# 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. Vickey says:

class Solution {

public int firstMissingPositive(int[] A) {

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

for(int num: nums){
if(num>m){