Dijkstra's Algorithm

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        This is a simple O(n^2) implementation of <a href="http://en.wikipedia.org/wiki/Dijkstra's_algorithm">Dijkstra's algorithm</a> for finding the shortest paths from a single source to all nodes in a graph.

Further explanation is given <a href="http://compprog.wordpress.com/2007/12/01/one-source-shortest-path-dijkstras-algorithm/">here</a>.

#include <stdio.h>

#define GRAPHSIZE 2048
#define INFINITY GRAPHSIZE*GRAPHSIZE
#define MAX(a, b) ((a > b) ? (a) : (b))

int e; /* The number of nonzero edges in the graph */
int n; /* The number of nodes in the graph */
long dist[GRAPHSIZE][GRAPHSIZE]; /* dist[i][j] is the distance between node i and j; or 0 if there is no direct connection */
long d[GRAPHSIZE]; /* d[i] is the length of the shortest path between the source (s) and node i */

void printD() {
	int i;
	for (i = 1; i <= n; ++i)
		printf("%10d", i);
	printf("\n");
	for (i = 1; i <= n; ++i) {
		printf("%10ld", d[i]);
	}
	printf("\n");
}

void dijkstra(int s) {
	int i, k, mini;
	int visited[GRAPHSIZE];

	for (i = 1; i <= n; ++i) {
		d[i] = INFINITY;
		visited[i] = 0; /* the i-th element has not yet been visited */
	}

	d[s] = 0;

	for (k = 1; k <= n; ++k) {
		mini = -1;
		for (i = 1; i <= n; ++i)
			if (!visited[i] && ((mini == -1) || (d[i] < d[mini])))
				mini = i;

		visited[mini] = 1;

		for (i = 1; i <= n; ++i)
			if (dist[mini][i])
				if (d[mini] + dist[mini][i] < d[i]) 
					d[i] = d[mini] + dist[mini][i];
	}
}

int main(int argc, char *argv[]) {
	int i, j;
	int u, v, w;

	FILE *fin = fopen("dist.txt", "r");
	fscanf(fin, "%d", &e);
	for (i = 0; i < e; ++i)
		for (j = 0; j < e; ++j)
			dist[i][j] = 0;
	n = -1;
	for (i = 0; i < e; ++i) {
		fscanf(fin, "%d%d%d", &u, &v, &w);
		dist[u][v] = w;
		n = MAX(u, MAX(v, n));
	}
	fclose(fin);

	dijkstra(1);

	printD();

	return 0;
}

Tags:
• algorithm
• C
• dijkstra
• graph
• path
• shortest path