POJ Tautology

た入场券 2022-07-10 04:16 142阅读 0赞

Tautology

<table> 
 <tbody> 
 <tr> 
 <td>Time Limit:&nbsp;1000MS</td> 
 <td>&nbsp;</td> 
 <td>Memory Limit:&nbsp;65536K</td> 
 </tr> 
 <tr> 
 <td>Total Submissions:&nbsp;12751</td> 
 <td>&nbsp;</td> 
 <td>Accepted:&nbsp;4861</td> 
 </tr> 
 </tbody> 
</table>

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, N*w* is a WFF
 *  if *w* and *x* are WFFs, K*wx*, A*wx*, C*wx*, and E*wx* 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.

<table> 
 <tbody> 
 <tr> 
 <td> Definitions of K, A, N, C, and E </td> 
 </tr> 
 </tbody> 
</table>

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

#include <iostream>
 
 using namespace std;
 
 const int maxn = 105;
 char str[maxn];
 int flag[10];
 int start;
 int judge()
 {
 int p,q;
 switch(str[++start])
 {
 case 'K': p = judge(); q = judge();return (p&&q);
 case 'A': p = judge(); q = judge();return (p||q);
 case 'N': return (!judge());
 case 'C': p = judge(); q = judge();return (!p||q);
 case 'E': return (judge() == judge());
 default : return (flag[str[start] - 'p']);
 }
 
 }
 int main()
 {
 while(cin>>str)
 {
 if(str[0] == '0')
 break;
 int ans = 1;
 for(int i=0;i<2;i++)
 {
 flag[0] = i;
 for(int j=0;j<2;j++)
 {
 flag[1] = j;
 for(int k=0;k<2;k++)
 {
 flag[2] = k;
 for(int s=0;s<2;s++)
 {
 flag[3] = s;
 }
 for(int t=0;t<2;t++)
 {
 flag[4] = t;
 start = -1;
 ans = (ans&&judge());
 if(!ans)
 break;
 }
 }
 }
 }
 if (!ans)cout<<"not"<<"\n";
 else cout<<"tautology"<<"\n";
 }
 return 0;
 }