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.
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: List[int]) -> int:
if len(nums) < 2:
return len(nums)
first_diff = 1
dp = [1] * len(nums)
ret = 1
for first_diff in [1, -1]:
dp = [1] * len(nums)
for i in range(1, len(nums)):
if first_diff * (nums[i] - nums[i-1]) > 0:
dp[i] = dp[i-1] + 1
first_diff *= -1
else:
dp[i] = dp[i-1]
ret = max(ret, max(dp))
return ret