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Bhanu Bisht

Template

Topological Sort Template: Pattern, Code & Cheat Sheet

The Topological Sort pattern is one of the most frequently tested coding interview patterns. Order nodes in a DAG respecting dependencies. This template gives you a reusable code skeleton, pseudocode, and implementation in multiple languages so you can solve 5+ problems using this single mental model.

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

When to Use This Template

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

1.Task scheduling — Problems asking to task scheduling

2.Build systems — Problems asking to build systems

3.Course prerequisites — Problems asking to course prerequisites

Prerequisites: Graph traversal, DFS

Problem count on W Code: 5 problems across Easy, Medium, and Hard difficulty levels.

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

Pseudocode Template

function topological_sortSolve(input):
    // Initialize data structures
    result = initial_value
    
    // Core logic for Topological Sort
    for each element in input:
        process(element)
        update(result)
    
    return result

Python Implementation

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

Java Implementation

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

C++ Implementation

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

Variations & Adaptations

The Topological Sort pattern has several variations you should master:

Variation 1: Kahn's Algorithm (BFS)

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

Variation 2: DFS-based Topological Sort

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

Variation 3: Cycle Detection variant

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

Common Mistakes & Edge Cases

When implementing Topological Sort, 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 Task scheduling, Build systems, Course prerequisites?

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 Topological Sort template?

The Topological Sort template applies to 5+ problems including: Task scheduling, Build systems, Course prerequisites. Look for problems that involve order nodes in a dag respecting dependencies..

What is the time complexity of Topological Sort?

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

What should I learn before Topological Sort?

Prerequisites include: Graph traversal, DFS. Make sure you are comfortable with these concepts first.

How do I recognize a Topological Sort problem in an interview?

Key signals: the problem involves task scheduling; the problem involves build systems; the problem involves course prerequisites. Practice identifying these cues by solving at least 10 problems using this pattern.

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