poj 2253 Longest Ordered Subsequence

Longest Ordered Subsequence

Time Limit: 2000MS Memory Limit: 65536KTotal Submissions: 39015 Accepted: 17142

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

71 7 3 5 9 4 8

Sample Output

4

Source

Northeastern Europe 2002, Far-Eastern Subregion

lis nlogn 

#include <iostream>#include <stdlib.h>#include <string.h>#include <math.h>#include <algorithm>#include <stdio.h>#include <vector>#include <queue>#include <stack>#include <set>#include <map>using namespace std;int p[1023];int lis[1023],n;int search_lis(int a[],int left,int right,int val){    int mid=(left+right)/2;    int r=right;int l=left;    while(l<r)    {        if(a[mid]==val) return mid;        else if(a[mid]>val)        {            r=mid;            mid=(l+r)/2;        }        else        {            l=mid+1;            mid=(l+r)/2;        }    }    return l;}int main(){    cin>>n;    int res=0;    for(int i=1;i<=n;i++) cin>>p[i];    for(int m=1;m<=n;m++)    {        int len_lis=1;        for(int i=1;i<=m;i++)        {            lis[len_lis]=23333;            int k=search_lis(lis,1,len_lis,p[i]);            if(k==len_lis) len_lis++;lis[k]=p[i];        }        len_lis--;        res=max(res,len_lis);    }    cout<<res;    return 0;}