Split Array Largest Sum

410. Split Array Largest Sum

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.
``````
``````public class Solution {
public int splitArray(int[] nums, int m) {
if (nums == null || nums.length == 0) {
return 0;
}

int max = 0;
long sum = 0;

for (int num : nums) {
max = Math.max(max, num);
sum += num;
}

if (m == 1) {
return (int)sum;
}

long left = max, right = sum;

while (left <= right) {
long middle = left + (right - left) / 2;

if (valid(nums, m, middle)) {
right = middle - 1;
} else {
left = middle + 1;
}
}

return (int)left;
}

private boolean valid(int[] nums, int m, long target) {
int count = 1;
long sum = 0;

for (int num : nums) {
sum += num;

if (sum > target) {
sum = num;
count++;

if (count > m) {
return false;
}
}
}

return true;
}
}
``````

Hope this helps,
Michael