# # 【LeetCode】376. Wiggle Subsequence 解题报告（Python）

## # 题目描述：

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
``````

Can you do it in O(n) time?

## # 解题方法

``````class Solution(object):
def wiggleMaxLength(self, nums):
"""
:type nums: List[int]
:rtype: int
"""
n = len(nums)
if n <= 1:
return n
inc, dec =  * n,  * n
for x in range(n):
for y in range(x):
if nums[x] > nums[y]:
inc[x] = max(inc[x], dec[y] + 1)
elif nums[x] < nums[y]:
dec[x] = max(dec[x], inc[y] + 1)
return max(inc[-1], dec[-1])
``````

``````class Solution(object):
def wiggleMaxLength(self, nums):
"""
:type nums: List[int]
:rtype: int
"""
n = len(nums)
if n <= 1:
return n
inc, dec =  * n,  * n
for x in range(1, n):
if nums[x] > nums[x - 1]:
inc[x] = dec[x - 1] + 1
dec[x] = dec[x - 1]
elif nums[x] < nums[x - 1]:
inc[x] = inc[x - 1]
dec[x] = inc[x - 1] + 1
else:
inc[x] = inc[x - 1]
dec[x] = dec[x - 1]
return max(inc[-1], dec[-1])
``````

``````class Solution(object):
def wiggleMaxLength(self, nums):
"""
:type nums: List[int]
:rtype: int
"""
n = len(nums)
if n <= 1:
return n
inc, dec = 1, 1
for x in range(1, n):
if nums[x] > nums[x - 1]:
inc = dec + 1
elif nums[x] < nums[x - 1]:
dec = inc + 1
return max(inc, dec)
``````