Add subset sum algorithm

[AliAlimohammadi]

Description

This PR implements the Subset Sum Problem using dynamic programming. The algorithm determines whether there exists a subset of a given array that sums to a specified target value.

The implementation uses a 2D DP table where dp[i][j] represents whether sum j can be achieved using the first i elements of the array. This is a classic dynamic programming problem with applications in resource allocation, partitioning, and combinatorial optimization.

• Implements subset sum problem using DP approach
• Includes comprehensive test cases with edge cases (empty arrays, zero sum, single elements)
• Time complexity: O(n * sum) where n is array length and sum is the target value
• Space complexity: O(n * sum) for the DP table

Type of change

• New feature (non-breaking change which adds functionality)

Checklist:

• I ran below commands using the latest version of rust nightly.

• I ran cargo clippy --all -- -D warnings just before my last commit and fixed any issue that was found.

• I ran cargo fmt just before my last commit.

• I ran cargo test just before my last commit and all tests passed.

• I added my algorithm to the corresponding mod.rs file within its own folder, and in any parent folder(s).

• I added my algorithm to DIRECTORY.md with the correct link.

• I checked CONTRIBUTING.md and my code follows its guidelines.

• Code structure follows repository patterns

• All tests are included and logically sound

• Documentation is comprehensive with examples

[codecov-commenter]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 95.44%. Comparing base (13710a7) to head (b61bec3).

Additional details and impacted files

@@            Coverage Diff             @@
##           master     #956      +/-   ##
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+ Coverage   95.39%   95.44%   +0.05%     
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  Files         332      333       +1     
  Lines       21496    21524      +28     
==========================================
+ Hits        20506    20544      +38     
+ Misses        990      980      -10     

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[AliAlimohammadi]

Hi @siriak. Could you please take a look at this PR? Thanks.

[Copilot]

Pull request overview

This PR implements the classic subset sum problem using dynamic programming. The algorithm determines whether a subset of a given array can sum to a target value using a 2D DP table approach where dp[i][j] represents if sum j is achievable using the first i elements.

Key changes:

• Adds subset sum DP algorithm with O(n * sum) time/space complexity
• Includes comprehensive test suite using macro-based test generation pattern
• Properly integrates into module system and documentation index

Reviewed changes

Copilot reviewed 3 out of 3 changed files in this pull request and generated 7 comments.

File	Description
src/dynamic_programming/subset_sum.rs	New implementation of subset sum algorithm with DP approach, includes function implementation and test suite
src/dynamic_programming/mod.rs	Adds module declaration and public export for is_sum_subset function
DIRECTORY.md	Adds entry for Subset Sum in the dynamic programming algorithms directory listing

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[siriak]

Please check the comments

[siriak]

Looks good, thanks!