poj 2533Longest Ordered Subsequence

Longest Ordered Subsequence

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

Source

Northeastern Europe 2002, Far-Eastern Subregion

题解 最长上升子序列，动态规划。

#include<stdio.h>
#include<string.h>
int a[100001];
int dp[100001];
int max(int a,int b)
{
    return a>b?a:b;
}

int main()
{
    int n;
    while(scanf("%d",&n)!=EOF)
    {
        for(int i=0;i<n;i++)
            scanf("%d",&a[i]);

        memset(dp,0,sizeof(dp));
        int res=0;
        for(int i=0;i<n;i++)
        {
            dp[i]=1;
            for(int j=0;j<=i;j++)
            {
                if(a[i]>a[j])
                {
                    dp[i]=max(dp[i],dp[j]+1);
                //  dp[i]=dp[j]+1;
                }

                res=max(res,dp[i]);
            }
        }

        printf("%d\n",res);
    }

    return 0;
}