POJ3295--Tautology

转自：http://www.cnblogs.com/lv-2012/archive/2012/10/27/2742751.html

Tautology

Time Limit: 1000MS		Memory Limit: 65536K
Total Submissions: 7220		Accepted: 2741

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 ofp. 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

#include<iostream>
#include<string>
#include<stack>

using namespace std;

string str;
stack<int> stk;
bool v[6];
bool tautology;

bool getSult()
{
	int a,b;
	for(int i=str.length()-1;i>=0;i--)
	{
		switch(str[i])
		{
			case 'K':
				a=stk.top();
				stk.pop();
				b=stk.top();
				stk.pop();
				stk.push(a&&b);
				break;
			case 'A':
				a=stk.top();
				stk.pop();
				b=stk.top();
				stk.pop();
				stk.push(a||b);
				break;
			case 'N':
				a=stk.top();
				stk.pop();
				stk.push(!a);
				break;
			case 'C':
				a=stk.top();
				stk.pop();
				b=stk.top();
				stk.pop();
				stk.push(!a||b);
				break;
			case 'E':
				a=stk.top();
				stk.pop();
				b=stk.top();
				stk.pop();
				stk.push(a==b);
				break;
			default:
				stk.push(v[str[i]-'p']);
		
		}
	}
	return stk.top();

}


int main()
{
	int i,j;
	while(cin>>str&&str!="0")
	{
		while(!stk.empty())
			stk.pop();
		tautology=true;
		for(i=0;i<31;i++)
		{
			for(j=0;j<5;j++)
				v[j]=(i>>j)%2;
			if(!getSult())
			{
				tautology=false;
				break;
			}
		}
		if(tautology)
		{
			cout<<"tautology"<<endl;
		}
		else
			cout<<"not"<<endl;
	
	}

	return 0;
}