Umesh Chandra

Dijkstra’s algorithm allows us to find the shortest path between any two vertices of a graph.

How Dijkstra’s Algorithm works

Dijkstra’s Algorithm works on the basis that any subpath B -> D of the shortest path A -> D between vertices A and D is also the shortest path between vertices B and D.

Djikstra used this property in the opposite direction i.e we overestimate the distance of each vertex from the starting vertex. Then we visit each node and its neighbors to find the shortest subpath to those neighbors.

The algorithm uses a greedy approach in the sense that we find the next best solution hoping that the end result is the best solution for the whole problem.

Implementation of Dijkstra’s Algorithm:

#include <limits.h>
#include <stdbool.h>
#include <stdio.h>

#define V 9

int minDistance(int dist[], bool sptSet[])
{
	// Initialize min value
	int min = INT_MAX, min_index;

	for (int v = 0; v < V; v++)
		if (sptSet[v] == false && dist[v] <= min)
			min = dist[v], min_index = v;

	return min_index;
}

void printSolution(int dist[])
{
	printf("Vertex \t\t Distance from Source\n");
	for (int i = 0; i < V; i++)
		printf("%d \t\t\t\t %d\n", i, dist[i]);
}


void dijkstra(int graph[V][V], int src)
{
	int dist[V];

	bool sptSet[V];	for (int i = 0; i < V; i++)
		dist[i] = INT_MAX, sptSet[i] = false;

	dist[src] = 0;

	for (int count = 0; count < V - 1; count++) {
		int u = minDistance(dist, sptSet);

		sptSet[u] = true;

		for (int v = 0; v < V; v++)

			if (!sptSet[v] && graph[u][v]
				&& dist[u] != INT_MAX
				&& dist[u] + graph[u][v] < dist[v])
				dist[v] = dist[u] + graph[u][v];
	}

	printSolution(dist);
}

int main()
{
	int graph[V][V] = { { 0, 4, 0, 0, 0, 0, 0, 8, 0 },
						{ 4, 0, 8, 0, 0, 0, 0, 11, 0 },
						{ 0, 8, 0, 7, 0, 4, 0, 0, 2 },
						{ 0, 0, 7, 0, 9, 14, 0, 0, 0 },
						{ 0, 0, 0, 9, 0, 10, 0, 0, 0 },
						{ 0, 0, 4, 14, 10, 0, 2, 0, 0 },
						{ 0, 0, 0, 0, 0, 2, 0, 1, 6 },
						{ 8, 11, 0, 0, 0, 0, 1, 0, 7 },
						{ 0, 0, 2, 0, 0, 0, 6, 7, 0 } };


	dijkstra(graph, 0);

	return 0;
}