POJ 2533 Longest Ordered Subsequence（DP 最长上升子序列）

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.

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 file must contain a single integer - the length of the longest ordered subsequence of the given sequence.

7
1 7 3 5 9 4 8

4

Northeastern Europe 2002, Far-Eastern Subregion

n*n算法

#include<iostream>
#include<algorithm>
#include<stdio.h>
#include<string.h>
#include<stdlib.h>
#include<queue>

using namespace std;

int n;
int a[1001];
int dp[1010];

int main()
{
    while(scanf("%d",&n)!=EOF)
    {
        int maxx = -1;
        for(int i=0;i<n;i++)
        {
            scanf("%d",&a[i]);
        }
        for(int i=0;i<n;i++)
        {
            dp[i] = 1;
            for(int j=0;j<i;j++)
            {
                if(a[i]>a[j] && dp[j]+1>dp[i])
                {
                    dp[i] = dp[j] + 1;
                }
            }
            if(maxx < dp[i])
            {
                 maxx = dp[i];
            }
        }
        printf("%d\n",maxx);
    }
    return 0;
}

n*logn算法：

#include<iostream>
#include<algorithm>
#include<stdio.h>
#include<string.h>
#include<stdlib.h>

#define inf 999999

using namespace std;

int n;
int dp[1010];
int a[1010];

int res(int len,int num)
{
    int l = 0,r = len;
    while(l!=r)
    {
        int mid = (l+r)>>1;
        if(dp[mid] == num)
        {
            return mid;
        }
        else if(dp[mid]<num)
        {
            l = mid + 1;
        }
        else if(dp[mid]>num)
        {
            r = mid;
        }
    }
    return l;
}

int main()
{
    while(scanf("%d",&n)!=EOF)
    {
        for(int i=1;i<=n;i++)
        {
            scanf("%d",&a[i]);
        }
        int len = 1;
        dp[0] = -1;
        for(int i=1;i<=n;i++)
        {
            dp[i] = inf;
            int k = res(len,a[i]);
            if(k == len)
            {
                len++;
            }
            dp[k] = a[i];
        }
        printf("%d\n",len-1);
    }
    return 0;
}