Bellman Ford Algorithm | Single Source Shortest Path | Dynamic Programming
In this video, we explore the Bellman Ford Algorithm, a powerful dynamic programming approach used to solve the Single Source Shortest Path (SSSP) problem in weighted directed graphs. Unlike Dijkstra's algorithm, Bellman-Ford can handle graphs with negative edge costs, making it a vital tool in graph theory and network routing.
What you will learn in this video:
The core concept of the Single Source Shortest Path problem. [00:09]
Why Dijkstra's algorithm fails with negative edges and how Bellman-Ford solves it. [00:30]
The step-by-step derivation of the Bellman-Ford formula. [02:45]
A complete walkthrough of a 7-vertex graph example across multiple stages. [05:16]
A detailed breakdown of the Bellman-Ford algorithm and its implementation. [34:42]
Time complexity analysis (O(n³) for adjacency matrices and O(n*e) for adjacency lists). [36:42]
Timestamps:
[00:00] - Introduction to Single Source Shortest Path
[00:30] - Bellman-Ford vs. Dijkstra (Handling Negative Edges)
[02:45] - Dynamic Programming Formula & Logic
[04:47] - How many stages are required? (n-1 stages)
[05:16] - Step-by-Step Example (7-Vertex Graph)
[11:59] - Stage 2 & 3 Calculations
[17:56] - Stage 4 & 5 Calculations
[28:48] - Stage 6 (Final Result)
[34:42] - Bellman-Ford Algorithm Code/Pseudocode
[36:42] - Time Complexity Analysis
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