376_Wiggle_Subsequence.py

"""
https://leetcode.com/problems/wiggle-subsequence/
"""

"""
A sequence of numbers is called a wiggle sequence if 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 fewer than two elements is trivially a wiggle sequence.

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

Given a sequence of integers, return the length of the longest subsequence that is a wiggle sequence. A subsequence is obtained by deleting some number of elements (eventually, also zero) from the original sequence, leaving the remaining elements in their original order.

Example 1:
    Input: [1,7,4,9,2,5]
    Output: 6
    Explanation: The entire sequence is a wiggle sequence.

Example 2:
    Input: [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].

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

Follow up:
Can you do it in O(n) time?
"""

class Solution:
    def wiggleMaxLength(self, nums):
        if len(nums) < 2:
            return len(nums)
        pred = nums[1] - nums[0]
        ans = 1 + (pred!=0)
        for i in range(2, len(nums)):
            diff = nums[i] - nums[i-1]
            if pred*diff < 0 or (diff!=0 and pred==0):
                ans += 1
                pred = diff
        return ans

nums = [1,2,1,2,3,4,5,4]
x = Solution()
x.wiggleMaxLength(nums)