Problem Description
A wiggle sequence is a sequence where the differences between successive numbers strictly alternate between positive and negative. The first difference (if one exists) may be either positive or negative. A sequence with one element and a sequence with two non-equal elements are trivially wiggle sequences. Given an integer array nums, return the length of the longest wiggle subsequence of nums.
Key Insights
- A wiggle sequence alternates between increases and decreases.
- The first difference can be either positive or negative.
- A subsequence can be created by deleting some elements while maintaining the order of the remaining elements.
- The goal is to find the longest subsequence that satisfies the wiggle condition.
Space and Time Complexity
Time Complexity: O(n)
Space Complexity: O(1)
Solution
We can solve this problem using a greedy approach. The idea is to traverse through the array and keep track of the direction of the last wiggle (up or down). We maintain a count of the length of the wiggle subsequence. Whenever we find a number that creates a wiggle (i.e., a positive difference followed by a negative difference or vice versa), we increment the count. We ignore numbers that do not contribute to the wiggle. This approach efficiently finds the length of the longest wiggle subsequence in a single pass through the array.