376. Wiggle Subsequence

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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

The following solution and pictures comes from www.leetcode.com:
We need not necessarily need dp to solve this problem. This problem is equivalent to finding the number of alternating max. and min. peaks in the array. Since, if we choose any other intermediate number to be a part of the current wiggle subsequence, the maximum length of that wiggle subsequence will always be less than or equal to the one obtained by choosing only the consecutive max. and min. elements.

This can be clarified by looking at the following figure:

这里写图片描述

From the above figure, we can see that if we choose C instead of D as the 2nd point in the wiggle subsequence, we can’t include the point E. Thus, we won’t obtain the maximum length wiggle subsequence.

Thus, to solve this problem, we maintain a variable prevdiff, where prevdiff is used to indicate whether the current subsequence of numbers lies in an increasing or decreasing wiggle. If prevdiff > 0, it indicates that we have found the increasing wiggle and are looking for a decreasing wiggle now. Thus, we update the length of the found subsequence when diff (nums[i]−nums[i−1]) becomes negative. Similarly, if prevdiff < 0, we will update the count when diff(nums[i]−nums[i−1]) becomes positive.

When the complete array has been traversed, we get the required count, which represents the length of the longest wiggle subsequence.

int wiggleMaxLength(vector<int>& nums)
{

    if (nums.size() <= 1)return nums.size();
    int max = 1, diff = 0;
    for (int i = 1; i < nums.size(); i++)
    {
        if ((diff <= 0 && nums[i] > nums[i - 1]))
        {
            max++;
            diff = 1;
        }
        if ((diff >= 0 && nums[i] < nums[i - 1]))
        {
            max++;
            diff = -1;
        }
    }
    return max;
}