POJ 3295-Tautology(构造法+栈)

Tautology

Time Limit: 1000MS Memory Limit: 65536KTotal Submissions: 9936 Accepted: 3774

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

ApNpApNq0

Sample Output

tautologynot

题意：输入由p、q、r、s、t、K、A、N、C、E共10个字母组成的逻辑表达式，
           其中p、q、r、s、t的值为1（true）或0（false），即逻辑变量；
            K、A、N、C、E为逻辑运算符，
           K --> and:  x && y
           A --> or:  x || y
           N --> not :  !x
          C --> implies :  (!x)||y
          E --> equals :  x==y
          问这个逻辑表达式是否为永真式。

思路：WFF的计算方法：从字符串WFF的末尾开始依次向前读取字符。构造一个栈stack，当遇到逻辑变量 p, q, r, s ,t 则将其当前的值压栈；遇到 N 则取栈顶元素进行非运算，运算结果的值压栈；遇到K, A, C, E则从栈顶中弹出两个元素进行相应的运算，将结果的值压栈。 由于输入是合法的，当字符串WFF扫描结束时，栈stack中只剩一个值，该值就是逻辑表达式WFF的值。

#include <stdio.h>#include <string.h>#include <stdlib.h>#include <iostream>#include <algorithm>#include <stack>using namespace std;char str[110];stack<int>Q;int p,q,r,s,t,len;int IN_stack(){        int i;        int x,y;        for(i=strlen(str)-1; i>=0; i--) {                if(str[i] == 'p')                        Q.push(p);                else if(str[i] == 'q')                        Q.push(q);                else if(str[i] == 'r')                        Q.push(r);                else if(str[i] == 's')                        Q.push(s);                else if(str[i] == 't')                        Q.push(t);                else if(str[i]== 'K') {                        x = Q.top();                        Q.pop();                        y = Q.top();                        Q.pop();                        Q.push(x && y);                } else if(str[i] == 'A') {                        x = Q.top();                        Q.pop();                        y = Q.top();                        Q.pop();                        Q.push(x || y);                } else if(str[i] == 'N') {                        x = Q.top();                        Q.pop();                        Q.push(!x);                } else if(str[i] == 'C') {                        x = Q.top();                        Q.pop();                        y = Q.top();                        Q.pop();                        Q.push((!x)||y);                } else if(str[i] == 'E') {                        x = Q.top();                        Q.pop();                        y = Q.top();                        Q.pop();                        Q.push(x == y);                }        }}int judge(){        for(p=0; p<2; p++)                for(q=0; q<2; q++)                        for(r=0; r<2; r++)                                for(s=0; s<2; s++)                                        for(t=0; t<2; t++) {                                                IN_stack();                                                if(Q.top()==0)                                                        return 0;                                        }        return 1;}int main(){        while(~scanf("%s",str)) {                getchar();                if(str[0] == '0')                        break;                if(judge()) {                        printf("tautology\n");                } else printf("not\n");        }        return 0;}