Longest Ordered Subsequence

http://poj.org/problem?id=2533

最长上升子序列的两种算法

(1) O(n^2)

#include <stdio.h>
#include <string.h>

const int N=10010;
int dp[N],a[N];//dp[i]表示0~i的最长上升子序列的长度
int n;

int main()
{
    int n;
    while(~scanf("%d",&n))
    {
        memset(dp,0,sizeof(dp));
        for (int i = 0; i < n; i++)
            scanf("%d",&a[i]);
        int Max = 1;
        dp[0] = 1;
        for (int i = 1; i < n; i++)
        {
            dp[i] = 1; //初始所有值的最长上升子序列长度
            for (int j = 0; j < i; j++)
            {
                if (a[i]> a[j] && dp[j]+1>dp[i])//用所有a[i]之前的并小于a[i]的数的上升子序列长度，更新dp[i]
                dp[i] = dp[j]+1;
            }
            if (Max < dp[i])
                Max = dp[i];//找出最长的上升子序列长度
        }
        printf("%d\n",Max);
    }
    return 0;
}

(2)O(nlogn)
 算法讲解

http://blog.csdn.net/dangwenliang/article/details/5728363

#include <stdio.h>
#include <string.h>
const int N=10010;
const int INF=-1<<28;
int c[N],n;

int Bin_search(int key,int len)
{
    int l = 1;
    int r = len;

    while(l <= r)
    {
        int mid = (l+r)>>1;
        if (key > c[mid])
            l = mid+1;
        else
            r = mid-1;
    }
    return l;
}
int main()
{
    while(~scanf("%d",&n))
    {
        int a,pos = 0,len=0;
        c[len] = INF;
        for (int i = 0; i < n; i++)
        {
            scanf("%d",&a);
            if (a  > c[len])
                pos = ++len;
            else
                pos = Bin_search(a,len);
            c[pos] = a;
        }

        printf("%d\n",len);
    }
    return 0;
}