LeetCode 410. Split Array Largest Sum

Description

https://leetcode.com/problems/split-array-largest-sum/

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)

Explanation

Python Solution

class Solution:
    def splitArray(self, nums: List[int], m: int) -> int:
        if not nums:
            return 0
        
        n = len(nums)
        start = max(nums)
        end = sum(nums)
        
        while start + 1 < end:
            largest_sum = (start + end) // 2
            if self.largest_sum_satisfy_m(nums, m, largest_sum):
                end = largest_sum
            else:
                start = largest_sum
                
        if self.largest_sum_satisfy_m(nums, m, start):
            return start
        
        return end
    
    def largest_sum_satisfy_m(self, nums, m, largest_sum):
        num_of_sub = 0
        current_sum = 0
        
        for num in nums:
            if current_sum + num <= largest_sum:
                current_sum += num
            else:
                num_of_sub += 1
                current_sum = num
        num_of_sub += 1
        
        return num_of_sub <= m
            
  • Time Complexity: ~NlogX where X = sum(nums) – max(nums)
  • Space Complexity: ~1.

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