Implement advanced dynamic programming patterns

Create implementations for advanced dynamic programming patterns:

## Fundamental patterns:
- 0/1 Knapsack
- Unbounded Knapsack
- Longest Common Subsequence
- Longest Increasing Subsequence
- Edit Distance
- Matrix Chain Multiplication

## Advanced patterns:
- State machine DP
- Interval DP
- Tree DP
- Digit DP
- Probability DP
- Bitmasking DP
- DP on broken profile

## Optimization techniques:
- Space optimization
- Recursive to iterative conversion
- Subproblem pruning
- Divide and conquer optimization
- Knuth's optimization

## Requirements:
- Provide detailed state transition formulations
- Include derivation of recurrence relations
- Create comprehensive test cases
- Document practical applications

This collection will demonstrate advanced dynamic programming techniques that go beyond the basics and show how to formulate complex problems as DP solutions.

No files, tests, or entry points are named. Start by surveying the repository's existing algorithm and data-structure implementations to find its organization and conventions, then scope the requested patterns into smaller changes. Done would require implementations, recurrence and state-transition explanations, comprehensive tests, and practical-application documentation for the agreed scope.

Written by the indexing model from the issue text.