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Split Array Largest Sum

Certification: Advanced Level Accuracy: 100% Submissions: 1 Points: 15

Write a Java program to split an array into m non-empty continuous subarrays. The objective is to minimize the largest sum among these m subarrays. Your task is to find and return this minimized largest subarray sum.

Example 1
    
  
  • Input: nums = [7,2,5,10,8], m = 2
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  • Output: 18
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  • Explanation:
    
      
      
    • Step 1: We need to split the array into 2 subarrays.
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    • Step 2: There are several ways to split the array, such as [7,2,5] and [10,8], or [7,2] and [5,10,8].
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    • Step 3: Among all possible splits, the one with the minimum largest subarray sum is [7,2,5] and [10,8].
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    • Step 4: The first subarray sum is 7+2+5=14, the second subarray sum is 10+8=18.
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    • Step 5: The largest of these sums is 18, which is the minimum largest subarray sum possible.
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Example 2
    
  
  • Input: nums = [1,2,3,4,5], m = 3
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  • Output: 6
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  • Explanation:
    
      
      
    • Step 1: We need to split the array into 3 subarrays.
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    • Step 2: The optimal split is [1,2], [3], and [4,5].
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    • Step 3: The subarray sums are 3, 3, and 9.
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    • Step 4: The largest sum among these is 9.
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    • Step 5: No other split results in a smaller maximum subarray sum.
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Constraints
    
  
  • 1 ≤ nums.length ≤ 1000
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  • 0 ≤ nums[i] ≤ 10^6
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  • 1 ≤ m ≤ min(50, nums.length)
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  • Time Complexity: O(n * log(sum of array))
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  • Space Complexity: O(1)
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Hint
Solution

Solution Hints

    
  
  • This problem can be solved using binary search on the answer.
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  • Define a search range where the minimum possible answer is max(nums) and the maximum possible answer is sum(nums).
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  • For each mid value, check if it's possible to split the array into m or fewer subarrays such that the largest sum doesn't exceed mid.
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  • If it's possible, search in the left half to find a smaller answer.
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  • If it's not possible, search in the right half for a larger answer.
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Steps to solve by this approach:

 Step 1: Define the search space for binary search, where left = maximum element in array and right = sum of all elements.

 Step 2: Perform binary search on this range to find the minimum largest subarray sum.

 Step 3: For each mid value, check if it's possible to split the array into m or fewer subarrays with maximum sum not exceeding mid.

 Step 4: If possible, search for an even smaller value by setting right = mid.

 Step 5: If not possible, search for a larger value by setting left = mid + 1.

 Step 6: The binary search continues until left and right converge, at which point we've found the minimum largest subarray sum.

 Step 7: Return the final left value as the answer.

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