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Kadane’s Algorithm: The Journey to Maximum Efficiency
Intro:
In the realm of algorithms, there existed a timeless problem: finding the maximum sum of a contiguous subarray in a sequence of numbers. Many brave programmers had attempted to solve it, but their solutions were slow, often getting tangled in nested loops and excessive computations. That was when Kadane emerged, a problem solver who believed in simplicity and efficiency.
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The Problem:
Given an array of integers, which might include positive, negative, or zero values, Kadane’s task was to determine the maximum sum of any contiguous subarray. For example, if given:
nums = [-2, 1, -3, 4, -1, 2, 1, -5, 4]
He needed to find the contiguous subarray with the highest sum. For this example, the answer would be 6, derived from the subarray [4, -1, 2, 1].
The Insight:
Kadane realized that solving this problem didn’t require evaluating every possible subarray. Instead, he could solve it in a single pass through the array by keeping track of two variables:
