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Split Array Largest Sum

Problem Statement​

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.

Leetcode link

Examples​

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)

Code​

Python3 Code
class Solution:
    def splitArray(self, nums: List[int], m: int) -> int:
        lo, hi = max(nums), sum(nums)
        while lo < hi:
            mid = (lo+hi)//2
            tot, cnt = 0, 1
            for num in nums:
                if tot+num<=mid:
                    tot += num
                else:
                    tot = num
                    cnt += 1
            if cnt>m: lo = mid+1
            else: hi = mid
        return hi