Longest Ordered Subsequence

Longest Ordered Subsequence

Time Limit: 1000ms, Special Time Limit:2500ms, Memory Limit:32768KB

Total submit users: 1884, Accepted users: 1572

Problem 10001 : No special judgement

Problem 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 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 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

Problem Source

HNU Contest

 

#include<stdio.h>  

int main()  
{ 
    int a[1001],b[1001],n,i,j,s=0;  
    scanf("%d",&n);  
    for(i=0;i<n;i++)  
    { 
        scanf("%d",&a[i]);  
        b[i]=1;  
    }  
    for(i=0;i<n-1;i++) 
        for(j=i+1;j<n;j++)  
            if(a[j]>a[i] && b[j]<=b[i])  
                b[j]=b[i]+1;  
            for(i=0;i<n;i++)  
                if(b[i]>s)  
                    s=b[i];  
    printf("%d\n",s);  
  return 0; 
}