376. Wiggle Subsequence 类别：动态规划 难度：medium

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

程序：

class Solution {
public:
int wiggleMaxLength(
4000
vector<int>& nums) {
if(nums.size() == 0)
return 0;

if(nums.size() == 1)
return 1;

vector<int> diff;
for(int i = 1;i < nums.size();i++)
diff.push_back(nums[i] - nums[i - 1]);

vector<int> dp(diff.size(),0);

for(int i = 0;i < diff.size();i++)
{
if(diff[i] > 0)
{
dp[i] = 1;
for(int j = 0;j < i;j++)
{
if(diff[j] < 0)
dp[i] = max(dp[i],1 + dp[j]);
}
}

else if(diff[i] < 0)
{
dp[i] = 1;
for(int j = 0;j < i;j++)
{
if(diff[j] > 0)
dp[i] = max(dp[i],1 + dp[j]);
}
}
}
return dp[dp.size() - 1] + 1;

}
};