codeforce 10D LCIS

This problem differs from one which was on the online contest.

The sequence a1, a2, …, an is called increasing, if ai < ai + 1 for i < n.

The sequence s1, s2, …, sk is called the subsequence of the sequence a1, a2, …, an, if there exist such a set of indexes 1 ≤ i1 < i2 < … < ik ≤ n that aij = sj. In other words, the sequence s can be derived from the sequence a by crossing out some elements.

You are given two sequences of integer numbers. You are to find their longest common increasing subsequence, i.e. an increasing sequence of maximum length that is the subsequence of both sequences.

Input
The first line contains an integer n (1 ≤ n ≤ 500) — the length of the first sequence. The second line contains n space-separated integers from the range [0, 109] — elements of the first sequence. The third line contains an integer m (1 ≤ m ≤ 500) — the length of the second sequence. The fourth line contains m space-separated integers from the range [0, 109] — elements of the second sequence.

Output
In the first line output k — the length of the longest common increasing subsequence. In the second line output the subsequence itself. Separate the elements with a space. If there are several solutions, output any.

Examples
input
7
2 3 1 6 5 4 6
4
1 3 5 6
output
3
3 5 6
input
5
1 2 0 2 1
3
1 0 1
output
2
0 1

题意

求两个串的最长公共上升子序列。

题解

f[i][j]表示a串进行到了i，上升序列以b序列的b[j]结尾的最长子序列。

然后就很好转移了。

感觉这个把状态体现以什么结尾是很不错的思想。

#include <cstdio>
#define N 550
using namespace std;
int a[N],b[N],f[N][N],g[N][N],n,m;
void print(int x)
{
    if (!x)
        return;
    print(g[n][x]);
    printf("%d ",b[x]);
}
main()
{
    scanf("%d",&n);
    for (int i=1;i<=n;i++)
        scanf("%d",&a[i]);
    scanf("%d",&m);
    for (int i=1;i<=m;i++)
        scanf("%d",&b[i]);
    for (int i=1;i<=n;i++)
    {
        int tp=0,pos=0;
        for (int j=1;j<=m;j++)
        {
            f[i][j]=f[i-1][j];
            g[i][j]=g[i-1][j];
            if (a[i]==b[j] && tp+1>f[i][j])
                f[i][j]=tp+1,g[i][j]=pos;
            if (b[j]<a[i] && f[i-1][j]>tp)
                tp=f[i-1][j],pos=j;
        }
    }
    int ans=1;
    for (int i=1;i<=m;i++)
        if (f[n][i]>f[n][ans])
            ans=i;
    printf("%d\n",f[n][ans]);
    if (f[n][ans])
        print(ans);
}