Matsushita's Blog

Maximum Subarray


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.


By dynamic programming, we can solve this problem in O(N) time.

Make Recurrence Relation

We can define dp(i) following
dp(i) := max(dp(i - 1) + arr[i], arr[i]

This dp(i) means that it is a max value in all subarrays that range is until position i.

Source Code