**Wiggle Subsequence ** 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:6Explanation: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:7Explanation: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] <= 100`

### Wiggle Subsequence Solutions

✅**Time:** O(n)

✅**Space:** O(n)

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