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
分析
up[i]表示以nums[i]以结尾且上升的状态时的最长子列，down[i]表示以nums[i]以结尾且下降的状态时的最长子列。动态分析根据状态来写状态转移方程。如果nums[i]>nums[i-1], up[i]=down[i-1]+1, down[i]=down[i-1]. 如果nums[i]<nums[i-1],up[i]=up[i-1],down[i]=up[i-1]+1; 如果nums[i]==nums[i-1], up[i]=up[i-1], down[i]=down[i-1].
class Solution {
public:
int wiggleMaxLength(vector<int>& nums) {
if(nums.size()==0) return 0;
vector<int> up(nums.size()),down(nums.size());
up[0]=down[0]=1;
for(int i=1;i<nums.size();i++){
if(nums[i]>nums[i-1]){
up[i]=down[i-1]+1;
down[i]=down[i-1];
}else if(nums[i]<nums[i-1]){
up[i]=up[i-1];
down[i]=up[i-1]+1;
}else{
up[i]=up[i-1];
down[i]=down[i-1];
}
}
return max(up[nums.size()-1],down[nums.size()-1]);
}
};