Optimised Space Complexity To O(sum)

[sankethl27]

fixes #5600

Problem:

This PR implements a solution to the "Subset Sum Equals to K" problem using dynamic programming while optimizing space complexity from O(n * sum) to O(sum). The problem is to determine whether there is a subset of a given array whose sum is exactly equal to a target integer K.

Approach:

The standard DP approach for the subset sum problem involves creating a 2D table where each entry dp[i][j] represents whether a subset of the first i elements of the array can sum to j. This has a space complexity of O(n * sum), where n is the number of elements in the array and sum is the target sum.

To optimize space complexity, we can use a 1D array of size sum + 1 instead of the 2D table. The key idea is that the current state of the DP table only depends on the previous row (i.e., whether the sum was possible with or without the current element). Thus, we can update the DP array in reverse order, ensuring that we do not overwrite values that are still needed.

Space Optimization:

The space-optimized approach reduces the space complexity to O(sum) by reusing a 1D DP array. At each iteration, we update the DP array from right to left to ensure we only use the previous values from the last iteration.

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• 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.
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[codecov-commenter]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 58.93%. Comparing base (0603acc) to head (73c7fc1).

Additional details and impacted files

@@             Coverage Diff              @@
##             master    #5651      +/-   ##
============================================
- Coverage     58.94%   58.93%   -0.02%     
+ Complexity     3773     3771       -2     
============================================
  Files           556      556              
  Lines         15945    15942       -3     
  Branches       3040     3038       -2     
============================================
- Hits           9399     9395       -4     
- Misses         6143     6144       +1     
  Partials        403      403              

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[sankethl27]

Hey @alxkm Thanks for the feedback.
I have Optimised the code to use single dp Array and Also removed the line which was cloning the array.
Let me know if there is anything else i can do to optimise the code further.

[alxkm]

Thank you for your contribution.