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Split Array Largest Sum

Updated: Mar 16, 2021

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)

Solution:

class Solution {
    public int splitArray(int[] nums, int m) {
        int left=0, right =0,mid;
        for(int i:nums)
        {
            left=Math.max(left,i);
            right+=i;
        }   
        while (left < right)
        {
            mid = left + (right - left) / 2;
            if(cansplit(mid,nums,m))
                right = mid;    
            else
                left = mid + 1; 
        }
        
    return left;
    }
    private boolean cansplit(int sum,int[] nums,int m)
    {
        int count = 1,total = 0;
        for (int n:nums)
        {
            total += n;
            if (total > sum)
            {
                 total = n;
                count++;
            }  
             if (count > m)
                    return false;
        }     
        return true;
    }
}


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