## DEV Community

Abhishek Chaudhary

Posted on

# 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: 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?

SOLUTION:

``````class Solution:
def maxWig(self, nums, i, n, inc):
if (i, inc) in self.cache:
return self.cache[(i, inc)]
maxSeq = 1
for j in range(i + 1, n):
if inc:
if nums[j] > nums[i]:
maxSeq = max(maxSeq, 1 + self.maxWig(nums, j, n, False))
else:
if nums[j] < nums[i]:
maxSeq = max(maxSeq, 1 + self.maxWig(nums, j, n, True))
self.cache[(i, inc)] = maxSeq
return maxSeq

def wiggleMaxLength(self, nums: List[int]) -> int:
self.cache = {}
n = len(nums)
maxSeq = 1
for i in range(n):
maxSeq = max(maxSeq, self.maxWig(nums, i, n, True))
maxSeq = max(maxSeq, self.maxWig(nums, i, n, False))
return maxSeq
``````