W Code - Pattern-Based DSA Learning Platform

Bhanu Bisht

Template

Backtracking Template: Pattern, Code & Cheat Sheet

The Backtracking pattern is one of the most frequently tested coding interview patterns. Explore all possibilities with systematic pruning. This template gives you a reusable code skeleton, pseudocode, and implementation in multiple languages so you can solve 12+ problems using this single mental model.

Difficulty: Medium | Time Complexity: O(2^n) or O(n!) | Space Complexity: O(n)

When to Use This Template

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

1.Permutations — Problems asking to permutations

2.Subsets — Problems asking to subsets

3.N-Queens — Problems asking to n-queens

4.Sudoku — Problems asking to sudoku

Prerequisites: Recursion

Problem count on W Code: 12 problems across Easy, Medium, and Hard difficulty levels.

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

Pseudocode Template

function backtrack(candidates, path, result):
    if isComplete(path):
        result.add(copy(path))
        return
    
    for each candidate in candidates:
        if isValid(candidate, path):
            path.add(candidate)
            backtrack(remaining, path, result)
            path.removeLast()  // undo choice

Python Implementation

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

Java Implementation

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

C++ Implementation

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

Variations & Adaptations

The Backtracking pattern has several variations you should master:

Variation 1: Subset Generation

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

Variation 2: Permutation Generation

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

Variation 3: Constraint Satisfaction (N-Queens)

This variation is useful when the problem specifically requires constraint satisfaction (n-queens). Adapt the main template by modifying the core loop/recursion logic accordingly.

Variation 4: Graph Coloring

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

Common Mistakes & Edge Cases

When implementing Backtracking, 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 Permutations, Subsets, N-Queens, Sudoku?

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(2^n) or O(n!) time and O(n) space

Frequently Asked Questions

What problems can I solve with the Backtracking template?

The Backtracking template applies to 12+ problems including: Permutations, Subsets, N-Queens, Sudoku. Look for problems that involve explore all possibilities with systematic pruning..

What is the time complexity of Backtracking?

The typical time complexity is O(2^n) or O(n!) with space complexity of O(n). Some variations may differ.

What should I learn before Backtracking?

Prerequisites include: Recursion. Make sure you are comfortable with these concepts first.

How do I recognize a Backtracking problem in an interview?

Key signals: the problem involves permutations; the problem involves subsets; the problem involves n-queens; the problem involves sudoku. Practice identifying these cues by solving at least 10 problems using this pattern.

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