Add Detailed Solutions for Exercise 3.25 in the Search Exercises Section

[UditNayak]

Issue: #848

This pull request adds the detailed solutions for Exercise 3.25 in the search-exercises section. The exercise involves proving specific relationships between different search algorithms or providing counterexamples where necessary.

Changes

• Created answer.md file for Exercise 3.25.
• Provided proofs and explanations for the following statements:
  • Breadth-first search is a special case of uniform-cost search.
  • Depth-first search is a special case of best-first tree search.
  • Uniform-cost search is a special case of A* search.

Detailed Description

Breadth-First Search as a Special Case of Uniform-Cost Search

• Proof that BFS is a special case of UCS when all edge costs are equal.
• Explained how UCS expands the least-cost node, which mirrors BFS behavior under uniform edge costs.

Depth-First Search as a Special Case of Best-First Tree Search

• Demonstrated that DFS can be seen as a special case of best-first tree search with an evaluation function favoring deeper nodes.
• Detailed how prioritizing nodes with greater depth in best-first search replicates DFS behavior.

Uniform-Cost Search as a Special Case of A* Search

• Proved that UCS is a special case of A* search with a heuristic function ( h(n) = 0 ).
• Explained the evaluation function simplification from ( f(n) = g(n) + h(n) ) to ( f(n) = g(n) ), aligning with UCS criteria.

Please review the changes and provide feedback or approval for merging.