博弈论6

Game

Description

One day, Caspar’s girlfriend Rapsac asked Caspar to play a game with her. This game called “The Trains”.  There are some cards, each of them is marked with an integer K (1<=K<=200).  Before the beginning of the game, they divide them to 2 sequences, one for Caspar and another for Rapsac. Then, they pick the first card of their cards out and put it to the game sequence in turn. The rule is that if one picks out card P and there has been already a card P in the game sequence, he or she would take the cards from the first card P to the end of the game sequence and put them to end of his or her sequence. And if someone has no card in his or her turn, he or she will lose.

 

 

Input

 

There are multiple testcases.

The first line of each testcase contains two integer N (1<=N<= 200) and M (1<=M<=200). The second line has N integers, indicating the sequence of cards of Caspar. The next line has M integers, indicating the sequence of cards of Rapsac. Caspar is always the first one to pick up card. 

 

 

Output

For each testcase, output the winner’s name.

 

Sample Input

3 4
1 3 1
2 3 2 1

Sample Output

Caspar

分析：

大致题意：

就是我们小时候玩的“接火车”，每人轮流拿一张牌出来，形成新的序列，如果这个序列里有和你的牌号一样的牌，你就可以将那张牌到你的牌之间的所有牌取出，放在你自己的序列里。例如：新序列为1,2,3,5,8,4，而如果此时你拿出的是一张3的话，你就可以将3,5,8,4,3取出，放入你自己的序列里，那么新序列就是1,2了。如果轮到一方，并且这方自己的序列没有牌了，那他(她)就算输了

思路：

其实这道题只需模拟一下整个过程就行了。由于新序列始终是从尾部取，所以用一个数组就行了，并记下尾部的位置；而由于博弈的双方要轮流的从头取牌，还会在尾部加牌，那用一个环形队列也就行了，环形队列节约并利用空间

代码如下：

# include<stdio.h>
# include<malloc.h>
#define MaxSize 400//由题意，所有的元素个数永远不会超过400
typedef int ElemType;
typedef struct node
{
    ElemType data[MaxSize];
    int front,rear;
}SqQueue;
void InitQueue(SqQueue *&q)
{
    q=(SqQueue *)malloc(sizeof(SqQueue));
    q->front=q->rear=0;
}
int EmptyQueue(SqQueue *q)
{
    return (q->front==q->rear);
}
void InsertQueue(SqQueue *&q,ElemType e)
{
    q->rear=(q->rear+1)%MaxSize;
    q->data[q->rear]=e;
}
int main()
{
    SqQueue *boy,*girl; 
    int dp[MaxSize+2];
    int numb,numg;
    int en,i,j,now;
    while((scanf("%d %d",&numb,&numg))!=EOF)
    {
        InitQueue(boy);
        InitQueue(girl);
        for(i=1;i<=numb;i++)
            scanf("%d",&boy->data[i]);
        boy->rear=numb;
        for(i=1;i<=numg;i++)
            scanf("%d",&girl->data[i]);
        girl->rear=numg;
        now=1;//记录轮到哪方出牌
        en=0;
        while(1)
        {
            if(now==1)
            {
                if(!EmptyQueue(boy))
                {
                    boy->front=(boy->front+1)%MaxSize;
                    dp[en++]=boy->data[boy->front];
                    now=2;
                }
                else 
                {
                    printf("Rapsac\n");//输出胜者
                    break;
                }
            }
            else if(now==2)
            {
                if(!EmptyQueue(girl))
                {
                    girl->front=(girl->front+1)%MaxSize;
                    dp[en++]=girl->data[girl->front];
                    now=1;
                }
                else 
                {
                    printf("Caspar\n");
                    break;
                }
            }
            for(i=en-2;i>=0;i--)
            {
                if(dp[i]==dp[en-1])
                {
                    if(now==2)
                    {
                        for(j=i;j<=en-1;j++)
                        {
                            InsertQueue(boy,dp[j]);
                        }
                    }
                    else if(now==1)
                    {
                        for(j=i;j<=en-1;j++)
                        {
                            InsertQueue(girl,dp[j]);
                        }
                    }
                    en=i;//取出牌后，尾标记也要更新
                    break;
                }
            }
        }
    }
    return 0;
}