| Time Limit: 1000MS | Memory Limit: 65536K | |
| Total Submissions: 10453 | Accepted: 3967 |
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
#include<string.h>
#include<stack>
#include<iostream>
#include<algorithm>
using namespace std;
char str[200];
int p,q,r,s,t;
stack<int>Q;
void instack(char c){
if(c=='p')
Q.push(p);
else if(c=='q')
Q.push(q);
else if(c=='r')
Q.push(r);
else if(c=='s')
Q.push(s);
else if(c=='t')
Q.push(t);
else
return;
}
void calculate(char c){
int a,b,temp;
if(c=='K'){
a=Q.top();
Q.pop();
b=Q.top();
Q.pop();
temp=a&b;
Q.push(temp);
}
else if(c=='A'){
a=Q.top();
Q.pop();
b=Q.top();
Q.pop();
temp=a||b;
Q.push(temp);
}
else if(c=='E'){
a=Q.top();
Q.pop();
b=Q.top();
Q.pop();
temp=(a==b);
Q.push(temp);
}
else if(c=='C'){
a=Q.top();
Q.pop();
b=Q.top();
Q.pop();
temp=(!a)||b;
Q.push(temp);
}
else if(c=='N'){
a=Q.top();
Q.pop();
temp=!a;
Q.push(temp);
}
else
return ;
}
int main(){
while(scanf("%s",str)!=EOF){
getchar();
if(strcmp(str,"0")==0)
break;
int len=strlen(str);
int flag;
for( p=0;p<=1;p++){
for( q=0;q<=1;q++){
for(r=0;r<=1;r++){
for( s=0;s<=1;s++){
for( t=0;t<=1;t++){
flag=0;
for(int i=len-1;i>=0;i--){
if(str[i]=='p'||str[i]=='q'||str[i]=='r'||str[i]=='s'||str[i]=='t')
instack(str[i]);
else
calculate(str[i]);
}
int ans=Q.top();
Q.pop();
if(ans==0){
flag=1;
break;
}
}
if(flag) break;
}
if(flag) break;
}
if(flag) break;
}
if(flag) break;
}
if(flag)
printf("not\n");
else
printf("tautology\n");
memset(str,0,sizeof(str));
}
return 0;
}