410. Split Array Largest Sum

Problem Link

Description

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Given an integer array nums and an integer k, split nums into k non-empty subarrays such that the largest sum of any subarray is minimized.

Return the minimized largest sum of the split.

A subarray is a contiguous part of the array.

 

Example 1:

Input: nums = [7,2,5,10,8], k = 2
Output: 18
Explanation: There are four ways to split nums into two subarrays.
The best way is to split it into [7,2,5] and [10,8], where the largest sum among the two subarrays is only 18.

Example 2:

Input: nums = [1,2,3,4,5], k = 2
Output: 9
Explanation: There are four ways to split nums into two subarrays.
The best way is to split it into [1,2,3] and [4,5], where the largest sum among the two subarrays is only 9.

 

Constraints:

• 1 <= nums.length <= 1000
• 0 <= nums[i] <= 106
• 1 <= k <= min(50, nums.length)

Solution

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Python3

class Solution:
    def splitArray(self, nums: List[int], m: int) -> int:
        
        def good(x):
            s = 0
            curr = 1
            
            for num in nums:
                s += num
                
                if s > x:
                    s = num
                    curr += 1
                
                if curr > m: return False
            
            return True
        
        left, right = max(nums), (10 ** 6) * 50
        
        while left < right:
            mid = left + (right - left) // 2
            
            if good(mid):
                right = mid
            else:
                left = mid + 1
        
        return left