POJ2533——DP（LCS+LDS）——Longest Ordered Subsequence

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

Source

Northeastern Europe 2002, Far-Eastern Subregion

大意：没什么好说的~模板题，取最大就行

#include<cstdio>
#include<algorithm>
#include<cstring>
using namespace std;
const int MAX = 11000;
int a[MAX],b[MAX];
int main()
{
    int n;
    int l,r,mid;
    scanf("%d",&n);
    for(int i = 1; i <= n ;i++)
        scanf("%d",&a[i]);
        // LCS
    b[1] = a[1];
    int k,i;
    for(i = 2, k = 1; i <= n ;i++){
            if(a[i] > b[k]) b[++k] = a[i];
           else {
            l = 1; r = k;
              while(l<=r){
                   mid = (l + r) >> 1;
                   if(b[mid] < a[i]) l = mid + 1;
                   else if(b[mid] > a[i]) r = mid - 1;
                   else break;
              }
              b[l] =a[i];
           }
    }
    int temp1 = k;
    // LDS
    memset(b,0,sizeof(b));
    b[1] = a[1];
    for(i = 2, k = 1; i <= n ;i++){
           if(a[i] < b[i]) b[++k] = a[i];
          else {
              l = 1; r = k;
             while(l <= r){
              mid = (l + r) >> 1;
             if(b[mid] > a[i]) l = mid + 1;
             else if(b[mid] < a[i]) r = mid -1;
             else break;
             }
             b[l] = a[i];
          }
    }
    int temp2 = k;
    printf("%d",max(temp1,temp2));
    return 0;
}