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.
如果一个连续序列的数字之间的差值按照正负交替出现，这个序列称为摇摆序列。摇摆序列的第一个差值既可以是正也可以是负。两个元素的序列也称为摇摆序列。给出一个正整数序列，返回最长摇摆子序列的长度。（子序列允许通过删除一些元素得到剩余的序列）
Input: [1,7,4,9,2,5] Output: 6 The entire sequence is a wiggle sequence.
Input: [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].
Input: [1,2,3,4,5,6,7,8,9] Output: 2
这道题用dp解。思路如下：每当新加入一个序列中的元素，只会有3种状态
nums[i] > nums[i - 1]，即向上摇摆nums[i] < nums[i - 1]，即向下摇摆nums[i] = nums[i - 1]，不摇摆那么我们需要每次加入新元素时分别记录向上摇摆up和向下摇摆down的最长序列的长度
如果向上摇摆，up = down + 1如果向下摇摆，down = up + 1如果不摇摆，跳过class Solution(object): def wiggleMaxLength(self, nums): """ :type nums: List[int] :rtype: int """ if len(nums) == 0: return 0 up, down = 1, 1 for index_n in range(1, len(nums)): if nums[index_n] > nums[index_n - 1]: up = down + 1 elif nums[index_n] < nums[index_n - 1]: down = up + 1 return max(down, up)新闻热点
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