Kadane's Algorithms Explanation | Max Sum Subarray Problem

#array #codinginterview #datastructures
Kadane's algorithm is a popular dynamic programming approach for solving the maximum sum subarray problem. This problem involves finding the contiguous subarray within a one-dimensional array of numbers that has the largest sum.

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The algorithm works by iterating through the array, keeping track of the current sum of the subarray seen so far, and updating the maximum subarray sum found. At each iteration, the algorithm compares the current element to the sum of the current element and the maximum subarray sum seen so far. If the latter is greater, the maximum subarray sum is updated to that value, and if the current element is greater, the subarray sum is reset to the current element.

The key insight behind Kadane's algorithm is that the maximum subarray sum must either be the current element or the sum of the current element and the maximum subarray sum seen so far. This is because if the current element is negative, it cannot contribute to the maximum subarray sum. Therefore, it is better to start a new subarray from the current element.

The algorithm has a time complexity of O(n) where n is the length of the input array. This makes it a very efficient solution for the maximum sum subarray problem.

Kadane's Algorithms
Maximum Sum Subarray Problems

We'll be solving the Largest Sum Contiguous Subarray Problem using Kadane's Algorithm
Maximum Sum Subarray Problem

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