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

One approach to solving the problem is to use binary search. We can use binary search to search for a largest subarray sum which can make the array split into m parts. The lower bound of the largest subarray sum is the maximum number of the array when m equals the length of the array. The higher bound is the sum of the array when m equals 1. We can base on how many pieces split to adjust the largest subarray sum value.

Python Solution

class Solution:
    def splitArray(self, nums: List[int], m: int) -> int:
        """
        :type nums: List[int]
        :type m: int
        :rtype: int
        """
        n = len(nums)
        
        start = max(nums)
        end = sum(nums)
        
        while start + 1< end:
            mid = start + (end - start) // 2
            
            if self.split_into_pieces(nums, mid) > m:
                start = mid + 1
            else:
                end = mid
                
        if self.split_into_pieces(nums, start) <= m:
            return start
                
        return end
    
    def split_into_pieces(self, nums, largest_sum):
        
        previous_sum = 0
        pieces = 1
        
        for num in nums:
            if previous_sum + num > largest_sum:
                previous_sum = num
                pieces += 1
            else:
                previous_sum += num
        
        return pieces
  • Time Complexity: O(Nlog(N))
  • Space Complexity: O(1)

One Thought to “LeetCode 410. Split Array Largest Sum”

  1. class Solution {

    public int firstMissingPositive(int[] A) {

    int m = 1;
    HashSet set = new HashSet();

    for(int num: nums){
    if(num>m){
    set.add(num);
    }else if(num==m){
    m++;
    while(set.contains(m)){
    set.remove(m);
    m++;
    }
    }
    }
    return m;
    }
    }

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