Maximum length of subarray with same sum at corresponding indices from two Arrays

Given two arrays A[] and B[] both consisting of N integers, the task is to find the maximum length of subarray [i, j] such that the sum of A[i... j] is equal to B[i... j].

Examples:

Input: A[] = {1, 1, 0, 1}, B[] = {0, 1, 1, 0}
Output: 3
Explanation: For (i, j) = (0, 2), sum of A[0... 2] = sum of B[0... 2] (i.e, A[0]+A[1]+A[2] = B[0]+B[1]+B[2] => 1+1+0 = 0+1+1 => 2 = 2). Similarly, for (i, j) = (1, 3), sum of A[1... 3] = B[1... 3]. Therefore, the length of the subarray with equal sum is 3 which is the maximum possible.

Input: A[] = {1, 2, 3, 4}, B[] = {4, 3, 2, 1}
Output: 4

Approach: The given problem can be solved by using a Greedy Approach with the help of unordered maps. It can be observed that for a pair (i, j), if the sum of A[i... j] = sum of B[i... j], then  must hold true. Therefore, a prefix sum array of the difference (A[x] - B[x]) can be created. It can be observed that the repeated values in the prefix sum array represent that the sum of a subarray between the two repeated values must be 0. Hence, keep a track of the maximum size of such subarrays in a variable maxSize which will be the required answer.

Below is the implementation of the above approach:

3

Time Complexity: O(N)
Auxiliary Space: O(N)