• I have read CONTRIBUTING.md.
• This pull request is all my own work -- I have not plagiarized it.
• All filenames are in PascalCase.
• All functions and variable names follow Java naming conventions.
• All new algorithms have a URL in their comments that points to Wikipedia or other similar explanations.
• All new algorithms include a corresponding test class that validates their functionality.
• All new code is formatted with clang-format -i --style=file path/to/your/file.java

Description

Adds an implementation of Optimal Binary Search Tree using dynamic programming with Knuth's optimization.

The implementation:

• sorts keys while preserving their frequencies
• computes the minimum weighted search cost
• validates null inputs, mismatched array lengths, duplicate keys, and negative frequencies

This pull request adds:

• OptimalBinarySearchTree
• OptimalBinarySearchTreeTest

Closes #7309

Test Case

Validated with:

• empty input -> cost 0
• single key -> cost equals its frequency
• small known examples with fixed expected costs
• reference example:
  • keys: [12, 10, 20, 42, 25, 37]
  • frequencies: [8, 34, 50, 3, 40, 30]
  • expected cost: 324
• cross-check cases against a brute-force recursive solver
• invalid input cases:
  • null arrays
  • mismatched lengths
  • duplicate keys
  • negative frequencies

Commands used:

• mvn -Dtest=OptimalBinarySearchTreeTest test
• mvn -DskipTests checkstyle:check