feat: Added Gomory–Hu Tree (all-pairs min-cuts via n1 max-flows)

[SamXop123]

Add Gomory–Hu Tree (all-pairs min-cuts via n−1 max-flows)

Summary

• Implements the Gomory–Hu tree for undirected graphs.
• API: GomoryHuTree.buildTree(int[][] cap) -> int[][] returns {parent, weight} arrays.

Files

• src/main/java/com/thealgorithms/graph/GomoryHuTree.java
• src/test/java/com/thealgorithms/graph/GomoryHuTreeTest.java
• DIRECTORY.md (entry added)

Algorithm

• For s = 1..n-1: compute max-flow between s and parent[s] (initially 0), collect the min-cut partition via reachability in the final residual graph, reassign parents on s’s side, and perform the parent re-linking step.
• The resulting tree satisfies: min edge on the unique path between s and t equals the s–t min-cut in the original graph.

API

• buildTree(int[][] cap) -> { parent, weight }
• parent[0] = -1, weight[0] = 0
• Input: square, non-negative matrix; symmetric for undirected graphs.

Tests

• Single-node graph
• Triangle undirected graph
• Random small symmetric graphs (n ≤ 6), verifying for all pairs (s, t) that the min edge along the tree path equals Edmonds–Karp max-flow.

Reference

• Wikipedia: https://en.wikipedia.org/wiki/Gomory%E2%80%93Hu_tree

Formatting & Conventions

• Class-level Javadoc includes the reference link.
• clang-format applied to new files.
• Follows package/naming conventions.

Issue Linkage

• Fixes [FEATURE REQUEST] Add Gomory–Hu Tree (all-pairs min-cuts via n−1 max-flows) #6817

Checklist

• 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 code is formatted with clang-format -i --style=file path/to/your/file.java.

[codecov-commenter]

Codecov Report

❌ Patch coverage is 91.48936% with 8 lines in your changes missing coverage. Please review.
✅ Project coverage is 77.89%. Comparing base (4858ec9) to head (f3c544b).

Files with missing lines	Patch %	Lines
...ain/java/com/thealgorithms/graph/GomoryHuTree.java	92.77%	3 Missing and 3 partials ⚠️
...healgorithms/randomized/MonteCarloIntegration.java	81.81%	1 Missing and 1 partial ⚠️

Additional details and impacted files

@@ Coverage Diff @@ ## master #6818 +/- ## ============================================ + Coverage 77.85% 77.89% +0.04%  - Complexity 6359 6386 +27  ============================================ Files 731 732 +1 Lines 21187 21277 +90 Branches 4140 4161 +21 ============================================ + Hits 16495 16574 +79  - Misses 4034 4040 +6  - Partials 658 663 +5 

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