poj2533 - Longest Ordered Subsequence(简单动规)

状态：d[i]表示a[1.....i]的最长上升子序列

状态转移：d[i] = max{d[j]+1|a[i]>a[j]}

代码如下：

#include <cstdio>
#include <cstring>
#define N 1005
int n, a[N], d[N];
int main ()
{
    int max;
    while(~scanf("%d",&n))
    {
        for(int i = 1; i <= n; i++) scanf("%d",&a[i]);
        memset(d,0,sizeof(d));
        d[1] = 1;
        max = 1;
        for(int i = 2; i <= n; i++)
        {
            int &ans = d[i];
            ans = 1;
            for(int j = 1; j < i; j++)
            {
                if(a[i]>a[j]&&ans<d[j]+1) ans = d[j]+1;
            }
            if(max<d[i]) max = d[i];
        }
        printf("%d\n",max);
    }
    return 0;
}

 o(nlogn)算法

代码如下：

#include <cstdio>
#include <cstring>
#define N 1005
int n, a[N], c[N], dp[N];
int search(int l, int r, int x)
{
    int mid;
    while(l<=r)
    {
        mid = (r+l)/2;
        if(c[mid]==x) return mid;
        else if(x>c[mid]) l = mid+1;
        else r = mid-1;
    }
    return l;
}
int main()
{
    while(~scanf("%d",&n))
    {
        for(int i = 1; i <= n; i++) scanf("%d",&a[i]);
        c[1] = a[1]; dp[1] = 1;
        int size = 1;
        for(int i = 2, j; i <= n; i++)
        {
            if(a[i]<c[1]) j = 1;
            else if(a[i]>c[size]) j = ++size;
            else j = search(1,size, a[i]);
            c[j] = a[i];
        }
        printf("%d\n",size);
    }
    return 0;
}