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POJ2533:Longest Ordered Subsequence

2024-07-10 22:41:41   224人阅读

Longest Ordered Subsequence


Longest Ordered Subsequence
Time Limit: 2000MS Memory Limit: 65536K
Total Submissions: 31680 Accepted: 13848

Description

A numeric sequence of ai is ordered if a1 < a2 < ... < aN. Let the subsequence of the given numeric sequence (a1, a2, ..., aN) be any sequence (ai1, ai2, ..., aiK), where 1 <= i1 < i2 < ... < iK <= 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


1735948

dp[]=0;

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

最后找出最大值然后加一；

具体实现如下：


#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;
}


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