes as NOT beeing in the minimum spanning tree */
	for (i = 0; i < n; ++i)
		inTree[i] = 0;

	/* Add the first node to the tree */
	printf("Adding node %c\n", 0 + 'A');
	inTree[0] = 1;
	updateDistances(0);

	int total = 0;
	int treeSize;
	for (treeSize = 1; treeSize < n; ++treeSize) {
		/* Find the node with the smallest distance to the tree */
		int min = -1;
		for (i = 0; i < n; ++i)
			if (!inTree[i])
				if ((min == -1) || (d[min] > d[i]))
					min = i;

		/* And add it */
		printf("Adding edge %c-%c\n", whoTo[min] + 'A', min + 'A');
		inTree[min] = 1;
		total += d[min];

		updateDistances(min);
	}

	printf("Total distance: %d\n", total);

	return 0;
}