# 53. Maximum Subarray

## Problem statement

Given an integer array `nums`, find the contiguous subarray (containing at least one number) which has the largest sum and return *its sum*.

A **subarray** is a **contiguous** part of an array.

### Example 1

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

### Example 2

```plaintext
Input: nums = [1]
Output: 1
```

### Example 3

```plaintext
Input: nums = [5,4,-1,7,8]
Output: 23
```

### Constraints

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

## Solution

The subarrays you want to find should not have negative prefix sums. A negative prefix sum would make the sum of the subarray smaller.

### Example 1

For `nums = [-2,1,-3,4,-1,2,1,-5,4]`, `[-2]` or `[-2,1]` or `[-2,1,-3]` should not be a prefix of the subarrays you want to find. Since it makes the sum of the result smaller.

### Code

```cpp
int maxSubArray(vector<int>& nums) {
    int maxSum = -10000;
    int currSum = 0;
    for (auto& num : nums) {
        currSum = currSum < 0 ? num : currSum + num;
        maxSum = max(maxSum, currSum);
    }
    return maxSum;
}
int main() {
    vector<int> nums = {-2,1,-3,4,-1,2,1,-5,4};
    cout << maxSubArray(nums) << endl;
    nums = {1};
    cout << maxSubArray(nums) << endl;
    nums = {5,4,-1,7,8};
    cout << maxSubArray(nums) << endl;
}
```

```plaintext
Output:
6
1
23
```

### Complexity

* Runtime: `O(N)`, where `N = nums.length`.
    
* Extra space: `O(1)`.
    

## References

* [https://leetcode.com/problems/maximum-subarray/](https://leetcode.com/problems/maximum-subarray/)
    

*Thanks for reading. Feel free to share your thought about my content and check out my* [***FREE book “10 Classic Coding Challenges”***](https://nhutnguyen.gumroad.com/l/10_classic)*.*