leetcode/apps/docs/content/(05-decision-space)/greedy/53-maximum-subarray.mdx

---
title: '53. Maximum Subarray'
description: Given an integer array nums, find the subarray with the largest sum, and return its sum
icon: dot
topics:
  - { name: "Array", slug: "array" }
  - { name: "Divide and Conquer", slug: "divide-and-conquer" }
  - { name: "Dynamic Programming", slug: "dynamic-programming" }
sidebar:
  label: 'Maximum Subarray'
  badge: 'Medium'
---

::::warning
If you have figured out the O(n) solution, try coding another solution using the divide and conquer approach, which is more subtle.
::::

### Example 1:
- Input: `nums = [-2,1,-3,4,-1,2,1,-5,4]`
- Output: `6`
- Explanation: The subarray `[4,-1,2,1]` has the largest sum `6`.

### Example 2:
- Input: `nums = [1]`
- Output: `1`
- Explanation: The subarray `[1]` has the largest sum `1`.

### Example 3:
- Input: `nums = [5,4,-1,7,8]`
- Output: `23`
- Explanation: The subarray `[5,4,-1,7,8]` has the largest sum `23`.

### Constraints:

- `1 <= nums.length <= 10^5`
- `-10^4 <= nums[i] <= 10^4`

## Solution

```py
class Solution:
    def maxSubArray(self, nums: list[int]) -> int:
        best, total = nums[0], nums[0]

        for i in range(1, len(nums)):
            if total < 0:
                total = nums[i]
            else:
                total = total + nums[i]
            best = max(best, total)

        return best
```