POJ 3295, Tautology

输入字符串为二叉树的先根遍历（Pre-order string），可采用堆栈或者递归。

一般pre-order 字符串计算使用递归， post-order 字符串计算使用堆栈

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

---

 

//  POJ3295.cpp : Defines the entry point for the console application.
//

#include  < iostream >
#include  < string >
using   namespace  std;

static   int  pos  =   - 1 ;
bool  WFF( const   string &  formula,  int  i)
{
     ++ pos;
     switch (formula[pos])
    {
     case   ' p ' :
         return  i  &   1 ;
     case   ' q ' :
         return  (i  >>   1 )  &   1 ;
     case   ' r ' :
         return  (i  >>   2 )  &   1 ;
     case   ' s ' :
         return  (i  >>   3 )  &   1 ;
     case   ' t ' :
         return  (i  >>   4 )  &   1 ;
     case   ' N ' :
         return   ! WFF(formula, i);
     case   ' K ' :
         return  WFF(formula, i)  &  WFF(formula, i);
     case   ' A ' :
         return  WFF(formula, i)  |  WFF(formula, i);
     case   ' C ' :
         return   ! WFF(formula, i)  |  WFF(formula, i);
     case   ' E ' :
         return  WFF(formula, i)  ==  WFF(formula, i);
    }
    
     return   false ;
};

bool  isTautology( string  formula)
{
     for  ( int  i  =   0 ; i  <   32 ;  ++ i)
    {
        pos  =   - 1 ;
         if  (WFF(formula, i) == false )  return   false ;;
    }
     return   true ;
};

int  main( int  argc,  char *  argv[])
{
     string  ln;
     while  (cin  >>  ln  &&  ln[ 0 ]  !=   ' 0 ' )
    {
         if  (isTautology(ln)) cout  <<   " tautology\n " ;
         else  cout  <<   " not\n " ;
    }
     return   0 ;
}