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Maximum Subarray Sum

Certification: Advanced Level Accuracy: 100% Submissions: 2 Points: 10

Write a Python function that finds the contiguous subarray within a one-dimensional number array with the largest sum using Kadane's algorithm.

Example 1
    
  
  • Input: [-2, 1, -3, 4, -1, 2, 1, -5, 4]
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  • Output: 6
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  • Explanation:
    
      
      
    • Step 1: Initialize variables for current sum and maximum sum to the first element.
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    • Step 2: Iterate through the array, updating the current sum at each step.
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    • Step 3: For each element, decide whether to extend the current subarray or start a new one.
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    • Step 4: The contiguous subarray [4, -1, 2, 1] has the largest sum = 6.
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    • Step 5: Return 6 as the maximum sum.
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Example 2
    
  
  • Input: [1, -2, 3, -2, 5]
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  • Output: 6
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  • Explanation:
    
      
      
    • Step 1: Initialize variables for current sum and maximum sum.
      • 
      
    • Step 2: Iterate through the array, maintaining a running sum.
      • 
      
    • Step 3: Reset the current sum to zero if it becomes negative.
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    • Step 4: The contiguous subarray [3, -2, 5] has the largest sum = 6.
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    • Step 5: Return 6 as the maximum sum.
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Constraints
    
  
  • 1 ≤ len(nums) ≤ 10^5
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  • -10^4 ≤ nums[i] ≤ 10^4
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  • Time Complexity: O(n), where n is the length of the input array
    • 
  
  • Space Complexity: O(1)
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ArraysFunctions / MethodsGoogleDeloitte
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Hint
Solution

Solution Hints

    
  
  • Initialize two variables: max_so_far = nums[0] and max_ending_here = nums[0]
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  • Iterate through the array starting from the second element
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  • For each element, update max_ending_here = max(nums[i], max_ending_here + nums[i])
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  • Update max_so_far = max(max_so_far, max_ending_here)
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  • The final value of max_so_far will be the maximum subarray sum
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  • Handle empty array as a special case
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Steps to solve by this approach:

 Step 1: Initialize two variables: max_so_far and max_ending_here with the first element.

 Step 2: Iterate through the array starting from the second element.

 Step 3: For each element, update max_ending_here as max(current element, max_ending_here + current element).

 Step 4: Update max_so_far as max(max_so_far, max_ending_here).

 Step 5: Continue until all elements are processed.

 Step 6: Return max_so_far as the maximum subarray sum.

Submitted Code :