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DecMaximum Subarray Sum Problem
23 Sep 2025
Beginner
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3 min read
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The Maximum Subarray Sum Problem is a classic algorithmic problem where you are given an array of integers (which may include negative numbers) and need to find the contiguous subarray with the largest sum. Return the maximum sum. This problem is efficiently solved using Kadane’s Algorithm.
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Example:
- Input: nums = [-2, 1, -3, 4, -1, 2, 1, -5, 4]
- Output: 6
- Explanation: The subarray [4, -1, 2, 1] has the largest sum = 6.
Logic
Enter an array of numbers (comma-separated) to find the maximum subarray sum.
Program (Python - Kadane’s Algorithm)
The following Python code uses Kadane’s Algorithm to solve the Maximum Subarray Sum Problem efficiently with O(n) time complexity.
def maxSubArray(nums):
max_sum = nums[0]
current_sum = nums[0]
for num in nums[1:]:
current_sum = max(num, current_sum + num)
max_sum = max(max_sum, current_sum)
return max_sum
# Example usage
nums = [-2, 1, -3, 4, -1, 2, 1, -5, 4]
print(maxSubArray(nums)) # Output: 6
Output
For the input nums = [-2, 1, -3, 4, -1, 2, 1, -5, 4], the output is:
6Explanation:
The subarray [4, -1, 2, 1] has the maximum sum of 6.
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