DisjointForest

A C++ implementation of a disjoint-set data structure (also known as union-find) using the disjoint forest representation with path compression and union by rank optimizations, with Python bindings included as well. This is intended to fill a void in too many existing standard libraries, which don't include a proper implementation of this despite its utility in many applications.

Features

• Template-based: Works with any data type
• Path Compression: Automatically compresses paths during find operations
• Union by Rank: Optimizes union operations by maintaining tree depth information
• Dynamic Operations: Expand capacity, contract nodes, and clear the forest
• Memory Efficient: STL vectors with automatic memory management
• Smart Pointers: Uses std::unique_ptr for automatic memory cleanup
• Exception Safety: Proper error handling with std::invalid_argument and std::runtime_error
• Comprehensive Testing: Full unit test suite using Google Test
• Python Bindings: Full Python interface with pybind11

Class Structure

Node

• data: The actual data stored in the node
• parent: Pointer to the parent node (self-referential for root nodes)
• rank: Depth of the subtree rooted at this node

DisjointForest

• makeSet(T data): Creates a new set containing the given data
• find(Node<T>* node): Finds the representative of the set containing the node
• unionSets(Node<T>* node1, Node<T>* node2): Merges two sets
• Constructor takes the maximum number of elements as parameter

Dynamic Operations

• expand(int additional_capacity): Increases the forest's capacity by the specified amount
• contract(Node<T>* node): Removes a node from the forest, updating parent references
• clear(): Removes all nodes and resets the forest to empty state
• size(): Returns the current number of nodes in the forest
• capacity(): Returns the total capacity allocated for the forest
• isEmpty(): Returns true if the forest contains no nodes
• getAllNodes(): Returns a vector of all current nodes in the forest

Building the Project

Prerequisites

• CMake 3.10 or higher
• C++17 compatible compiler
• Google Test library
• Python 3.6+ (for Python bindings)
• pybind11 (for Python bindings)

Install Google Test

Ubuntu/Debian

sudo apt-get install libgtest-dev

macOS

brew install googletest

CentOS/RHEL/Fedora

sudo yum install gtest-devel
# or for newer versions
sudo dnf install gtest-devel

Arch Linux

sudo pacman -S gtest

Build Steps

Using CMake

# Create build directory
mkdir build
cd build

# Configure and build
cmake ..
make

# Run tests
make test
# or directly
./disjoint_forest_test

# Run example
./disjoint_forest_example

Using Makefile (Alternative)

# Build everything including Python bindings
make all

# Build only C++ components
make cpp

# Build Python bindings
make python-bindings

# Run all tests
make test

# Run Python tests
make python-test

# Run examples
make example
make python-example

# Clean build artifacts
make clean

Running Tests

The test suite covers:

1. Basic Operations: Constructor, destructor, makeSet
2. Find Operations: Single node find, path compression
3. Union Operations: Basic union, union by rank, same set union
4. Dynamic Operations: Expand capacity, contract nodes, clear forest, size/capacity queries
5. Complex Scenarios: Multiple unions, large datasets, dynamic capacity changes
6. Edge Cases: Empty forests, single element forests, contraction edge cases
7. Memory Management: Large operations, proper cleanup, dynamic memory allocation
8. Template Support: Tests with different data types (int, string)

Example Usage

Basic Operations

#include "disjoint_forest.h"

// Create a forest with capacity for 100 elements
DisjointForest<int> forest(100);

// Create some sets
Node<int>* node1 = forest.makeSet(1);
Node<int>* node2 = forest.makeSet(2);
Node<int>* node3 = forest.makeSet(3);

// Union sets
forest.unionSets(node1, node2);
forest.unionSets(node1, node3);

// Find representatives
Node<int>* rep1 = forest.find(node1);
Node<int>* rep2 = forest.find(node2);
Node<int>* rep3 = forest.find(node3);

// All should have the same representative
assert(rep1 == rep2 && rep2 == rep3);

Dynamic Operations

// Expand capacity when needed
forest.expand(50);  // Add capacity for 50 more elements

// Check current state
std::cout << "Size: " << forest.size() << std::endl;
std::cout << "Capacity: " << forest.capacity() << std::endl;
std::cout << "Is empty: " << (forest.isEmpty() ? "Yes" : "No") << std::endl;

// Get all nodes for iteration
auto all_nodes = forest.getAllNodes();
for (auto* node : all_nodes) {
    std::cout << "Node data: " << node->data << std::endl;
}

