POJ2533:Longest Ordered Subsequence

Posted 2021-11-28 mqxnongmin

Longest Ordered Subsequence

Longest Ordered Subsequence

Time Limit:?2000MS	?	Memory Limit:?65536K
Total Submissions:?31680	?	Accepted:?13848

Description

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

这是一道动归题。

n=3

1

7

3

5

9

4

8

dp[]=0;

1	ap[1]=0
7	dp[2]=1
3	dp[3]=1
5	d[4]=2
9	d[5]=3
4	d[6]=2
8	d[7]=3

最后找出最大值然后加一；

详细实现例如以下：

#include<cstdio>
#include<cstring>
#include<algorithm>
#include<iostream>

using namespace std;

const int M = 1000+5;
int sequence[M];    //输入的数据
int dp[M];          

int main()
{
    int n;
    while(scanf("%d", &n)!=EOF)
    {
        for(int i=1; i<=n; i++)
            scanf("%d",  &sequence[i]);
        memset(dp, 0, sizeof(dp));          //初始化为0
        for(int i=1; i<=n; i++)
            for(int j=1; j<i; j++)
            {
                if(sequence[i]>sequence[j])
                    dp[i] = max(dp[i], dp[j] + 1);    //动归方程
            }
        int ans=0;
        for(int i=1; i<=n; i++)
            ans = max(ans, dp[i]);
        printf("%d\n", ans+1);
    }
    return 0;
}