Tautology

Time Limit: 1000MS		Memory Limit: 65536K
Total Submissions: 10061		Accepted: 3826

Description

WFF 'N PROOF is a logic game played with dice. Each die has six faces representing some subset of the possible symbols K, A, N, C, E, p, q, r, s, t. A Well-formed formula (WFF) is any string of these symbols obeying the following rules:

• p, q, r, s, and t are WFFs
• if w is a WFF, Nw is a WFF
• if w and x are WFFs, Kwx, Awx, Cwx, and Ewx are WFFs.

The meaning of a WFF is defined as follows:

• p, q, r, s, and t are logical variables that may take on the value 0 (false) or 1 (true).
• K, A, N, C, E mean and, or, not, implies, and equals as defined in the truth table below.

Definitions of K, A, N, C, and E

w  x	Kwx	Awx	Nw	Cwx	Ewx
1  1	1	1	0	1	1
1  0	0	1	0	0	0
0  1	0	1	1	1	0
0  0	0	0	1	1	1

 

A tautology is a WFF that has value 1 (true) regardless of the values of its variables. For example, ApNp is a tautology because it is true regardless of the value of p. On the other hand, ApNq is not, because it has the value 0 for p=0, q=1.

You must determine whether or not a WFF is a tautology.

Input

Input consists of several test cases. Each test case is a single line containing a WFF with no more than 100 symbols. A line containing 0 follows the last case.

Output

For each test case, output a line containing tautology or not as appropriate.

Sample Input

ApNpApNq0

Sample Output

tautologynot

Source

, 2006.9.30

1 #include
       
         2 #include
        
          3 #include
         
           4 using namespace std; 5 int p , q , r , s , t ; 6 int K[2][2] = {
     0 , 0 , 0 , 1} , A[2][2] = {
     0 , 1 , 1 , 1} , N[2] = {
     1 , 0} , C[2][2] = {
     1 , 1 , 0 , 1} , E[2][2] = {
     1 , 0 , 0 , 1} ; 7 string st ; 8 int now ; 9 bool flag ;10 11 int calc ()12 {13     now++ ;14     switch (st[now])15     {16         case 'K' : return K[calc()][calc()] ;17         case 'A' : return A[calc()][calc()] ;18         case 'N' : return N[calc()] ;19         case 'C' : return C[calc()][calc()] ;20         case 'E' : return E[calc()][calc()] ;21         case 'p' : return p ;22         case 'q' : return q ;23         case 'r' : return r ;24         case 's' : return s ;25         case 't' : return t ;26     }27 }28 int main ()29 {30    // freopen ("a.txt" , "r" , stdin) ;31     while (cin >> st && st != "0") {32         flag = 0 ;33         for (p = 0 ; p < 2 && !flag ; p++)34             for (q = 0 ; q < 2 && !flag ; q++)35                 for (r = 0 ; r < 2 && !flag ; r++)36                     for (s = 0 ; s < 2 && !flag ; s++)37                         for (t = 0 ; t < 2 && !flag ; t++) {38                                 now = -1 ;39                             if ( !calc() )40                                 flag = true ;41                         }42         if (flag)43             puts ("not") ;44         else45             puts ("tautology") ;46     }47     return 0 ;48 }
         
        
       

漂亮的使用了回溯。

转载：http://blog.csdn.net/allenlsy/article/details/4885948

tautology : 中文叫套套理论 ， 或 永真式 ， 就是无论位运算中的variable怎么变，最后答案都为1

题目里的implies 指 蕴涵 ， 当且仅当 (条件q = 1) ----> (结论s = 0) 时为假 ，其余都为真