Free Candies

题目：

Little Bob is playing a game. He wants to win some candies in it - as many as possible.

There are 4 piles, each pile contains N candies. Bob is given a basket which can hold at most 5 candies. Each time, he puts a candy at the top of one pile into the basket, and if there're two candies of the same color in it ,he can take both of them outside the basket and put them into his own pocket. When the basket is full and there are no two candies of the same color, the game ends. If the game is played perfectly, the game will end with no candies left in the piles.

For example, Bob may play this game like this (N=5):

Step1	Initial Piles		Step2	Take one from pile #2
Piles	Basket	Pocket	Piles	Basket	Pocket
1 2 3 4 1 5 6 7 2 3 3 3 4 9 8 6 8 7 2 1	nothing	nothing	1 3 4 1 5 6 7 2 3 3 3 4 9 8 6 8 7 2 1	2	nothing
Step3	Take one from pile #2		Step4	Take one from pile #3
Piles	Basket	Pocket	Piles	Basket	Pocket
1 3 4 1 6 7 2 3 3 3 4 9 8 6 8 7 2 1	2 5	nothing	1 4 1 6 7 2 3 3 3 4 9 8 6 8 7 2 1	2 3 5	nothing
Step5	Take one from pile #2		Step6	put two candies into his pocket
Piles	Basket	Pocket	Piles	Basket	Pocket
1 4 1 6 7 2 3 3 4 9 8 6 8 7 2 1	2 3 3 5	nothing	1 4 1 6 7 2 3 3 4 9 8 6 8 7 2 1	2 5	a pair of 3

Note that different numbers indicate different colors, there are 20 kinds of colors numbered 1..20.

'Seems so hard...'Bob got very much puzzled. How many pairs of candies could he take home at most?

 

Input

The input will contain no more than 10 test cases. Each test case begins with a line containing a single integer n(1<=n<=40) representing the height of the piles. In the following n lines, each line contains four integers xi1,xi2,xi3,xi4 (in the range 1..20). Each integer indicates the color of the corresponding candy. The test case containing n=0 will terminate the input, you should not give an answer to this case.

 

Output

Output the number of pairs of candies that the cleverest little child can take home. Print your answer in a single line for each test case.

 

Sample Input

5
1 2 3 4
1 5 6 7
2 3 3 3
4 9 8 6
8 7 2 1
1
1 2 3 4
3
1 2 3 4
5 6 7 8
1 2 3 4
0

Sample Output

8
0

3

题意：

一共有四堆糖果；

给你一个数n，代表每堆有n个糖果。篮子能放5个糖果，每一次只能从每一堆的顶端取一个糖果放在篮子里，如果篮子里有两个颜色一样的糖果就可以把这两个糖果放进自己的口袋，如果篮子满了游戏就结束了；

让你求出来你最多可以得到几对糖果；

思路：

这道题肯定要用记忆化搜索，因为直接搜索会超时，把每一种顶端出现的情况记录下来再进行搜索；

代码如下：

#include<stdio.h>
#include<string.h>
#include<algorithm>
using namespace std;

int n;
int a[5][50];//存放每堆糖果；
int dp[50][50][50][50];//存储出现的各种情况；
int book[50]；//标记出现过的糖果；
int top[5];//记录每堆糖果的顶端情况；

int dfs(int s)
{
    int i,ss;
    if(dp[top[0]][top[1]][top[2]][top[3]]!=-1)//如果这种情况出现过直接返回结果；
        return dp[top[0]][top[1]][top[2]][top[3]];
    if(s==5)//篮子满了，游戏结束；
        return dp[top[0]][top[1]][top[2]][top[3]]=0;
    int ans=0;
    for(i=0; i<4; i++)
    {
        if(top[i]==n)//这一堆糖果取完了，换下一堆；
            continue;
        ss=a[i][top[i]];//记录这种糖果的颜色；
        top[i]+=1;//这一堆糖果取走的数量加一，取到了top[i]+1个；
        if(book[ss])//篮子中有这种颜色的糖果；
        {
            book[ss]=0;//篮子中现在没有这种颜色的糖果，因为成对被取走；
            ans=max(ans,dfs(s-1)+1);//篮子中糖果数量减少，成对被取走的糖果数量加一；
            book[ss]=1;//否则还原；
        }
        else//篮子中没有这种颜色的糖果；
        {
            book[ss]=1;//篮子中现在有这种颜色的糖果；
            ans=max(ans,dfs(s+1));//篮子中糖果数量增加；
            book[ss]=0;//还原；
        }
        top[i]-=1;//没被取走；
    }
    return dp[top[0]][top[1]][top[2]][top[3]]=ans;
}

int main()
{
    while(~scanf("%d",&n)&&n)
    {
        int i,j;
        for(i=0; i<n; i++)
        {
            for(j=0; j<4; j++)
            {
                scanf("%d",&a[j][i]);
            }
        }
        memset(book,0,sizeof book);
        memset(dp,-1,sizeof dp);
        memset(top,0,sizeof top);
        int ans=dfs(0);
        printf("%d\n",ans);
    }
    return 0;
}