feat: Implement Kadane's Algorithm for Maximum Subarray Sum

[Harsh-Kumar-Mishra2006]

Overview

This PR adds an implementation of Kadane's Algorithm, an efficient dynamic programming approach to solve the Maximum Subarray Sum problem in O(n) time.

Details

• Problem: Find the contiguous subarray with the maximum sum within a given one-dimensional array of numbers.
• Approach: Dynamic Programming (Kadane's Algorithm)
• Time Complexity: O(n)
• Space Complexity: O(1)

Implementation Highlights

• Implements both basic and enhanced versions of Kadane's Algorithm
• Basic version returns only the maximum sum
• Enhanced version returns the sum along with subarray indices
• Includes comprehensive test cases covering various scenarios
• Handles edge cases: empty arrays, all negative numbers, single elements
• Clean, commented, and easy-to-follow C++ code

Example

Input: [-2, 1, -3, 4, -1, 2, 1, -5, 4]
Output: 6 (Subarray: [4, -1, 2, 1])

Files Added

• algorithms/kadane_algorithm.cpp - Complete implementation with test cases

Key Features

• ✅ Follows dynamic programming approach as requested in issue Add Kadane's Algorithm for Maximum Subarray Sum (DP Approach) #25
• ✅ O(n) time complexity with O(1) space complexity
• ✅ Comprehensive test suite with multiple edge cases
• ✅ Well-documented code with clear comments
• ✅ Enhanced version that can return the actual subarray