# 376. 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. In 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.
Input: [1,7,4,9,2,5] Output: 6 Explanation: The entire sequence is a wiggle sequence.
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].
Input: [1,2,3,4,5,6,7,8,9] Output: 2
Approach 1: DP.
Approach 2: greedy.
# Code (Python)
def wiggleMaxLength(self, nums: List[int]) -> int: # DP -- keep 2 tables, for the current index being the peak and being the valley if not nums: return 0 if len(nums) == 1: return 1 as_peak, as_valley =  * len(nums),  * len(nums) global_max = 2 for i in range(1, len(nums)): for j in range(i): if nums[j] < nums[i]: as_peak[i] = max(as_peak[i], as_valley[j] + 1) # don't have to update as_valley because it's never going to exceed the previous ones elif nums[j] > nums[i]: as_valley[i] = max(as_valley[i], as_peak[j] + 1) # again don't have to update as_peak or as_valley for == return max(max(as_peak), max(as_valley))
def wiggleMaxLength(self, nums: List[int]) -> int: # greedy: think of nums as a stack, we need to go through the nums and get the max and min peak, and count the alternations if len(nums) <= 1: return len(nums) if len(nums) == 2: return 1 if nums == nums else 2 diffs = list(filter(lambda x: x != 0, [nums[i] - nums[i-1] for i in range(1, len(nums))])) if not diffs: return 1 max_len = 1 for i in range(1, len(diffs)): if diffs[i] * diffs[i-1] < 0: max_len += 1 return max_len + 1
# Code (C++)