Longest Alternating Subarray

Problem Description

You are given a 0-indexed integer array nums. A subarray s of length m is called alternating if:

• m is greater than 1.
• s[1] = s[0] + 1.
• The 0-indexed subarray s looks like [s[0], s[1], s[0], s[1],...,s[(m-1) % 2]].

Return the maximum length of all alternating subarrays present in nums or -1 if no such subarray exists.

Key Insights

• An alternating subarray must have at least two elements.
• The first element of the subarray must be followed by an element that is exactly one greater.
• The pattern alternates between increasing and decreasing by 1.
• The solution involves scanning through the array and checking for valid alternating patterns.

Space and Time Complexity

Time Complexity: O(n)
Space Complexity: O(1)

Solution

To solve this problem, we will iterate through the nums array while checking for alternating subarrays. We'll maintain a counter to track the length of the current valid alternating subarray. Whenever we find a valid pair of elements (where the second element is one greater than the first), we extend our current subarray. If we encounter a break in the pattern, we reset the counter. We will also keep track of the maximum length found during our iteration.

The algorithm primarily relies on a single pass through the array (O(n) time complexity) and uses a constant amount of space (O(1) space complexity) since we only store a few variables.

Code Solutions