## 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.

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?

## Rust Solution

``````struct Solution;
use std::cmp::Ordering::*;

impl Solution {
fn wiggle_max_length(nums: Vec<i32>) -> i32 {
let n = nums.len();
if n == 0 {
return 0;
}
let mut up: Vec<usize> = vec!;
let mut down: Vec<usize> = vec!;
for i in 1..n {
match nums[i].cmp(&nums[i - 1]) {
Greater => {
down.push(up[i - 1] + 1);
up.push(up[i - 1]);
}
Less => {
down.push(down[i - 1]);
up.push(down[i - 1] + 1);
}
Equal => {
down.push(down[i - 1]);
up.push(up[i - 1]);
}
}
}
up.into_iter().chain(down.into_iter()).max().unwrap() as i32
}
}

#[test]
fn test() {
let nums = vec![1, 7, 4, 9, 2, 5];
let res = 6;
assert_eq!(Solution::wiggle_max_length(nums), res);
let nums = vec![1, 17, 5, 10, 13, 15, 10, 5, 16, 8];
let res = 7;
assert_eq!(Solution::wiggle_max_length(nums), res);
let nums = vec![1, 2, 3, 4, 5, 6, 7, 8, 9];
let res = 2;
assert_eq!(Solution::wiggle_max_length(nums), res);
}
``````

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