Dijkstra's Algorithm Explained | Shortest Path in Weighted Graphs Made Easy | Graph data Structure

Dijkstra's Algorithm is a fundamental algorithm in computer science used to find the shortest path from a source node to all other nodes in a weighted graph. It works efficiently when all edge weights are non-negative. The algorithm was introduced by the Dutch computer scientist Edsger Dijkstra in 1956 and later published in 1959.

The process begins by initializing the distance to all nodes as infinity, except for the source node, which is set to zero. A priority queue (or min-heap) is used to keep track of the nodes with the smallest known distance. At each step, the algorithm removes the node with the smallest distance from the queue and examines its neighbors. For each neighbor, it calculates the new possible distance from the source node through the current node. If this new distance is smaller than the previously recorded distance, it updates the value and adds the neighbor to the priority queue.

This process continues until the priority queue is empty. By the end, the algorithm will have determined the shortest possible distance from the starting node to every other node in the graph. Dijkstra’s approach is greedy in nature—it always chooses the node with the current smallest known distance in each iteration, making it both efficient and effective for a wide range of applications such as routing and navigation systems.

The algorithm does not work correctly with graphs that have negative edge weights, as it assumes that once a node's shortest path is found, it will not need to be updated again. In scenarios with negative weights, algorithms like Bellman-Ford are more appropriate.

Overall, Dijkstra’s algorithm is a reliable and widely-used solution for shortest path problems in graphs with non-negative weights.

[PavanKumar-oyfd]

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[maniReddi]

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