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How do you find the maximum subarray sum?

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01

Understand the problem

Explain Kadane's algorithm.

kadanedp
02

Attempt it yourself

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03

Study the solution

Kadane's algorithm: track a running sum, resetting it to the current element whenever it would go negative, and keep the best seen. It finds the max contiguous sum in O(n) time, O(1) space.

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04

Read the code

Kadane's algorithm
Run Playground
def max_subarray(nums):
    max_ending = best = nums[0]
    for x in nums[1:]:
        max_ending = max(x, max_ending + x)  # extend or restart
        best = max(best, max_ending)
    return best


# --- demo ---
print(max_subarray([-2, 1, -3, 4, -1, 2, 1, -5, 4]))   # 6  -> [4,-1,2,1]
05

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