POJ 3295, Tautology

输入字符串为二叉树的先根遍历（Pre-order string），可采用堆栈或者递归。

一般pre-order 字符串计算使用递归， post-order 字符串计算使用堆栈

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
Waterloo Local Contest, 2006.9.30

---

// POJ3295.cpp : Defines the entry point for the console application.
//

#include <iostream>
#include <string>
using namespace std;

static int pos = -1;
bool WFF(const string& formula, int i)
{
    ++pos;
    switch(formula[pos])
    {
    case 'p':
        return i & 1;
    case 'q':
        return (i >> 1) & 1;
    case 'r':
        return (i >> 2) & 1;
    case 's':
        return (i >> 3) & 1;
    case 't':
        return (i >> 4) & 1;
    case 'N':
        return !WFF(formula, i);
    case 'K':
        return WFF(formula, i) & WFF(formula, i);
    case 'A':
        return WFF(formula, i) | WFF(formula, i);
    case 'C':
        return !WFF(formula, i) | WFF(formula, i);
    case 'E':
        return WFF(formula, i) == WFF(formula, i);
    }
    
    return false;
};

bool isTautology(string formula)
{
    for (int i = 0; i < 32; ++i)
    {
        pos = -1;
        if (WFF(formula, i)==false) return false;;
    }
    return true;
};

int main(int argc, char* argv[])
{
    string ln;
    while (cin >> ln && ln[0] != '0')
    {
        if (isTautology(ln)) cout << "tautology\n";
        else cout << "not\n";
    }
    return 0;
}