376. Wiggle Subsequence

Discription:

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

Explanation:
For every position in the array, there are 3 position status as follows:
1. up position, it means nums[i]>nums[i-1]
2. down position, it means nums[i]<nums[i-1]
3. equals position, it means nums[i]=nums[i-1]


we use two arrays up[], down[] to store the max wiglle sequence length so far at index i;
we define down[i], up[i] as the max length of the wiggle subsequence which is end at nums[i] and the relation between nums[i] and nums[i-1] is up or down position.


down[0]=up[0]=1
else 
if nums[i]>nums[i-1] , means up position, the element before it must be a down position, so up[i] = down[i-1]+1, down[i] keeps the same with before
if nums[i]<nums[i-1], means down position, the element before it must be a up position, so down[i] = up[i-1]+1, up[i]keeps the same with before
if nums[i]=nums[i-1], means no change , so down[i] and up[i] keep the same with before together.




Implement code:
C++:
class Solution {
public:
    int wiggleMaxLength(vector<int>& nums) {
        
        int l=nums.size();
        if(l<2)return l;
        
        vector<int> up(l, 0);
        vector<int> down(l, 0);
        up[0]=down[0]=1;
        
        for(int i=1; i<l; ++i)
        {
            if(nums[i] > nums[i-1])
            {
                up[i] = down[i-1]+1;
                down[i] = down[i-1];
            }
            else if(nums[i] < nums[i-1])
            {
                up[i] = up[i-1];
                down[i] = up[i-1]+1;
            }
            else if(nums[i] == nums[i-1])
            {
                up[i] = up[i-1];
                down[i] = down[i-1];
            }
        }
        
        return max(up[l-1], down[l-1]);
    }
};


/*
[1,7,4,9,2,5]
[]
[1,1,2,3]
[1,1,2,3,2,1]
*/


Java:
public class Solution {
    public int wiggleMaxLength(int[] nums) {
        int l=nums.length;
        
        if(l<2)return l;
        
        int[] up = new int[l];
        int[] down = new int[l];
        
        up[0]=down[0]=1;
        
        for(int i=1; i<l; ++i)
        {
            if(nums[i]>nums[i-1])
            {
                up[i]=down[i-1]+1;
                down[i] = down[i-1];
            }
            else if(nums[i]<nums[i-1])
            {
                down[i] = up[i-1]+1;
                up[i] = up[i-1];
            }
            else
            {
                down[i] = down[i-1];
                up[i] = up[i-1];
            }
        }
        
        return Math.max(down[l-1], up[l-1]);
    }
}