Add 10 graph interview questions with 2 approaches each

[Copilot]

Overview

This PR adds a comprehensive collection of graph algorithm interview questions to the repository, following the request to "add 10 graph interview and answer with 2 approach for each questions".

Changes

Created a new file graphProblems.js containing 10 common graph algorithm problems, each implemented with 2 different approaches to demonstrate alternative problem-solving techniques.

Graph Problems Included

1. Depth First Search (DFS) - Recursive and Iterative (Stack-based) implementations
2. Breadth First Search (BFS) - Queue-based and Level-order traversal approaches
3. Detect Cycle in Directed Graph - DFS with recursion stack and Color-based detection (White/Gray/Black)
4. Detect Cycle in Undirected Graph - DFS with parent tracking and Union-Find (Disjoint Set)
5. Shortest Path (Dijkstra's Algorithm) - Priority Queue implementation and Array-based approach
6. Topological Sort - DFS-based and Kahn's Algorithm (BFS-based)
7. Find All Paths Between Two Nodes - DFS with path tracking and Backtracking with visited set
8. Check if Graph is Bipartite - BFS-based coloring and DFS-based coloring
9. Number of Connected Components - DFS-based counting and Union-Find
10. Clone a Graph - DFS-based cloning and BFS-based cloning

Code Quality

• ✅ All implementations include clear comments explaining the approach
• ✅ Test cases provided for each problem (commented out to avoid console noise)
• ✅ Follows the existing repository coding style and patterns
• ✅ Syntax validated with Node.js
• ✅ Ready to use in both browser and Node.js environments
• ✅ Total of 633 lines of production-ready code

Usage

The new graph problems can be used by:

1. Opening index.html in a browser (script is auto-included)
2. Uncommenting the test console.log statements to see results
3. Calling functions directly from the browser console or in Node.js

Example:

const graph = {
    0: [1, 2],
    1: [3, 4],
    2: [5],
    3: [],
    4: [],
    5: []
};

// Use either approach
console.log(dfsRecursive(graph, 0));  // Approach 1
console.log(dfsIterative(graph, 0));  // Approach 2

This addition complements the existing array, string, number, and object problem sets in the repository.

Original prompt

add 10 graph interview and answer with 2 approach for each questions

---

💡 You can make Copilot smarter by setting up custom instructions, customizing its development environment and configuring Model Context Protocol (MCP) servers. Learn more Copilot coding agent tips in the docs.