[LeetCode] 410. Split Array Largest Sum

Problem

Given an array 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.

Note:
If n is the length of array, assume the following constraints are satisfied:

1 ≤ n ≤ 1000
1 ≤ m ≤ min(50, n)
Examples:

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.

Solution

class Solution {
    public int splitArray(int[] nums, int m) {
        long sum = 0L, max = 0L;
        for (int num: nums) {
            sum += (long) num;
            max = (long) Math.max(max, num);
        }
        
        if (m == 1) return (int) sum;
        
        long l = max, r = sum;
        while (l <= r) {
            long mid = l + (r-l)/2;
            if (valid(nums, mid, m)) r = mid-1;
            else l = mid+1;
        }
        
        return (int) l;
    }
    
    private boolean valid(int[] nums, long target, int m) {
        int count = 1;
        long sum = 0L;
        for (int num: nums) {
            sum += num;
            if (sum > target) {
                count++;
                sum = num;
                if (count > m) return false;
            }
        }
        return true;
    }
}