Wiggle Subsequence

arraydynamic programminggreedy

Problem Statement

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 .

Examples

Example 1

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

🤔

Medium

Difficulty

Topic Info

ModuleDSA

CategoryArray

Sub-topicDynamic Programming