Single Source Shortest Path using Dijkstra’s Algorithm | Greedy Method Explained
In this video, we dive deep into Dijkstra's Algorithm, a popular Greedy Method approach to solving the Single Source Shortest Path problem in graph theory.We begin by discussing the real-world applications of graphs, such as airport networks and highway structures [00:19]. You will learn how the algorithm uses the Node Relaxation technique [05:13] to find the shortest path from a source vertex to all other vertices in a weighted graph with non-negative edges.
The tutorial includes:
An introduction to optimization problems and the greedy approach.
A detailed step-by-step walkthrough of a 6-vertex graph example [05:29].
An explanation of the cost adjacency matrix and distance arrays.A breakdown of the algorithm's pseudocode [16:38].
Time complexity analysis O(n^2) [19:28].
Key Topics Covered:
[00:00] Introduction to Single Source Shortest Path
[01:48] Problem Definition & Greedy Strategy
[02:40] Constraints of Dijkstra's Algorithm
[03:24] Node Relaxation Technique Explained
[05:29] Step-by-Step Numerical Example
[16:28] Dijkstra's Algorithm Pseudocode
[19:28] Time Complexity Analysis
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