Master-Mind Hints

MasterMind is a game for two players. One of them, Designer, selects asecret code. The other, Breaker, tries to break it. A code is no morethan a row of colored dots. At the beginning of a game, the playersagree upon the length N that a code must have and upon the colors thatmay occur in a code.

In order to break the code, Breaker makes anumber of guesses, each guess itself being a code. After each guessDesigner gives a hint, stating to what extent the guess matches hissecret code.

In this problem you will be given a secret code and a guess , and are to determine the hint. A hint consists of a pair of numbers determined as follows.

A match is a pair (i,j), and , such that . Match (i,j) is called strong when i = j, and is called weakotherwise. Two matches (i,j) and (p,q) are called independentwhen i = p if and only if j = q. A set of matches is called independent when all of its members are pairwise independent.

Designer chooses an independent set M of matches for which the total number ofmatches and the number of strong matches are both maximal. The hintthen consists of the number of strong followed by the number of weakmatches in M. Note that these numbers are uniquely determined by thesecret code and the guess. If the hint turns out to be (n,0), then theguess is identical to the secret code.

Input

The input will consist of data for a number of games. The input for each game begins with an integer specifying N (the lengthof the code). Following these will be the secret code, representedas N integers, which we will limit to the range 1 to 9. There will thenfollow an arbitrary number of guesses, each also represented as Nintegers, each in the range 1 to 9. Following the last guess in eachgame will be N zeroes; these zeroes are not to be considered as a guess.

Following the data for the first game will appear data forthe second game (if any) beginning with a new value for N. The lastgame in the input will be followed by a single zero (when a value for Nwould normally be specified). The maximum value for N will be 1000.

Output

The output for each game should list the hints thatwould be generated for each guess, in order, one hint per line. Eachhint should be represented as a pair of integers enclosed in parentheses and separated by a comma. The entire list of hints for each gameshould be prefixed by a heading indicating the game number; games arenumbered sequentially starting with 1. Look at the samples below for the exact format.

Sample Input

4
1 3 5 5
1 1 2 3
4 3 3 5
6 5 5 1
6 1 3 5
1 3 5 5
0 0 0 0
10
1 2 2 2 4 5 6 6 6 9
1 2 3 4 5 6 7 8 9 1
1 1 2 2 3 3 4 4 5 5
1 2 1 3 1 5 1 6 1 9
1 2 2 5 5 5 6 6 6 7
0 0 0 0 0 0 0 0 0 0
0

Sample Output

Game 1:
    (1,1)
    (2,0)
    (1,2)
    (1,2)
    (4,0)
Game 2:
    (2,4)
    (3,2)
    (5,0)
    (7,0)


#include <stdio.h>
#include <string.h>
#define clr( a ) memset ( a, 0, sizeof ( a ) )
#define min( a, b ) a < b ? a : b
const int maxn = 1005;
int init[maxn], guess[maxn], v_in[10], v_gue[10];
int is_ok ( int n )
{
    for ( int i = 0; i < n; i ++ )  //判断是否全0
        if ( guess[i] )
            return 0;
    return 1;
}
int main ( )
{
    int cas = 1, A, B, n;
    while ( ~ scanf ( "%d", &n ) && n )
    {
        clr ( v_in );
        for ( int i = 0; i < n; i ++ )
        {
            scanf ( "%d", &init[i] );
            v_in[init[i]] ++;   //统计出现的次数
        }
        printf ( "Game %d:\n", cas ++ );
        while ( 1 )
        {
            A = B = 0;
            clr ( v_gue );
            for ( int i = 0; i < n; i ++ )
            {
                scanf ( "%d", &guess[i] );
                v_gue[guess[i]] ++;
            }
            if ( is_ok ( n ) )
                break ;
            for ( int i = 0; i < n; i ++ )
                if ( init[i] == guess[i] )
                    A ++;
            for ( int i = 0; i < 10; i ++ )
                B = B+( min ( v_in[i], v_gue[i] ) );
            printf ( "    (%d,%d)\n", A, B-A );
            //A是同一位置出现的次数,B为数字出现的次数
            //所以错位就是B-A
        }
    }
    return 0;
}