Longest Ordered Subsequence

Posted 2020-10-16 给杰瑞一块奶酪~

A numeric sequence of a_i is ordered if a₁ < a₂ < ... < a_N. Let the subsequence of the given numeric sequence ( a₁, a₂, ..., a_N) be any sequence ( a_i1, a_i2, ..., a_iK), where 1 <= i₁ < i₂ < ... < i_K <= N. For example, sequence (1, 7, 3, 5, 9, 4, 8) has ordered subsequences, e. g., (1, 7), (3, 4, 8) and many others. All longest ordered subsequences are of length 4, e. g., (1, 3, 5, 8).

Your program, when given the numeric sequence, must find the length of its longest ordered subsequence.

Input

The first line of input file contains the length of sequence N. The second line contains the elements of sequence - N integers in the range from 0 to 10000 each, separated by spaces. 1 <= N <= 1000

Output

Output file must contain a single integer - the length of the longest ordered subsequence of the given sequence.

Sample Input

7
1 7 3 5 9 4 8

Sample Output

4

动态规划

#include <iostream>
#include <cstdio>
#include <cmath>
#include <cstring>
#include <algorithm>
#include <map>
#define Max 1001
using namespace std;

int s[1000];
int dp[1001];
int main()
{
    int n,d = 0;
    while(cin>>n){
    d = 1;
    for(int i = 1;i <= n;i ++)
    {
        dp[i] = 1;
        cin>>s[i];
    }

    for(int i = 2;i <= n;i ++)
    {
        for(int j = 1;j < i;j ++)
            if(s[i] > s[j])dp[i] = max(dp[i],dp[j] + 1);
        d = max(d,dp[i]);
    }
    cout<<d<<endl;}
}

二分加数组

#include <iostream>
#include <cstdio>
#include <cmath>
#include <cstring>
#include <algorithm>
#include <map>
#define Max 1001
using namespace std;


int main()
{
    int n,d,no;
    int s[100000];
    while(cin>>n)
    {
        no = 0;
        while(n --)
        {
            cin>>d;
            if(!no || s[no - 1] < d)s[no ++] = d;
            else
            {
                int *p = upper_bound(s,s + no,d);
                *p = d;
            }
        }
        cout<<no<<endl;
    }
}