Problem:
Problem C: How can I satisfy thee? Let me count the ways...

Three-valued logic is a logic system that has, in addition to "true" and
"false", "unknown" as a valid value.

In the following, logical values "false", "unknown" and "true" are
represented by 0, 1 and 2 respectively.

Let "-" be a unary operator (i.e. a symbol representing one argument function)
and let both "*" and "+" be binary operators (i.e. symbols representing
two argument functions).
These operators represent negation (NOT), conjunction (AND) and
disjunction (OR) respectively.
These operators in three-valued logic can be defined in Table C-1.

Table C-1: Truth tables of three-valued logic operators

-X

(X*Y)

(X+Y)

Let P, Q and R be variables ranging over three-valued logic values.
For a given formula, you are asked to answer the number of triples (P,Q,R)
that satisfy the formula, that is, those which make the value of the
given formula 2.
A formula is one of the following form (X and Y represent formulas).

Constants: 0, 1 or 2

Variables: P, Q or R

Negations: -X

Conjunctions: (X*Y)

Disjunctions: (X+Y)

Note that conjunctions and disjunctions of two formulas are always
parenthesized.

For example, when formula (P*Q) is given as an input, the value of
this formula is 2 when and only when (P,Q,R) is (2,2,0), (2,2,1) or (2,2,2).
Therefore, you should output 3.

Input

The input consists of one or more lines. Each line contains a formula.
A formula is a string which consists of 0, 1, 2, P, Q, R, -, *, +, (, ).
Other characters such as spaces are not contained.
The grammar of formulas is given by the following BNF.

<formula> ::= 0 | 1 | 2 | P | Q | R |
-<formula> | (<formula>*<formula>) | (<formula>+<formula>)

All the formulas obey this syntax and thus you do not have to care about
grammatical errors.
Input lines never exceed 80 characters.

Finally, a line which
contains only a "." (period) comes, indicating the end of the input.

Output

You should answer the number (in decimal) of triples (P,Q,R) that make the
value of the given formula 2. One line containing the number should be
output for each of the formulas, and no other characters should be output.

Sample Input

(P*Q)
(--R+(P*Q))
(P*-P)
2
1
(-1+(((---P+Q)*(--Q+---R))*(-R+-P)))
.

Output for the Sample Input

3
11
0
27
0
7

Solution in JAVA (judge verdict: Accepted)

import java.util.Arrays; 
import java.util.LinkedList;
import java.util.PriorityQueue;
import java.util.Scanner;

public class Main {

	
	public static interface Fomula{
		int eval(int[] input);
	}
	
	public static class Minus implements Fomula{
		Fomula inner;
		
		public Minus(Fomula in){
			inner = in;
		}

		@Override
		public int eval(int[] input) {
			return 2 - inner.eval(input);
		}
		
		public String toString(){
			return "-" + inner;
		}
	}
	
	public static class Add implements Fomula{
		Fomula left, right;
		
		public Add(Fomula left, Fomula right){
			this.left = left;
			this.right = right;
		}

		@Override
		public int eval(int[] input) {
			return Math.max(left.eval(input), right.eval(input));
		}
		
		public String toString(){
			return "(" + left + "+" + right + ")";
		}
	}
	
	public static class Mul implements Fomula{
		Fomula left, right;
		
		public Mul(Fomula left, Fomula right){
			this.left = left;
			this.right = right;
		}

		@Override
		public int eval(int[] input) {
			return Math.min(left.eval(input), right.eval(input));
		}
		
		public String toString(){
			return "(" + left + "*" + right + ")";
		}
	}
	
	public static class Const implements Fomula{
		int con;
		
		public Const(int con){
			this.con = con;
		}

		@Override
		public int eval(int[] input) {
			return con;
		}
		
		public String toString(){
			return "" + con;
		}
	}
	
	public static class Var implements Fomula{
		int var;
		
		public Var(int v){
			var = v;
		}

		@Override
		public int eval(int[] input) {
			return input[var];
		}
		
		public String toString(){
			return (char)(var + 'P')+"";
		}
	}
	
	public static Fomula parse(char[] input, int start, int end){
		int k_lv = 0;
		int k_s = -1, k_e = -1;
		int m_s = -1;
		int a_p = -1, m_p = -1;
		
		for(int pos = start; pos <= end; pos++){
			if(input[pos] == '('){
				if(k_lv == 0){
					k_s = pos;
				}
				k_lv++;
			}else if(input[pos] == ')'){
				k_lv--;
				if(k_lv == 0){
					k_e = pos;
					break;
				}
			}else if(input[pos] == '-' && k_lv == 0 && m_s == -1){
				m_s = pos;
				break;
			}else if(input[pos] == '*' && k_lv == 1){
				m_p = pos;
			}else if(input[pos] == '+' && k_lv == 1){
				a_p = pos;
			}			
		}
		
		if(k_s != -1 && k_e != -1){
			if(m_p != -1){
				return new Mul(parse(input, k_s + 1, m_p - 1), parse(input, m_p + 1, k_e - 1));
			}else{
				return new Add(parse(input, k_s + 1, a_p - 1), parse(input, a_p + 1, k_e - 1));
			}
		}else if(m_s != -1){
			return new Minus(parse(input, m_s + 1, end));
		}else if('0' <= input[start] && input[start] <= '2'){
			return new Const(input[start] - '0');
		}else {
			return new Var(input[start] - 'P');
		}
	}
	
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		
		while(true){
			String str = sc.next();
			
			if(".".equals(str)){
				break;
			}
			
			char[] input = str.toCharArray();
			
			Fomula fomula = parse(input, 0, input.length - 1);
			
			//System.out.println(fomula);
			
			int count = 0;
			int[] array = new int[3];
			for(int p = 0; p <= 2; p++){
				array[0] = p;
				
				for(int q = 0; q <= 2; q++){
					array[1] = q;
					
					for(int r = 0; r <= 2; r++){
						array[2] = r;
						
						if(fomula.eval(array) == 2){
							count++;
						}
					}
				}
			}
			
			System.out.println(count);
		}
		
	}
}