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

Follow up:
Can you do it in O(n) time?

详见：https://leetcode.com/problems/wiggle-subsequence/description/

C++：

class Solution {

public:

    int wiggleMaxLength(vector<int>& nums)

    {

        if (nums.empty())

        {

            return 0;

        }

        vector<int> p(nums.size(), 1);

        vector<int> q(nums.size(), 1);

        for (int i = 1; i < nums.size(); ++i)

        {

            for (int j = 0; j < i; ++j)

            {

                if (nums[i] > nums[j])

                {

                    p[i] = max(p[i], q[j] + 1);

                }

                else if (nums[i] < nums[j])

                {

                    q[i] = max(q[i], p[j] + 1);

                }

            }

        }

        return max(p.back(), q.back());

    }

};

参考：https://www.cnblogs.com/grandyang/p/5697621.html