LeetCode 376. Wiggle Subsequence

原题链接在这里：https://leetcode.com/problems/wiggle-subsequence/description/

题目：

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?

题解：

up表示到目前为止longest最后是上升的wiggle subsequence长度.

down表示到目前为止longest最后是下降的wiggle subsequence长度.

递推时, 若num[i] > nums[i-1], 就用之前下降的最长wiggle subsequence长度+1.

若nums[i] < nums[i-1], 就用之前上升的最长wiggle subsequence长度+1.

Note: there could be equal number like [0, 0]. The result is 1. Thus it needs to check else if(nums[i] < nums[i - 1]), but not just use else.

Time Complexity: O(nums.length).

Space: O(1).

AC Java:

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

类似Wiggle Sort, Rearrange Array Elements by Sign.