Maximum Subarray

MediumGreedy

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Problem

Given an integer array nums, find the contiguous subarray with the largest sum and return that sum.

Examples

Example 1

Input:nums = [-2,1,-3,4,-1,2,1,-5,4]

Output:6

[4,-1,2,1] has the largest sum.

Example 2

Input:nums = [1]

Output:1

Constraints

1 <= nums.length <= 10^5

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How to approach it: the Greedy pattern

Make the choice that looks best right now, without reconsidering it later, and trust that a sequence of locally optimal choices adds up to a globally optimal answer. It only works when the problem actually has that property.

Look for this pattern when

Sorting the input by some key, then making one pass with simple local decisions, intuitively seems to produce the best answer.
The problem involves intervals, scheduling, or resource allocation where "always take the best available option" tends to work.

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Video walkthroughs

Original problem on LeetCode ↗