#122 Medium Time O(n) Space O(1) Animated

Maximum Subarray

Find the contiguous subarray with the largest sum (Kadane's).

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Pattern Greedy choice with a local proof

Commit to the locally best safe choice only after identifying why it cannot block an optimal answer.

Approach: Kadane's Algorithm

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Core Insight

Commit to the locally best safe choice only after identifying why it cannot block an optimal answer.

Common Pitfall

Sort or define the selection order before applying the greedy rule.

Description

Find the contiguous subarray with the largest sum (Kadane's).

Constraints

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

Solution — Kadane's Algorithm

TimeO(n) SpaceO(1)

Implementation Plan

Translate the invariant into these small, testable moves.

Order candidates by the greedy criterion.
Inspect the next candidate.
Accept it only when it preserves feasibility.
Return the accumulated result.

def maxSubArray(nums):
    res = nums[0]
    total = 0
    
    for n in nums:
        if total < 0:
            total = 0
        total += n
        res = max(res, total)
        
    return res

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Maximum Subarray

Steps

Description

Constraints

Tags

Solution — Kadane's Algorithm