// Contract (remove) a node
forest.contract(node2);

// Clear the entire forest
forest.clear();

Algorithm Complexity

• makeSet: O(1)
• find: O(α(n)) amortized, where α is the inverse Ackermann function
• unionSets: O(α(n)) amortized
• expand: O(1) amortized (vector doubling strategy)
• contract: O(1) (marking nodes as invalid)
• clear: O(n) where n is the number of nodes
• size/capacity/isEmpty: O(1)
• getAllNodes: O(n) where n is the number of nodes
• Space: O(n) where n is the number of elements

Use Cases

Disjoint-set data structures are fundamental to many algorithms and applications:

• Graph Algorithms: Connected components, minimum spanning trees (Kruskal's algorithm)
• Image Processing: Connected component labeling, flood fill algorithms
• Network Analysis: Community detection, clustering algorithms
• Game Development: Pathfinding, collision detection systems
• Database Systems: Transaction management, dependency resolution
• Compiler Design: Register allocation, live variable analysis

Python Bindings

The project includes Python bindings that provide a unified interface for working with any Python object type. The bindings are built using pybind11 and offer the same functionality as the C++ implementation.

Features

• Type Flexibility: Works with integers, strings, lists, dictionaries, custom objects, etc.
• Unified API: Single DisjointForest class that handles any Python object type
• Safe Operations: Built-in safety checks and error handling
• Memory Management: Automatic cleanup of Python references

Installation

# Install Python dependencies
cd python
pip3 install -r requirements.txt

# Build the Python module
make build

# Test the bindings
make test

# Run the example
make example

Python Usage

import disjoint_forest

# Create a forest
forest = disjoint_forest.DisjointForest(10)

# Create sets with different types
node1 = forest.make_set(42)
node2 = forest.make_set("hello")
node3 = forest.make_set([1, 2, 3])

# Union operations
forest.union_sets(node1, node2)

# Find representatives
rep = forest.find(node1)
print(f"Representative: {rep.data}")

# Dynamic operations
forest.expand(20)
print(f"Capacity: {forest.capacity()}")
print(f"Size: {forest.size()}")

# Get all nodes
all_nodes = forest.get_all_nodes()
for node in all_nodes:
    print(f"Node: {node.data}")

Implementation Details

STL Vector Usage

The implementation uses std::vector instead of fixed-size arrays, providing several advantages:

• Dynamic Capacity: The forest can grow beyond its initial capacity using the expand() method
• Automatic Memory Management: Vectors handle memory allocation and deallocation automatically
• Efficient Resizing: STL vectors use exponential growth strategies for optimal performance
• Exception Safety: Vector operations provide strong exception guarantees

Memory Management

• Smart Pointers: std::unique_ptr ensures automatic cleanup of Node objects
• RAII Principles: Resource acquisition is tied to object lifetime
• Exception Safety: Memory is properly cleaned up even when exceptions occur
• Python Integration: Python bindings include reference counting and safe memory management

Notes

• The implementation automatically handles path compression during find operations
• Union by rank ensures balanced trees for optimal performance
• Memory is automatically managed with proper cleanup in the destructor
• Python bindings provide safe access to all C++ functionality
• Dynamic operations maintain the forest's integrity while allowing flexible capacity management

Troubleshooting

Common Build Issues

Google Test Not Found

If you encounter linking errors with Google Test:

# The Makefile will automatically install Google Test if needed
make install-deps

# Or manually install for your system (see Prerequisites section)

Python Import Errors

If Python can't import the module:

# Ensure the module is built
cd python
make build

# Check if the shared library exists
ls -la *.so

# Verify Python path
python3 -c "import sys; print(sys.path)"

Memory Issues

The implementation uses smart pointers and RAII principles. If you encounter memory issues:

• Ensure you're not manually deleting Node pointers
• Use the provided methods (clear(), contract()) instead of manual memory management
• Check that Python bindings are properly handling object lifetimes

Contributing

We welcome contributions to improve the implementation, test coverage, or documentation. Please:

1. Fork the repository and create a feature branch
2. Follow the existing code style and naming conventions
3. Add tests for new functionality
4. Update documentation to reflect any changes
5. Submit a pull request with a clear description of your changes

Development Setup

# Clone and setup
git clone <your-fork-url>
cd disjoint_set

# Install development dependencies
make install-deps

# Run all tests to ensure everything works
make test
make python-test

# Build everything
make all