backtracking: add unique permutation algorithm with test cases

[shreeya-g10]

What does this PR do?

This pull request adds a new backtracking algorithm to generate UNIQUE permutations
of a given string, even when duplicate characters exist.

Features of this contribution:

• Handles duplicate characters using sorted array + duplicate-skip logic
• Uses backtracking with boolean usage tracking
• Generates permutations in lexicographical order
• Time complexity: O(n! * n)

Test Cases Added

Added JUnit test file UniquePermutationTest.java with:

• AAB → ["AAB", "ABA", "BAA"]
• ABC → 6 permutations
• Empty string → [""]
  These ensure correctness and edge case handling.

Folder Structure

• src/main/java/com/thealgorithms/backtracking/UniquePermutation.java
• src/test/java/com/thealgorithms/backtracking/UniquePermutationTest.java

Why this is useful

This algorithm is a fundamental backtracking pattern and
is not currently present in the repository in unique form.
It adds educational value and ensures correctness through test cases.

Validation

• Code compiles successfully
• All tests pass locally using JUnit

• [ x] I have read CONTRIBUTING.md.
• [ x] This pull request is all my own work -- I have not plagiarized it.
• [ x] All filenames are in PascalCase.
• [ x] 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 81.81818% with 4 lines in your changes missing coverage. Please review.
✅ Project coverage is 78.45%. Comparing base (1c97ad8) to head (016a76f).

Files with missing lines	Patch %	Lines
.../thealgorithms/backtracking/UniquePermutation.java	81.81%	3 Missing and 1 partial ⚠️

Additional details and impacted files

@@             Coverage Diff              @@
##             master    #7078      +/-   ##
============================================
- Coverage     78.46%   78.45%   -0.01%     
- Complexity     6738     6745       +7     
============================================
  Files           757      758       +1     
  Lines         22317    22339      +22     
  Branches       4380     4384       +4     
============================================
+ Hits          17510    17527      +17     
- Misses         4104     4107       +3     
- Partials        703      705       +2     

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[alxkm]

Thank you for the contribution.