## Maximum Subarray

06/27/2016 Array Dynamic Programming Divide and Conquer

## Question

Find the contiguous subarray within an array (containing at least one number) which has the largest sum.

For example, given the array [−2,1,−3,4,−1,2,1,−5,4], the contiguous subarray [4,−1,2,1] has the largest sum = 6.

More practice:

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

## Solution

Result: Accepted Time: 4 ms

Here should be some explanations.

int maxSubArray(int* nums, int numsSize) {
if(!numsSize)
return 0;
int max_sum = nums[0],sum = nums[0];
for(int i = 1; i < numsSize; i++)
{
sum = sum > 0 ? (nums[i] + sum) : (nums[i]);
max_sum = sum > max_sum ? sum:max_sum;
}
return max_sum;
}


Complexity Analytics

• Time Complexity: $O(n)$
• Space Complexity: $O(1)$