# Maximum Subarray

## Description

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

**Example:**

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

**Follow up:**

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

## Solutions

### My solution

```cpp
class Solution {
public:
    int maxSubArray(vector<int>& nums) {
        int max_sum = INT_MIN; // maximum subarray sum
        int sum = 0;
        int min_sum = 0; // minimum sum of first k elements
        for(int i = 0; i < nums.size(); ++i){
            sum += nums[i];
            max_sum = max(max_sum, sum - min_sum);
            min_sum = min(min_sum, sum);
        }
        return max_sum;
    }
};
```

### A slightly more efficient solution

```cpp
class Solution {
public:
    int maxSubArray(vector<int>& nums) {
        int ans = INT_MIN;
        int max_sum = 0; // maximum sum of subarray ending with the previous element;
        for(int i = 0; i < nums.size(); ++i){
            // need to consider too cases to update max_sum
            // case 1: without the previous element, i.e., use only the current element:
            //     max_sum = nums[i]
            // case 2: with the previous element:
            //     max_sum = nums[i] + max_sum
            max_sum = max(nums[i], nums[i] + max_sum);
            ans = max(ans, max_sum);
        }
        return ans;
    }
};
```
