410. Split Array Largest Sum

Hard

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Given an array nums which consists of non-negative integers and an integer m, you can split the array into m non-empty continuous subarrays.

Write an algorithm to minimize the largest sum among these m subarrays.

Example 1:

Input: nums = [7,2,5,10,8], m = 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], m = 2
Output: 9

Example 3:

Input: nums = [1,4,4], m = 3
Output: 4

Constraints:

• 1 <= nums.length <= 1000

• 0 <= nums[i] <= 106

• 1 <= m <= min(50, nums.length)

class Solution:
    def splitArray(self, nums: List[int], m: int) -> int:
        low = max(nums) # 10
        high = sum(nums) # 32
        result = -1
        while low <= high:
            mid = (high+low)//2 # 21
            if self.valid_splits(nums, mid, m):
                result = mid
                high = mid - 1
            else:
                low = mid + 1
        return result
    
    def valid_splits(self, nums, mid, m):
        count = 0
        current = 0
        for num in nums:
            if num + current > mid:
                current = 0
                count += 1
            current += num
        return count < m