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            coreBugZJ

            此 blog 已棄。

            A hard Aoshu Problem, ACM/ICPC 2010/2011 亞洲,福州區域賽 J, UVA 5107

            5107 - A hard Aoshu Problem
            Asia - Fuzhou - 2010/2011

             

            Math Olympiad is called ``Aoshu" in China. Aoshu is very popular in elementary schools. Nowadays, Aoshu is getting more and more difficult. Here is a classic Aoshu problem:

             

             

            ABBDE$\displaystyle \_$$\displaystyle \_$$\displaystyle \_abccc$ = BDBDE

            In the equation above, a letter stands for a digit(0 - 9), and different letters stands for different digits. You can fill the blank with `+', `-`, ` x' or `÷'.

            How to make the equation right? Here is a solution:

             

             

            12245 + 12000 = 24245

            In that solution, A = 1, B = 2, C = 0, D = 4, E = 5, and `+' is filled in the blank.

            When I was a kid, finding a solution is OK. But now, my daughter's teacher tells her to find all solutions. That's terrible. I doubt whether her teacher really knows how many solutions are there. So please write a program for me to solve this kind of problems.

             

            Input 

            The first line of the input is an integer T (T$ \le$20) indicating the number of test cases.

            Each test case is a line which is in the format below:

             


            s1 s2 s3

             


            s1, s2 and s3 are all strings which are made up of capital letters. Those capital letters only include ` A',' B', ' C',' D' and ` E', so forget about ` F' to ` Z'. The length of s1, s2 or s3 is no more than 8.

            When you put a `=' between s2 and s3, and put a operator (`+','-`, ` x' or `÷'.) between s1 and s2, and replace every capital letter with a digit, you get a equation.

            You should figure out the number of solutions making the equation right.

            Please note that same letters must be replaced by same digits, and different letters must be replaced by different digits.

            If a number in the equation is more than one digit, it must not have leading zero.

             

            Output 

            For each test case, print an integer in a line. It represents the number of solutions.

             

            Sample Input 

             

            2 
            A A A
            BCD BCD B

             

            Sample Output 

             

            5
            72

            Fuzhou 2010-2011


            暴力搜索之。。。

            我的代碼:

             1 #include <stdio.h>
             2 #include <string.h>
             3 
             4 typedef long long Lint;
             5 
             6 #define  L  10
             7 
             8 char s1[ L ], s2[ L ], s3[ L ];
             9 
            10 #define  DIGIT  6
            11 
            12 int digit[ DIGIT ], used[ DIGIT ];
            13 int a[ L ], b[ L ], c[ L + L ];
            14 
            15 void parse( char s[], int a[], int size ) {
            16         int i, len = strlen( s );
            17         memset( a, 0, size );
            18         for ( i = 0; i < len; ++i ) {
            19                 used[ a[ len - i - 1 ] = s[ i ] - 'A' + 1 ] = 1;
            20         }
            21 }
            22 
            23 void init() {
            24         memset( used,  0sizeof(used)  );
            25         parse( s1, a, sizeof(a) );
            26         parse( s2, b, sizeof(b) );
            27         parse( s3, c, sizeof(c) );
            28 }
            29 
            30 int parseInt( int a[], int n, Lint *num ) {
            31         int i = n-1;
            32         while ( (i>=0&& (a[i]==0) ) --i;
            33         if ( (i<0|| ((i>0)&&(digit[a[i]]==0)) ) return 0;
            34         *num = 0;
            35         for ( ; i >= 0--i ) {
            36                 if ( digit[ a[ i ] ] > 9 ) return 0;
            37                 *num = (*num) * 10 + digit[ a[ i ] ];
            38         }
            39         return 1;
            40 }
            41 
            42 int equal() {
            43         Lint x, y, z;
            44         int i, ans = 0;
            45         for ( i = 1; i < DIGIT; ++i ) {
            46                 if ( (digit[i]<10&& (used[i]==0) ) {
            47                         return 0;
            48                 }
            49         }
            50         if ( !parseInt( a, sizeof(a)/sizeof(a[0]), &x ) ) return 0;
            51         if ( !parseInt( b, sizeof(b)/sizeof(b[0]), &y ) ) return 0;
            52         if ( !parseInt( c, sizeof(c)/sizeof(c[0]), &z ) ) return 0;
            53         if ( x + y == z ) ++ans;
            54         if ( x - y == z ) ++ans;
            55         if ( x * y == z ) ++ans;
            56         if ( (y!=0&& (x%y==0&& (x/y==z) ) ++ans;
            57         return ans;
            58 }
            59 
            60 int solve() {
            61         int ans = 0, have[ 22 ] = { 0 };
            62 #define  F(i) for ( digit[ i ] = 0; digit[ i ] < 11; ++digit[ i ] ) { \
            63                 if ( have[ digit[ i ] ] ) continue; \
            64                 if ( digit[ i ] < 10 ) have[ digit[ i ] ] = 1;
            65 #define  E(i)  have[ digit[ i ] ] = 0; \
            66         }
            67         F(1) F(2) F(3) F(4) F(5) {
            68                 ans += equal();
            69         } E(5) E(4) E(3) E(2) E(1)
            70         return ans;
            71 }
            72 
            73 int main() {
            74         int td;
            75         scanf( "%d"&td );
            76         while ( td-- > 0 ) {
            77                 scanf( "%s%s%s", s1, s2, s3 );
            78                 init();
            79                 printf( "%d\n", solve() );
            80         }
            81         return 0;
            82 }
            83 


            posted on 2011-03-24 22:14 coreBugZJ 閱讀(2097) 評論(3)  編輯 收藏 引用 所屬分類: ACM

            Feedback

            # re: A hard Aoshu Problem, ACM/ICPC 2010/2011 亞洲,福州區域賽, UVA 5107 2011-03-25 09:53 電腦知識與技術

            全都是英文。看不懂啊  回復  更多評論   

            # re: A hard Aoshu Problem, ACM/ICPC 2010/2011 亞洲,福州區域賽, UVA 5107[未登錄] 2011-03-25 15:45 Bill

            純建議,不要一次發一堆文章到主頁上。可以慢慢發。  回復  更多評論   

            # re: A hard Aoshu Problem, ACM/ICPC 2010/2011 亞洲,福州區域賽, UVA 5107 2011-03-25 16:21 coreBugZJ

            @Bill
            我是剛來的菜鳥,不懂事,謝謝提醒。。。  回復  更多評論   


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