W Code - Pattern-Based DSA Learning Platform

Bhanu Bisht

Template

Graph Traversal Template: Pattern, Code & Cheat Sheet

The Graph Traversal pattern is one of the most frequently tested coding interview patterns. BFS and DFS for exploring graph structures. This template gives you a reusable code skeleton, pseudocode, and implementation in multiple languages so you can solve 16+ problems using this single mental model.

Difficulty: Medium | Time Complexity: O(V + E) | Space Complexity: O(V)

When to Use This Template

Use the Graph Traversal template when you see these signals in a problem:

1.Connected components — Problems asking to connected components

2.Shortest path — Problems asking to shortest path

3.Cycle detection — Problems asking to cycle detection

Prerequisites: Trees, Queues, Adjacency lists

Problem count on W Code: 16 problems across Easy, Medium, and Hard difficulty levels.

If the problem does not match these signals, consider alternative patterns.

Pseudocode Template

function graph_traversalSolve(input):
    // Initialize data structures
    result = initial_value
    
    // Core logic for Graph Traversal
    for each element in input:
        process(element)
        update(result)
    
    return result

Python Implementation

python
def solve(input_data):
    """Graph Traversal solution template."""
    result = []
    # Implement graph traversal logic here
    for item in input_data:
        # Process each item
        result.append(item)
    return result

Java Implementation

java
public Object solve(Object[] input) {
    // Graph Traversal template
    // Implement core logic here
    return null;
}

C++ Implementation

cpp
auto solve(vector<int>& input) {
    // Graph Traversal template
    // Implement core logic
    return result;
}

Variations & Adaptations

The Graph Traversal pattern has several variations you should master:

Variation 1: BFS (Shortest Path)

This variation is useful when the problem specifically requires bfs (shortest path). Adapt the main template by modifying the core loop/recursion logic accordingly.

Variation 2: DFS (Connected Components)

This variation is useful when the problem specifically requires dfs (connected components). Adapt the main template by modifying the core loop/recursion logic accordingly.

Variation 3: Topological Sort

This variation is useful when the problem specifically requires topological sort. Adapt the main template by modifying the core loop/recursion logic accordingly.

Variation 4: Dijkstra's Algorithm

This variation is useful when the problem specifically requires dijkstra's algorithm. Adapt the main template by modifying the core loop/recursion logic accordingly.

Common Mistakes & Edge Cases

When implementing Graph Traversal, watch out for:

1.Off-by-one errors — Carefully handle boundary conditions in loops

2.Missing base case — Ensure recursion terminates properly

3.Integer overflow — Use appropriate data types for large inputs

4.Empty input — Handle null/empty arrays, strings, or graphs

5.Single element — Test with minimal inputs

Edge cases to always test:

•Empty input → expected output

•Single element → correct result

•All same elements → no infinite loop

•Maximum constraints → within time limit

Step-by-Step Problem Solving Guide

1.Identify the pattern: Does the problem involve Connected components, Shortest path, Cycle detection?

2.Choose the template: Select the variation from above that best fits

3.Define variables: Map problem-specific entities to template variables

4.Implement the core logic: Fill in the template skeleton

5.Handle edge cases: Add boundary checks

6.Verify with examples: Trace through sample inputs

7.Analyze complexity: Confirm O(V + E) time and O(V) space

Frequently Asked Questions

What problems can I solve with the Graph Traversal template?

The Graph Traversal template applies to 16+ problems including: Connected components, Shortest path, Cycle detection. Look for problems that involve bfs and dfs for exploring graph structures..

What is the time complexity of Graph Traversal?

The typical time complexity is O(V + E) with space complexity of O(V). Some variations may differ.

What should I learn before Graph Traversal?

Prerequisites include: Trees, Queues, Adjacency lists. Make sure you are comfortable with these concepts first.

How do I recognize a Graph Traversal problem in an interview?

Key signals: the problem involves connected components; the problem involves shortest path; the problem involves cycle detection. Practice identifying these cues by solving at least 10 problems using this pattern.

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