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?
dp:
方法一：
public class Solution { //两层循环 dp 很不好的算法 public int wiggleMaxLength(int[] nums) { if(nums.length<=1) return nums.length; int[] dp1=new int[nums.length];//大于上一个 int[] dp2=new int[nums.length];//小于上一个 dp1[0]=dp2[0]=1; int max=1; for(int i=0;i<nums.length;i++){ for(int j=0;j<i;j++){ if(nums[j]>nums[i]){ dp2[i]=Math.max(dp1[j]+1,dp2[i]); }else if(nums[j]<nums[i]){ dp1[i]=Math.max(dp2[j]+1,dp1[i]); } } max=Math.max(max,Math.max(dp1[i],dp2[i])); } return max; } } 方法二： public class Solution2 { //由于大小关系的传递性 根本没有必要动态规划 public int wiggleMaxLength(int[] nums) { if(nums.length<=1) return nums.length; int dp1=1;//当前比上一个候选者大的时候的最长串 上一个候选者不一定是第i-1个 int dp2=1;//同理 for(int i=1;i<nums.length;i++){ if(nums[i]>nums[i-1]) dp1=dp2+1; else if(nums[i]<nums[i-1]) dp2=dp1+1; } return Math.max(dp1,dp2); } // 1,3,2,1,4 //dp1 1 2 2 2 4 //dp2 1 1 3 3 3 }