376. Wiggle Subsequence

376. Wiggle Subsequence

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?

代码如下：

class Solution {
public:
    int wiggleMaxLength(vector<int>& nums) {
        int len = nums.size();
        if (len < 2)  return len;
        int flag = 0;
        for (int i = 1; i < nums.size(); i++) {
            if (nums[i] == nums[i - 1]) len--;
            else if (nums[i] > nums[i - 1])
                flag == 1 ? len-- : flag = 1;
            else
                flag == -1 ? len-- : flag = -1;
        }
        return len;
    }
};

解题思路：

• 本题采用贪心算法。
• 对于一个序列[ 1, 3, 4, 10, 5, 6, 7, 9 ]， 最开始[1, 3]符合摆动序列，当到了[ 1, 3, 4，10 ]时出现了问题，其中3，4，10均大于1，为了让之后的数字可选择性更大，我们贪心的选择最大的那一个，即10，此时[10, 5 ]符合要求（若选3或4则有：[ 3, 5 ]，[ 4, 5 ]不合题意）；同理[ 5，6，7 ]中当然选择7最合适，继续这样下去；
• 那么我们所要求的即是在一个递增或者递减区间中选择最大或者最小的那一个，把其他的数字从序列中减去。