leetcode 376. Wiggle Subsequence 最长摆动序列 + 动态规划DP + 这道题很棒

忘是亡心i 2022-06-07 02:49 140阅读 0赞

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

想了好久没想到怎么做，网上看到了一个DP的做法，真的很妙。

使用用up\[i\]和down\[i\]分别记录到第i个元素为止以上升沿和下降沿结束的最长“摆动”序列长度，遍历数组，如果nums\[i\]>nums\[i-1\]，表明第i-1到第i个元素是上升的，因此up\[i\]只需在down\[i-1\]的基础上加1即可，而down\[i\]保持down\[i-1\]不变；如果nums\[i\]

/*
     * 用up[i]和down[i]分别记录到第i个元素为止以上升沿和下降沿结束的最长“摆动”
     * 序列长度，遍历数组，如果nums[i]>nums[i-1]，表明第i-1到第i个元素是上升的，
     * 因此up[i]只需在down[i-1]的基础上加1即可，而down[i]保持down[i-1]不变；
     * 如果nums[i]<nums[i-1]，表明第i-1到第i个元素是下降的，因此down[i]
     * 只需在up[i-1]的基础上加1即可，而up[i]保持up[i-1]不变；如果nums[i]==nums[i-1]，
     * 则up[i]保持up[i-1]，down[i]保持down[i-1]。比较最终以上升沿和下降沿结束的
     * 最长“摆动”序列长度即可获取最终结果
     * */
    class Solution 
    {
        public int wiggleMaxLength(int[] nums) 
        {
            if(nums==null || nums.length<=0)
                return 0;
            int[] up=new int[nums.length];
            int[] down=new int[nums.length];
            up[0]=down[0]=1;
            for(int i=1;i<nums.length;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 Math.max(up[nums.length-1], down[nums.length-1]);
        }
    }

下面是C++的做法

很明显这就是一个动态规划DP问题，但是没想清楚怎么做，看了一下答案，就是这么做，这道题太棒啦，很值得学习和反思

代码如下：

#include <iostream>
    #include <vector>
    #include <map>
    #include <unordered_map>
    #include <set>
    #include <unordered_set>
    #include <queue>
    #include <stack>
    #include <string>
    #include <climits>
    #include <algorithm>
    #include <sstream>
    #include <functional>
    #include <bitset>
    #include <numeric>
    #include <cmath>
    #include <regex>
    
    using namespace std;
    
    
    
    class Solution
    {
    public:
        int wiggleMaxLength(vector<int>& nums) 
        {
            if (nums.size() <= 1)
                return nums.size();
            vector<int> up(nums.size(), 0);
            vector<int> down(nums.size(), 0);
            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.back(), down.back());
        }
    };