Added Dinic’s Max Flow algorithm with tests [Graphs]

[SamXop123]

Add Dinic’s Max Flow algorithm with tests

Summary

• What: Implemented Dinic’s algorithm for maximum flow and added unit tests. Updated project index.
• Why: Complements existing max-flow implementations (e.g., EdmondsKarp) with a typically faster algorithm on many graphs.
• How: Level graph via BFS + blocking-flow DFS with current-edge optimization; mirrors input validation and API style used by EdmondsKarp.

Changes

• [new] src/main/java/com/thealgorithms/graph/Dinic.java
  • Public API: Dinic.maxFlow(int[][] capacity, int source, int sink).
  • Validates input matrix (square, non-null, non-negative capacities).
  • Builds level graph (BFS), finds blocking flow (DFS), updates residual capacities.
  • Javadoc includes reference:
    • @see https://en.wikipedia.org/wiki/Dinic%27s_algorithm
• [new] src/test/java/com/thealgorithms/graph/DinicTest.java
  • CLRS network example → expected flow 23.
  • Edge cases: disconnected graph, source == sink, invalid matrix shape.
  • Parity test vs EdmondsKarp on random small graphs (same max flow).
• [updated] DIRECTORY.md
  • Added Dinic to the graph/ section.

Complexity

• Worst-case time: O(E · V^2).
• Typically faster in practice; near O(E · sqrt(V)) on unit networks.

How to verify

• Local:

  mvn -q -DskipITs verify

  Ensures compile, tests, Checkstyle, PMD, SpotBugs, and JaCoCo run cleanly.
• CI:
  • All GitHub Actions checks should pass on this PR.

Checklist

• I have read CONTRIBUTING.md.
• This pull request is all my own work.
• Filenames are in PascalCase.
• Functions and variable names follow Java naming conventions.
• New algorithm has a URL in comments (Dinic.java Javadoc).
• Code formatted (ran clang-format) and passes mvn verify.

Issue linkage

• Fixes [FEATURE REQUEST] Add Dinic's Algorithm to the Graph Algorithms #6731

Notes for reviewers

• Kept API and validation consistent with EdmondsKarp.
• Tests include parity checks to ensure identical max-flow values across implementations.
• Happy to add more edge cases or an example of min-cut extraction using the final residual graph if desired.

@SamXop123
Contributor

[codecov-commenter]

Codecov Report

❌ Patch coverage is 84.90566% with 8 lines in your changes missing coverage. Please review.
✅ Project coverage is 77.33%. Comparing base (387ecef) to head (2cfa1b8).

Files with missing lines	Patch %	Lines
src/main/java/com/thealgorithms/graph/Dinic.java	84.90%	3 Missing and 5 partials ⚠️

Additional details and impacted files

@@ Coverage Diff @@ ## master #6762 +/- ## ============================================ + Coverage 77.31% 77.33% +0.01%  - Complexity 6151 6171 +20  ============================================ Files 720 721 +1 Lines 20536 20589 +53 Branches 3974 3992 +18 ============================================ + Hits 15877 15922 +45  - Misses 4052 4055 +3  - Partials 607 612 +5 

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[alxkm]

Looks good. Thank you for the contribution.