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Speeding up Dijkstra's Algorithm

Demonstrates a way of speeding up the O(n<sup>2</sup>) version of Dijkstra's Algorithm by about 4x.

Here, dist[][] is the adjacency matrix representing the graph and n is the number of nodes. d2[] is where the lengths of the shortest paths are saved.

For a full explanation, see this.

void dijkstra2(int s) {
	int queue[GRAPHSIZE];
	char inQueue[GRAPHSIZE];
	int begq = 0,
	    endq = 0;
	int i, mini;
	int visited[GRAPHSIZE];

	for (i = 1; i <= n; ++i) {
		d2[i] = INFINITY;
		visited[i] = 0; /* the i-th element has not yet been visited */
		inQueue[i] = 0;
	}

	d2[s] = 0;
	queue[endq] = s;
	endq = (endq + 1) % GRAPHSIZE;


	while (begq != endq) {
		mini = queue[begq];
		begq = (begq + 1) % GRAPHSIZE;
		inQueue[mini] = 0;

		visited[mini] = 1;

		for (i = 1; i <= n; ++i)
			if (dist[mini][i])
				if (d2[mini] + dist[mini][i] < d2[i]) { 
					d2[i] = d2[mini] + dist[mini][i];
					if (!inQueue[i]) {
						queue[endq] = i;
						endq = (endq + 1) % GRAPHSIZE;
						inQueue[i] = 1;
					}
				}
	}
}

Dijkstra's Algorithm

This is a simple O(n^2) implementation of Dijkstra's algorithm for finding the shortest paths from a single source to all nodes in a graph.

Further explanation is given here.

#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;
}
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