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

 1 #include<stdio.h>
 2 #include<string.h>
 3 #include<iostream>
 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         else
45             puts ("tautology") ;
46     }
47     return 0 ;
48 }

View Code

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