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0053-maximum-subarray.md

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# 53. Maximum Subarray
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LeetCode problem: [53. Maximum Subarray](https://leetcode.com/problems/maximum-subarray/)
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## Problem
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## LeetCode problem description
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> Given an integer array nums, find the subarray with the largest sum, and return its sum.
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```
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nums = [-2, 1, -3, 4, -1, 2, 1, -5, 4]
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dp = [-2, 1, -2, 4, 3, 5, 6, 1, 5]
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```
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* After analyzing the sample `dp` data, we can derive the `recurrence formula`:
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* After analyzing the sample `dp` array, we can derive the `Recurrence Formula`:
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```dp[i] = max(nums[i], dp[i - 1] + nums[i])```
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4. Determine the `dp` array's traversal order
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* `dp[i]` depends on `dp[i - 1]`, so we should traverse the `dp` array from left to right.

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