Implement Union-Find (Disjoint Set) data structure

Create an efficient implementation of the Union-Find (Disjoint Set) data structure:

## Core operations:
- MakeSet - Create a new set with a single element
- Find - Determine which set an element belongs to
- Union - Merge two sets

## Optimizations to implement:
- Path compression for Find operation
- Union by rank/size
- Path splitting
- Path halving

## Applications to demonstrate:
- Kruskal's algorithm for MST
- Cycle detection in undirected graphs
- Connected components in a graph
- Least common ancestor in trees
- Percolation problems

## Requirements:
- Provide detailed complexity analysis
- Include amortized analysis
- Create comprehensive test cases
- Document practical applications

This data structure is fundamental for efficient implementations of many graph algorithms and has applications in network connectivity problems.