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.
如果一個連續序列的數字之間的差值按照正負交替出現，這個序列稱為搖擺序列。搖擺序列的第一個差值既可以是正也可以是負。兩個元素的序列也稱為搖擺序列。給出一個正整數序列，返回最長搖擺子序列的長度。（子序列允許通過刪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
這道題用dp解。思路如下：每當新加入一個序列中的元素，只會有3種狀態
nums[i] > nums[i - 1]，即向上搖擺nums[i] < nums[i - 1]，即向下搖擺nums[i] = nums[i - 1]，不搖擺那么我們需要每次加入新元素時分別記錄向上搖擺up和向下搖擺down的最長序列的長度
如果向上搖擺，up = down + 1如果向下搖擺，down = up + 1如果不搖擺，跳過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)新聞熱點
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