poj 3295 Tautology

Tautology

Time Limit: 1000MS		Memory Limit: 65536K
Total Submissions: 10430		Accepted: 3961

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
/*
英语太渣，在万能的标哥的帮助下用了一天才能懂，说多了都是泪啊，脑残的孩子慢慢学吧
*/
#include <iostream>
#include <cstring>
#include <cstdio>
#include <cmath>
#include <algorithm>
#include <queue>
#include <stack>
#include <string>

using namespace std;

int Arr[6];
stack<int >a;
string str;

void Bit(int n)
{
    int top = 0;
    memset(Arr,0,sizeof(Arr));
    while(n)
    {
        Arr[top++] = n%2;
        n/=2;
    }
}

bool Judge(char s)
{
    switch(s)
    {
    case 'p':
        a.push(Arr[0]);
        break;
    case 'q':
        a.push(Arr[1]);
        break;
    case 'r':
        a.push(Arr[2]);
        break;
    case 't':
        a.push(Arr[3]);
        break;
    case 's':
        a.push(Arr[4]);
        break;
    default :
        return false;
    }
    return true;
}

void Count(char s)
{
    switch(s)
    {
    case 'K':
    {
        int x = a.top();
        a.pop();
        int y = a.top();
        a.pop();
        a.push(x&&y);
        break;
    }
    case 'A':
    {
        int x = a.top();
        a.pop();
        int y = a.top();
        a.pop();
        a.push(x||y);
        break;
    }
    case 'N':
    {
        int x = a.top();
        a.pop();
        a.push(!x);
        break;
    }
    case 'C':
    {
        int x = a.top();
        a.pop();
        int y = a.top();
        a.pop();
        a.push((!x)||y);
        break;
    }
    case 'E':
    {
        int x = a.top();
        a.pop();
        int y = a.top();
        a.pop();
        a.push(x==y);
        break;
    }
    }
}
bool Col()
{
    int len = str.length();
    for(int i=0; i<32; i++)
    {
        Bit(i);
        for(int j=len-1; j>=0; j--)
        {
            if(!Judge(str[j]))
            {
                Count(str[j]);
            }
        }
        int x = a.top();
        a.pop();
        if(!x)
            return false;
    }
    return true;
}
int main()
{
    //freopen("in.txt","r",stdin);
    while(cin>>str && str[0]!='0')
    {
        if(Col())
            cout<<"tautology"<<endl;
        else
            cout<<"not"<<endl;
    }
    return 0;
}