# 376. Wiggle Subsequence (1)

[Link](https://leetcode.com/problems/wiggle-subsequence/submissions/)

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.

**Example 1:**

```
Input: [1,7,4,9,2,5]
Output: 6
Explanation: The entire sequence is a wiggle sequence.
```

**Example 2:**

```
Input: [1,17,5,10,13,15,10,5,16,8]
Output: 7
Explanation: There are several subsequences that achieve this length. One is [1,17,10,13,10,16,8].
```

**Example 3:**

```
Input: [1,2,3,4,5,6,7,8,9]
Output: 2
```

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

**Solution**

DP,  觀察到目前的maxLength(i)根據nums\[i]跟num\[i-1]的關係，

會是上一個 accendingSeqLength + 1 or decendingSeqLength + 1

```
class Solution {
    public int wiggleMaxLength(int[] nums) {
        if (nums.length < 2) return nums.length;
        int upLength = 1; //final element is a accending one
        int downLength = 1; //final element is a decending one
        for(int i = 1; i < nums.length; i++){
            if(nums[i] > nums[i-1]){
                upLength = downLength + 1;
            }
            else if (nums[i] < nums[i-1]){
                downLength = upLength + 1;
            }
        }
        return Math.max(upLength, downLength);
    }
}
```
