Tautology(POJ_3295)

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

代码                                   

//方法可能略挫，看到其他人都是逆序入栈，就我是顺序入栈= =

#include <iostream>
#include <stack>
#include <cstdio>
#include <cstring>

using namespace std;

int main()
{
    char str[1100];
    while(scanf("%s", str) != EOF)
    {
        int flag[5];
        memset(flag, -1, sizeof(-1));
        if(strcmp(str, "0") == 0)
            break;
        int len = strlen(str);
        stack<char> s;
        while(s.size())
            s.pop();
        for(int i = 0; i < len; i++)
        {
            if(str[i] >= 'p' && str[i] <= 't')
                flag[str[i]-'p'] = 0;
        }
        bool ans = 1;
        while(1)
        {
            for(int i = 0; i < len; i++)
            {
                if(str[i] >= 'A' && str[i] <= 'N')
                {
                    s.push(str[i]);
                    continue;
                }
                else
                    s.push(flag[str[i]-'p']+'0');
                while(s.size() > 1)
                {
                    char x = s.top();
                    s.pop();
                    char w = s.top();
                    s.pop();
                    if(w == 'N' && isdigit(x))
                    {
                        s.push((x-'0'+1)%2+'0');
                    }
                    else if(isdigit(x) && isdigit(w))
                    {
                        char c = s.top();
                        s.pop();
                        if(c == 'A')
                        {
                            if(w == '0' && x == '0')
                                s.push('0');
                            else
                                s.push('1');
                        }
                        else if(c == 'K')
                        {
                            if(w == '1' && x == '1')
                                s.push('1');
                            else
                                s.push('0');
                        }
                        else if(c == 'C')
                        {
                            if(w == '1' && x == '0')
                                s.push('0');
                            else
                                s.push('1');
                        }
                        else if(c == 'E')
                        {
                            if(w != x)
                                s.push('0');
                            else
                                s.push('1');
                        }
                    }
                    else
                    {
                        s.push(w);
                        s.push(x);
                        break;
                    }
                }
            }
            if(s.size() == 1 && s.top() == '0')
            {
                ans = 0;
                break;
            }
            while(s.size())
                s.pop();
            int i;
            for(i = 4; i >= 0; i--)
            {
                if(flag[i] != -1)
                    flag[i] = (flag[i] + 1) % 2;
                if(flag[i] == 1)
                    break;
            }
            if(i == -1)
                break;
        }
        if(ans)
            printf("tautology\n");
        else
            printf("not\n");
    }
    return 0;
}

//听了QAQ巨巨的讲解疯狂优化了下我的代码= =正序也改成逆序惹，还是简洁明了的代码看起来舒服，仰慕高端QAQ。

#include <iostream>
#include <stack>
#include <cstdio>
#include <cstring>

using namespace std;

char str[110];

bool Cal(char c, bool a, bool b)
{
    if(c == 'A') return a||b;
    if(c == 'K') return a&&b;
    if(c == 'C') return a==b || ((!a)&&b);
    return a==b;
}

bool Judge()
{
    bool flag[5], a, b;
    for(int i = 0; i < (1 << 5); i++)
    {
        for(int j = 0, k = i; j < 5; j++)
        {
            flag[j] = k % 2;
            k /= 2;
        }
        stack<bool> s;
        int len = strlen(str);
        for(int j = len-1; j >= 0; j--)
        {
            if(str[j] >= 'p' && str[j] <='t')
                s.push(flag[str[j]-'p']);
            else if(str[j] == 'N')
            {
                a = s.top();
                s.pop();
                s.push(!a);
            }
            else
            {
                a = s.top();
                s.pop();
                b = s.top();
                s.pop();
                s.push(Cal(str[j], a, b));
            }
        }
        if(!s.top()) return 0;
    }
    return 1;
}

int main()
{
    while(scanf("%s", str) && str[0] != '0')
    {
        printf(Judge() == 1 ? "tautology\n" : "not\n");
    }
    return 0;
}