Wiggle Subsequence

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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: 6The entire sequence is a wiggle sequence.Input: [1,17,5,10,13,15,10,5,16,8]Output: 7There 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?

解析:

O(n)的复杂度,分析情况,从当前位置到下个位置如果是递增的则找到增加到最大的元素,再减小,减小的话也找到连续的最小的元素为当前减小的元素,并记录每次增加或者减小的方向。

代码:

class Solution {public:    int wiggleMaxLength(vector<int>& nums) {        if (nums.empty()) return 0;       if (nums.size()==1) return 1;       if (nums.size()==2)       {           if (nums[0]==nums[1])           return 1;           return 2;       }              int ans=0;       int cur;       int flag=INT_MIN;       int i;       for ( i=1; i<nums.size(); i++)       {           if (nums[i]!=nums[0])           break;       }       if (i==(nums.size()))       return 1;       flag=nums[0]-nums[i];              cur=nums[i];       ans=2;       i++;       for (; i<nums.size(); i++)       {           if (flag<0)//上次递增           {               if (nums[i]>=cur)               {                   cur=nums[i];               }               else               {                   ans++;                   flag=1;                   cur=nums[i];               }                          }           else           {               if (nums[i]<=cur)               {                   cur=nums[i];               }               else               {                   ans++;                   flag=-1;                   cur=nums[i];               }           }       }       return ans;           }};




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