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# Maximum Subarray / Kadane's Algorithm

Updated: Mar 25, 2021

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

Example 1:

```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:

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

Example 3:

```Input: nums = [0]
Output: 0
```

Example 4:

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

Example 5:

```Input: nums = [-100000]
Output: -100000
```

Constraints:

• 1 <= nums.length <= 3 * 104

• -105 <= nums[i] <= 105

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.

Solution:

Approach 1: Brute Force O(n^2)

```class Solution {
public int maxSubArray(int[] nums) {
int max=Integer.MIN_VALUE;
for(int i=0; i<nums.length;i++)
{
int sum=0;
for(int j=i;j<nums.length;j++)
{
sum+=nums[j];
max=Math.max(max,sum);
}
}
return max;

}
}
```

```class Solution {
public int maxSubArray(int[] nums) {
int sum=nums[0];
int output=nums[0];
for(int i=1; i<nums.length;i++)
{
sum=Math.max(nums[i],sum+nums[i]);
output=Math.max(output,sum);
}
return output;

}
}```