Data Structures and Algorithms

# What is Dijkstra Algorithm and How Does it Work?

In this article, I will explain What is Dijkstra Algorithm and How Does it Work.

Basically, Dijkstra’s algorithm is a greedy algorithm used to find the shortest path between a source vertex and all other vertices in a weighted graph. It works by initially assigning a tentative distance to each vertex in the graph, which is set to infinity for all vertices except the source vertex, which is set to zero.

At each step, Dijkstra’s algorithm selects the vertex with the smallest tentative distance and relaxes all edges that connect the selected vertex to its adjacent vertices. Furthermore, relaxing an edge means updating the tentative distance of the adjacent vertex if it can be improved by going through the selected vertex. The algorithm repeats this process until all vertices have been visited or the smallest tentative distance is infinity, which indicates that the remaining vertices are not connected to the source vertex.

In fact, we can implement Dijkstra’s algorithm using a priority queue to efficiently select the vertex with the smallest tentative distance at each step. Also, the time complexity of Dijkstra’s algorithm is O(E log V), where E is the number of edges in the graph and V is the number of vertices. Moreover, if the graph is represented using an adjacency matrix, the time complexity can be improved to O(V^2) using an array instead of a priority queue.

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