376 Wiggle Subsequence

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?

Solution

class Solution {
public:
    int wiggleMaxLength(vector<int>& nums) {
        int n = nums.size();
        if ( n <= 1 ) return n;
        int last1 = nums[0], last2;
        int i = 1; 
        while ( i <= n-1 and nums[i] == nums[0] ) i += 1;
        if ( i == n ) return 1;
        last2 = nums[i];
        int length = 2;
        i += 1;
        for ( ; i <= n-1; i++ ) {
            if ((last2-last1)*(nums[i]-last2) < 0 ) {
                length += 1;
                last1 = last2;
                last2 = nums[i];
            }
            else last2 = nums[i];
        }
        return length;
    }
};

Thoughts

• The wiggle sub-sequence stops when (nums[i-1]-nums[i])*(nums[i] - nums[i+1]) >= 0. When it happens, always keep track of the last number in the monotonic increasing/decreasing sequence.
• For example,

  [1, 17, 5, 10, 13, 15, 5, 16, 8]
  

  When we scan to 5, 10, 13, the wiggle stops. We should use 13 as last2 for further probing, to maximize the probability of wiggle.