POJ Tautology-蒲公英云

POJ Tautology

た入场券 2022-07-10 04:16 227阅读 0赞

Tautology

Time Limit: 1000MS		Memory Limit: 65536K
Total Submissions: 12751		Accepted: 4861

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
#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;
}