Maximum Length Subarray with Given Sum

Given an integer array \(arr\) and an integer \(k\), your task is to find the maximum length of a contiguous subarray that sums exactly to \(k\). If such a subarray does not exist, output \(0\). Note that the array can contain both positive and negative numbers.

Input: The first line contains an integer \(n\) denoting the number of elements in the array. The second line contains \(n\) space-separated integers representing the array elements. The third line contains the integer \(k\).

Output: Print the maximum length of a contiguous subarray whose sum equals \(k\). If no such subarray exists, print \(0\).

Example: For \(n = 5, arr = [1, -1, 5, -2, 3]\) and \(k = 3\), the answer is \(4\) because the subarray \([1, -1, 5, -2]\) sums up to \(3\) and has the maximum length.

inputFormat

Input is read from standard input (stdin) in the following format:

• The first line contains a single integer \(n\) (the size of the array).
• The second line contains \(n\) space-separated integers representing the elements of the array \(arr\).
• The third line contains a single integer \(k\), the target sum.

outputFormat

Output a single integer to standard output (stdout): the maximum length of a contiguous subarray whose sum equals \(k\). If no such subarray exists, output \(0\).

5
1 -1 5 -2 3
3

4