W Code - Pattern-Based DSA Learning Platform

Bhanu Bisht

Template

Union Find Template: Pattern, Code & Cheat Sheet

The Union Find pattern is one of the most frequently tested coding interview patterns. Disjoint set union for tracking connected components. This template gives you a reusable code skeleton, pseudocode, and implementation in multiple languages so you can solve 6+ problems using this single mental model.

Difficulty: Medium | Time Complexity: O(α(n)) | Space Complexity: O(n)

When to Use This Template

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

1.Connected components — Problems asking to connected components

2.Kruskal's MST — Problems asking to kruskal's mst

3.Redundant connections — Problems asking to redundant connections

Prerequisites: Graph basics

Problem count on W Code: 6 problems across Easy, Medium, and Hard difficulty levels.

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

Pseudocode Template

function union_findSolve(input):
    // Initialize data structures
    result = initial_value
    
    // Core logic for Union Find
    for each element in input:
        process(element)
        update(result)
    
    return result

Python Implementation

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

Java Implementation

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

C++ Implementation

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

Variations & Adaptations

The Union Find pattern has several variations you should master:

Variation 1: Basic Union-Find

This variation is useful when the problem specifically requires basic union-find. Adapt the main template by modifying the core loop/recursion logic accordingly.

Variation 2: Union by Rank

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

Variation 3: Path Compression

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

Variation 4: Weighted Union-Find

This variation is useful when the problem specifically requires weighted union-find. Adapt the main template by modifying the core loop/recursion logic accordingly.

Common Mistakes & Edge Cases

When implementing Union Find, 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, Kruskal's MST, Redundant connections?

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(α(n)) time and O(n) space

Frequently Asked Questions

What problems can I solve with the Union Find template?

The Union Find template applies to 6+ problems including: Connected components, Kruskal's MST, Redundant connections. Look for problems that involve disjoint set union for tracking connected components..

What is the time complexity of Union Find?

The typical time complexity is O(α(n)) with space complexity of O(n). Some variations may differ.

What should I learn before Union Find?

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

How do I recognize a Union Find problem in an interview?

Key signals: the problem involves connected components; the problem involves kruskal's mst; the problem involves redundant connections. Practice identifying these cues by solving at least 10 problems using this pattern.

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