Add Yen’s K-shortest loopless paths with tests [GRAPHS]

[SamXop123]

Yen’s K-shortest loopless paths with tests

Summary

• What: Implement YensKShortestPaths to compute up to K loopless shortest paths in a directed, non-negative weighted graph.
• Why: Enables alternative path analysis beyond the single shortest path, complementing existing graph algorithms.
• How: Yen’s algorithm using Dijkstra to compute spur paths, a candidate min-heap ordered by total cost with deterministic tie-breaking, and loopless constraints.

Changes

• [new] src/main/java/com/thealgorithms/graph/YensKShortestPaths.java
  • Public API: List<List<Integer>> kShortestPaths(int[][] weights, int src, int dst, int k).
  • Input contract: adjacency matrix with -1 for no edge; otherwise non-negative weights.
  • Validations: square matrix, valid indices, k >= 1, weights >= -1.
• [new] src/test/java/com/thealgorithms/graph/YensKShortestPathsTest.java
  • Basic small-graph K-paths with deterministic ordering.
  • K larger than available paths.
  • No path returns empty list.
  • Source equals destination returns trivial path.
  • Negative weight rejection (values < -1).
• [updated] DIRECTORY.md
  • Added YensKShortestPaths under the graph/ section.

Complexity

• Approximately O(K · (V + E) log V) per spur iteration (depends on Dijkstra and graph density).

How to verify

mvn -q -DskipITs verify

• Ensures compile, tests, and quality gates (Checkstyle, PMD, SpotBugs).
• Code formatted via clang-format with --style=file.

References

• Wikipedia: https://en.wikipedia.org/wiki/Yen%27s_algorithm

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 (will add if maintainers request).
• Code formatted (clang-format) and mvn verify passes locally.

Issue linkage

• Fixes [FEATURE REQUEST] Add Yen’s K-shortest loopless paths algorithm to Graphs #6772

Notes for reviewers

• The implementation uses an adjacency matrix for consistency with many graph algorithms in this repo.
• Tie-breaking is deterministic (cost, then lexicographic on node sequences) to stabilize test outputs.
• Happy to add an adjacency-list variant in a follow-up if preferred.

[codecov-commenter]

Codecov Report

❌ Patch coverage is 73.75000% with 42 lines in your changes missing coverage. Please review.
✅ Project coverage is 77.40%. Comparing base (8b8434c) to head (31e8229).

Files with missing lines	Patch %	Lines
...va/com/thealgorithms/graph/YensKShortestPaths.java	81.42%	13 Missing and 13 partials ⚠️
...rithms/datastructures/bloomfilter/BloomFilter.java	20.00%	8 Missing and 8 partials ⚠️

Additional details and impacted files

@@             Coverage Diff              @@
##             master    #6773      +/-   ##
============================================
- Coverage     77.42%   77.40%   -0.02%     
- Complexity     6208     6240      +32     
============================================
  Files           722      723       +1     
  Lines         20680    20839     +159     
  Branches       4019     4064      +45     
============================================
+ Hits          16012    16131     +119     
- Misses         4055     4075      +20     
- Partials        613      633      +20     

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[alxkm]

Looks good. Thank you for the contribution.