Summary

1. Depth-first Search:

   • Use for exploring all paths, connectivity checks, or any scenario where deep exploration is required.

2. Breadth-first Search:

   • Use for shortest paths, level-wise exploration, and when you need to explore all possibilities nearest to the starting point first.

3. Dynamic Programming:

   • Use for problems with overlapping subproblems and optimal substructure, where you can break a problem into smaller, solvable subproblems and reuse results.

Which Algorithm to Use?

Problem Type	Use BFS	Use DFS	Use DP
Shortest Path	✅	❌	❌
Exploring All Paths	❌	✅	❌
Finding Any Path	❌	✅	❌
Generating All Solutions	❌	✅	❌
Overlapping Subproblems (e.g., Fibonacci)	❌	❌	✅
Optimal Substructure (e.g., Knapsack)	❌	❌	✅