Kadane's Algorithm – Maximum Subarray (Dynamic Programming)
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Maximum subarray is a popular LeetCode interview questions asked at Microsoft, Amazon, Apple, LinkedIn, ByteDance, Google, Adobe, and several other top tech companies. This problem is solved in the most efficient way using dynamic programming with an algorithm known as Kadane’s algorithm.
Kadane’s algorithm finds a contiguous subarray with the largest sum in linear time. Using this algorithm, as we iterate through our array, we compute the max subarray at each step using the following recurrence relation; current is equal to the max between the current and the current plus the previous. Since we overwrite the formula values with the array we are given, the algorithm provides a constant space complexity in addition to the linear time complexity.
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