# Question

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

# Code

``````public class Solution {
public class Data {
public int pre;
public int count;

public Data(int index) {
this.pre = index;
this.count = 1;
}
}

public int wiggleMaxLength(int[] nums) {
if (nums.length <= 1) return nums.length;
Data[] dp = new Data[nums.length];
dp = new Data(0);

int max = 1;
for (int i = 1; i < dp.length; i++) {
dp[i] = new Data(i);
for (int j = 0; j < i; j++) {
if (nums[j] != nums[i]) {
if (dp[j].pre == j) {
dp[i].count = Math.max(dp[i].count, 1 + dp[j].count);
dp[i].pre = j;
continue;
}

int first = nums[dp[j].pre], second = nums[j], third = nums[i];
if ((second - first < 0 && third - second > 0) || (second - first > 0 && third - second < 0)) {
dp[i].count = Math.max(dp[i].count, 1 + dp[j].count);
dp[i].pre = j;
}
}
}
max = Math.max(max, dp[i].count);
}

return max;
}
}
``````

# Solution

dp[i].count表示以nums[i]结尾的序列的最长长度。

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