leetcode——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.

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

解析：如果一段連續子序列爲遞增或者遞減，顯然有且僅且只能取1個數字加入到最長擺動序列中，因此最長擺動序列元素數目即等於序列中波峯波谷的數目，所以只要計算其遞增以及遞減序列的數目。具體代碼如下，算法時間複雜度爲O(n)，空間複雜度爲O(1).

class Solution {
public:
	int wiggleMaxLength(vector<int>& nums) {
		if(nums.size() < 2)	return nums.size();
		bool Ascending = true;
		int num = 1, n = nums.size(), i;
		for(i=1; i<n; i++)
			if(nums[i] != nums[i-1])
			{
				if(nums[i++] < nums[0])	Ascending = false;
				num = 2;
				break;
			}
		for(; i<n; i++)
			if(nums[i] < nums[i-1] && Ascending || nums[i] > nums[i-1] && !Ascending)
			{
				Ascending = !Ascending;
				num ++;
			}
		return num;
	}
};