# 410. Split Array Largest Sum

#### Hard

***

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)`

```python
class Solution:
    def splitArray(self, nums: List[int], m: int) -> int:
        low = max(nums) # 10
        high = sum(nums) # 32
        result = -1
        while low <= high:
            mid = (high+low)//2 # 21
            if self.valid_splits(nums, mid, m):
                result = mid
                high = mid - 1
            else:
                low = mid + 1
        return result
    
    def valid_splits(self, nums, mid, m):
        count = 0
        current = 0
        for num in nums:
            if num + current > mid:
                current = 0
                count += 1
            current += num
        return count < m
```