Tautology(structure）

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

ApNp
ApNq
0

Sample Output

tautology
not

Source

Waterloo Local Contest, 2006.9.30

 #include<stdio.h>
 #include<string.h>
 #include<iostream>
 using namespace std;
 int p , q , r , s , t ;
 int K[][] = { ,  ,  , } , A[][] = { ,  ,  , } , N[] = { , } , C[][] = { ,  ,  , } , E[][] = { ,  ,  , } ;
 string st ;
 int now ;
 bool flag ;

 int calc ()
 {
     now++ ;
     switch (st[now])
     {
         case 'K' : return K[calc()][calc()] ;
         case 'A' : return A[calc()][calc()] ;
         case 'N' : return N[calc()] ;
         case 'C' : return C[calc()][calc()] ;
         case 'E' : return E[calc()][calc()] ;
         case 'p' : return p ;
         case 'q' : return q ;
         case 'r' : return r ;
         case 's' : return s ;
         case 't' : return t ;
     }
 }
 int main ()
 {
    // freopen ("a.txt" , "r" , stdin) ;
     while (cin >> st && st != "") {
         flag =  ;
         for (p =  ; p <  && !flag ; p++)
             for (q =  ; q <  && !flag ; q++)
                 for (r =  ; r <  && !flag ; r++)
                     for (s =  ; s <  && !flag ; s++)
                         for (t =  ; t <  && !flag ; t++) {
                                 now = - ;
                             if ( !calc() )
                                 flag = true ;
                         }
         if (flag)
             puts ("not") ;
         else
             puts ("tautology") ;
     }
     return  ;
 }

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