Longest Subarray With Sum Divisible By K.

In this video, we will explore the problem of finding the longest subarray with a sum divisible by a given integer k. We begin with the naive approach, which involves iterating over all possible subarrays and calculating their sums. If the sum of a subarray is divisible by k, we update the length of the longest such subarray found. While this approach has a time complexity of O(n^2), it provides a straightforward solution to the problem.

Next, we discuss an optimized approach using the Prefix Sum technique along with Hashing, which significantly reduces the time complexity to O(n). By maintaining a prefix sum modulo k, we can efficiently find the longest subarray with a sum divisible by k. Using a hash map to track the first occurrence of each prefix sum, we can determine the length of the subarray in constant time. This approach provides an efficient solution with auxiliary space of O(min(n, k)), making it ideal for large datasets.

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