POJ-3295-Tautology-2013-12-04 20:44:18

Tautology

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
• ifwis a WFF, Nwis a WFF
• ifwandxare WFFs, Kwx, Awx, Cwx, and Ewxare 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 meanand, or, not, implies,andequalsas defined in the truth table below.

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

# include<stdio.h>
# include<string.h>
# include<stdlib.h>
char wff[210];
int stack[210];
int caller(char c,int w,int x)
{
    switch(c)
    {
    case'K':
        return w & x;
    case'A':
        return w | x;
    case'C':
        return !w | x;
    case'E':
        return w == x;
    }
}

int getv(char c,int p,int q,int r,int s,int t)  
{  
    switch (c)  
    {  
        case 'p': 
            return p;
        case 'q': 
            return q;
        case 'r': 
            return r;
        case 's': 
            return s;
        case 't': 
            return t;
    }  
}  


int main()
{
//  freopen("input.txt","r",stdin);
//  freopen("output.txt","w",stdout);
    
    int i,len,top,state;
    int p,q,r,s,t;
    memset(wff,0,sizeof(wff));
    memset(stack,0,sizeof(stack));
    while(scanf("%s",wff) && wff[0]!='0')
    {
        len = strlen(wff);
        
        state = 1;
        for(p=0;p<=1;p++)
        {
            for(q=0;q<=1;q++)
            {
                for(r=0;r<=1;r++)
                {
                    for(s=0;s<=1;s++)
                    {
                        for(t=0;t<=1;t++)
                        {    
                            top = 1;
                            memset(stack,0,sizeof(stack));

                            for(i=len-1;i>=0;i--)
                            {
                                if(wff[i]>='p' && wff[i]<='t')
                                    stack[top++] = getv(wff[i],p,q,r,s,t);
                                else if(wff[i]=='K'|| wff[i]=='A'|| wff[i]=='C'|| wff[i]=='E')
                                {
                                        
                                    stack[top-2] = caller(wff[i],stack[top-1],stack[top-2]);
                                    top--;
                                }
                                else if(wff[i]=='N')
                                {
                                    stack[top-1] = (1 - stack[top-1]);
                                }
                            }
                            
                            if(!stack[top-1])
                            {
                                state = 0;
                                    break;    
                            }
                        }

                    }
                }
            }
        }
        
        if(state==1)
            printf("tautology\n");
        else
            printf("not\n");
        
        memset(wff,0,sizeof(wff));
        
    }
    return 0;
}