Tautology

Tautology

Time Limit: 1000MS		Memory Limit: 65536K
Total Submissions: 12135		Accepted: 4627

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

 

#include<iostream>
#include<cstring>
#include<string>
const int stackmax = 1000;
using namespace std;
int arr[stackmax];
string str;
int p,q,r,s,t;
int K,A,N,C,E;
void stak()
{
	int top = 0;
	int len = str.size();
	for(int i = len-1;i >= 0;i--)
	{
		if(str[i] == 'p')
			arr[top++] = p;
		else if(str[i] == 'q')
		    arr[top++] = q;
		else if(str[i] == 'r')
		     arr[top++] = r;
		else if(str[i] == 's')
		     arr[top++] = s;
		else if(str[i] == 't')
		     arr[top++] = t;
		else if(str[i] == 'K')
		{
			int a = arr[--top];
			int b = arr[--top];
			arr[top++] = (a && b);
		}
		else if(str[i] == 'A')
		{
			int a = arr[--top];
			int b = arr[--top];
			arr[top++] = (a || b);
		}
		else if(str[i] == 'N')
		{
			int a = arr[--top];
			arr[top++] = (!a);
		}
		else if(str[i] == 'C')
		{
			int a = arr[--top];
			int b = arr[--top];
			if((a&&b) || (!a&&!a) || (!a&&b))
				arr[top++] = 1;
			else
				arr[top++] = 0;
		}
		else if(str[i] == 'E')
		{
			int a = arr[--top];
			int b = arr[--top];
			if((a&&b) || (!a&&!b))
				arr[top++] = 1;
			else
				arr[top++] = 0;
		}
	}
}
int judge()
{
	for(p = 0;p < 2;p++)
	{
		for(q = 0;q < 2;q++)
		{
			for(r = 0;r < 2;r++)
			{
				for(s = 0;s < 2;s++)
				{
					for(t = 0;t < 2;t++)
					{
					    stak();
						if(arr[0] == 0)
							return false;
					}
				}
			}
		}
	}
	return true;
}
int main()
{
	while(cin >> str)
	{
		if(str == "0") break;
		if(judge())
			cout << "tautology" << endl;
		else
			cout << "not" << endl;
	}
	return 0;
}