POJ 3295 Tautology

Tautology (http://acm.pku.edu.cn/JudgeOnline/problem?id=3295)

Time Limit: 1000MS
Memory Limit: 65536K

Total Submissions: 2551
Accepted: 983

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.

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

---------------------------------------------------------------------------------

Solution

Stack+Queue

import java.util.Scanner;

public class POJ_3295 {
	public static boolean parse(String str, boolean p, boolean q, boolean r,
			boolean s, boolean t) {
		char[] stack = str.toCharArray();
		int sp = stack.length - 1;
		boolean[] queue = new boolean[100];
		int qp = 0;
		boolean a, b, c = false;
		while (sp != -1) {
			if (stack[sp] == 'p' || stack[sp] == 'q' || stack[sp] == 'r'
					|| stack[sp] == 's' || stack[sp] == 't' || stack[sp] == 'z'
					|| stack[sp] == 'x') {
				switch (stack[sp--]) {
				case 'p':
					queue[qp++] = p;
					break;
				case 'q':
					queue[qp++] = q;
					break;
				case 'r':
					queue[qp++] = r;
					break;
				case 's':
					queue[qp++] = s;
					break;
				case 't':
					queue[qp++] = t;
					break;
				case 'z':
					queue[qp++] = true;
					break;
				case 'x':
					queue[qp++] = false;
					break;
				}

			} else {
				switch (stack[sp--]) {
				case 'K':
					a = queue[--qp];
					b = queue[--qp];
					c = a && b;
					break;
				case 'A':
					a = queue[--qp];
					b = queue[--qp];
					c = a || b;
					break;
				case 'N':
					a = queue[--qp];
					c = !a;
					break;
				case 'C':
					a = queue[--qp];
					b = queue[--qp];
					if (a == b == true)
						c = true;
					else if (a && !b)
						c = false;
					else if (!a && b)
						c = true;
					else
						c = true;
					break;
				case 'E':
					a = queue[--qp];
					b = queue[--qp];
					if (a == b)
						c = true;
					else
						c = false;
					break;
				}
				if (c)
					stack[++sp] = 'z';
				else
					stack[++sp] = 'x';
			}
		}
		return queue[0];
	}

	public static String preprocess(String str){
		String match = "NN";
		while(str.contains(match)){
			int i = str.indexOf(match);
			String second = str.substring(i+2);
			String first = str.substring(0, i);
			str = first.concat(second);
		}
		return str;
	}
	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
		String input;
		while (!(input = in.next()).equalsIgnoreCase("0")){
			input = preprocess(input);
			boolean p, q, r, s, t, result = false, pre, temp, init = false;
			boolean bool[] = { true, false };
			for (boolean a : bool) {
				p = a;
				for (boolean b : bool) {
					q = b;
					for (boolean c : bool) {
						r = c;
						for (boolean d : bool) {
							s = d;
							for (boolean e : bool) {
								t = e;
								temp = parse(input, p, q, r, s, t);
								if (init == false) {
									init = true;
									pre = result = temp;
								} else {
									pre = result;
									result = temp;
								}
								if (pre != result) {
									System.out.println("not");
									System.exit(0);
								}
							}
						}
					}
				}
			}
			System.out.println("Tautology");
		}
	}
}