LeetCode 376: Wiggle Subsequence

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.

For example, [1, 7, 4, 9, 2, 5] is a wiggle sequence because the differences (6, -3, 5, -7, 3) alternate between positive and negative.
In contrast, [1, 4, 7, 2, 5] and [1, 7, 4, 5, 5] are not wiggle sequences. The first is not because its first two differences are positive, and the second is not because its last difference is zero.

A subsequence is obtained by deleting some elements (possibly zero) from the original sequence, leaving the remaining elements in their original order.

Given an integer array nums, return the length of the longest wiggle subsequence of nums.

Example 1:

Input: nums = [1,7,4,9,2,5]
Output: 6
Explanation: The entire sequence is a wiggle sequence with differences (6, -3, 5, -7, 3).

Example 2:

Input: nums = [1,17,5,10,13,15,10,5,16,8]
Output: 7
Explanation: There are several subsequences that achieve this length.
One is [1, 17, 10, 13, 10, 16, 8] with differences (16, -7, 3, -3, 6, -8).

Example 3:

Input: nums = [1,2,3,4,5,6,7,8,9]
Output: 2

Constraints:

1 <= nums.length <= 1000
0 <= nums[i] <= 1000

Follow up: Could you solve this in O(n) time?

Difficulty: Medium

Tags: array, dynamic programming, greedy

Rating: 96.89%

Solution

Here’s my Python solution to this problem:

class Solution:
    def wiggleMaxLength(self, nums: List[int]) -> int:
        n = len(nums)
        if n < 2: return n

        length = 1 #First num always part of sequence
        prev_diff = None

        for i in range(1, n):
            curr_diff = nums[i] - nums[i-1]

            if (curr_diff != 0 and
            (prev_diff == None or
            (curr_diff > 0 and prev_diff < 0) or
            (curr_diff < 0 and prev_diff > 0))):
                length += 1
                prev_diff = curr_diff
        
        return length

Complexity Analysis

The solution has the following complexity characteristics:

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

Note: This is an automated analysis and may not capture all edge cases or specific algorithmic optimizations.