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Given an integer array arr[], find the subarray (containing at least one element) which has the maximum possible sum, and return that sum.
Note: A subarray is a continuous part of an array.
Examples:
Input: arr[] = [2, 3, -8, 7, -1, 2, 3]
Output: 11
Explanation: The subarray [7, -1, 2, 3] has the largest sum 11.Input: arr[] = [-2, -4]
Output: -2
Explanation: The subarray [-2] has the largest sum -2.Input: arr[] = [5, 4, 1, 7, 8]
Output: 25
Explanation: The subarray [5, 4, 1, 7, 8] has the largest sum 25.
Table of Content
The idea is to run two nested loops to iterate over all possible subarrays and find the maximum sum. The outer loop will mark the starting point of a subarray and inner loop will mark the ending point of the subarray.
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The idea of Kadane's algorithm is to traverse over the array from left to right and for each element, find the maximum sum among all subarrays ending at that element. The result will be the maximum of all these values.
To calculate the maximum sum of subarray ending at current element, say maxEnding, we can use the maximum sum ending at the previous element.
So for any element, we have two choices:
Choice 1: Extend the maximum sum subarray ending at the previous element by adding the current element to it. If the maximum subarray sum ending at the previous index is positive, then it is always better to extend the subarray.
Choice 2: Start a new subarray starting from the current element. If the maximum subarray sum ending at the previous index is negative, it is always better to start a new subarray from the current element.
This means that maxEnding at index i = max(maxEnding at index (i - 1) + arr[i], arr[i]) and the maximum value of maxEnding at any index will be our answer.
Illustration:
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