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.

Examples:

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

本题要求在O(n)时间内求解。用delta储存相邻两个数的差，如果相邻的两个delta不同负号，那么说明子序列摇摆了一次。参看下图的nums的plot。这个例子的答案是7。平的线段部分我们支取最左边的一个点。除了最左边的边界点，我们要求delta != 0, 并且newDelta * delta <= 0。（这里不能只取<号），否则dot 5和7就会被忽略，因为他们的newDelta*delta = 0。

     def wiggleMaxLength(self, nums):

         """

         :type nums: List[int]

         :rtype: int

         """

         n = len(nums)

         if n <= 1:

             return n

         delta = nums[1] - nums[0]

         cnt = 1 + (delta != 0)

         for i in range(1, n-1):

             newDelta = nums[i+1] - nums[i]

             if newDelta != 0 and newDelta*delta <= 0:

                 cnt += 1

                 delta = newDelta

         return cnt

还可以用inc 和 dec来维护最后小段是升序列，或者是降序列的子序列长度。所以如果nums[x] > nums[x - 1]，说明最后一小段是升序列，由于我们需要的摇摆子序列，所以inc = dec + 1。反之同理。最后比较一下inc和dec哪个更长。这么做的好处是避免了分情况处理边界值。

 def wiggleMaxLength(self, nums):

         """

         :type nums: List[int]

         :rtype: int

         """

         size = len(nums)

         inc, dec = 1, 1

         for x in range(1, size):

             if nums[x] > nums[x - 1]:

                 inc = dec + 1

             elif nums[x] < nums[x - 1]:

                 dec = inc + 1

         return max(inc, dec) if size else 0