Create running_sum_1d_array

[MeloveGupta]

This PR adds the implementation of the Running Sum of 1D Array problem in Python.
The algorithm computes a running (prefix) sum where each element at index i is the sum of all previous elements up to that index.

Key Details:

Algorithm Used: Prefix Sum

Time Complexity: O(n)

Space Complexity: O(n)

Approach:

Initialize an array ans of the same size as nums.

Set the first element of ans equal to nums[0].

Iterate from the second element onward, updating ans[i] = ans[i-1] + nums[i].

Return the resulting list as the running sum.

Files Added:

running_sum_1d_array.py → Main implementation with docstrings and inline examples.

[github-actions]

🎉 Welcome to Hacktoberfest 2025, @MeloveGupta! 🎃

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• ✅ Code Validation: Failed
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[github-actions]

🤖 Automated PR Status

🔍 Code Validation

❌ Failed - Please check file naming conventions and directory structure.

🧪 Compilation Tests

❌ Failed - Please fix compilation errors and try again.

📋 Overall Status

⚠️ Needs Work - Please address the issues above.
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