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You are given an array of integers that may contain both positive and negative values. Your task is to identify a contiguous segment (subarray) within this array such that the sum of its elements is maximized. A subarray must contain at least one element and consists of consecutive elements from the original array. Return the maximum sum achievable by any such contiguous subarray.
This is a foundational problem in algorithm design that appears in numerous computational scenarios. The challenge lies in efficiently determining which consecutive sequence of elements yields the highest total sum, especially when the array contains negative numbers that create complex trade-offs between extending or restarting the current segment.
nums = [-2,1,-3,4,-1,2,1,-5,4]6The contiguous subarray [4,-1,2,1] has the maximum sum of 6. Starting from index 3 and ending at index 6, this segment achieves the optimal total despite containing the negative element -1.
nums = [1]1With only one element in the array, the maximum subarray is the entire array itself, yielding a sum of 1.
nums = [5,4,-1,7,8]23The entire array [5,4,-1,7,8] forms the optimal contiguous subarray with a sum of 23. Even though -1 is negative, including it allows us to capture both 7 and 8, making the overall sum higher.
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