The Longest Subsequence with Equal Step 最长等差序列/最长等差数列

Bupt_Luke

已于 2022-10-25 15:47:49 修改

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分类专栏： OJ codes 文章标签：最长等差序列最长等差数列

于 2022-10-25 10:54:59 首次发布

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博客围绕给定整数数组和整数，求数组中最长等差子序列长度展开。给出了输入输出格式示例，输入为数组字符串和整数，输出为整数。还说明了 10 个测试用例的数组长度约束条件。

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Description

Given an array of integers X and an integer step, find the length of the longest subsequence of X where integers in this subsequence form an arithmetic sequence with difference of step.

Sample Input

The string form of an array is in the first line.

The second lind is an integer (string form).

2 4 1 7 -2 -3 -5
-3

Sample Output

An integer.

Explanation of Sample

The longest desired subsequence is [4, 1, -2, -5], and the length is 4.

Constraints of 10 test cases

Case 1: 0<X.length<10

Case 2-4: 100<X.length<1000

Case 5-7: 1000<X.length<10000

Case 8-10: 10000<X.length<100000

#include <cstdio>
#include <map>
using namespace std;
int main(){
    int a[100005];
    int n = 0;
    map<int,int>dp;
    while (scanf("%d",&a[n])) {
        n++;
        char ch = getchar();
        if (ch == '\n')
            break;
    }
    int tar;
    scanf("%d",&tar);
    int ans=0;
    for(int i=0;i<n;i++){
        dp[a[i]] = dp[a[i]-tar] + 1;
        if(ans<dp[a[i]])
            ans=dp[a[i]];
    }
    printf("%d\n",ans);
    return 0;
}