| Time Limit: 1000MS | Memory Limit: 65536K | |
| Total Submissions: 10428 | Accepted: 3959 |
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
实在是读不懂什么意思，后来找篇博客，才知道什么意思，英语好渣#include <iostream>
#include <cstring>
#include <cstdio>
#include <cmath>
#include <string>
#include <stack>
#include <algorithm>
using namespace std; const int Max=1100000; int Arr[6];
int top;
string str;
stack<int>a;
void Bit(int num)
{
int top=0;
memset(Arr,0,sizeof(Arr));
while(num)
{
Arr[top++]=num%2;
num/=2;
}
}
bool Jud(char s)
{
switch(s)
{
case 'p':a.push(Arr[0]);break;
case 'q':a.push(Arr[1]);break;
case 'r':a.push(Arr[2]);break;
case 's':a.push(Arr[3]);break;
case 't':a.push(Arr[4]);break;
default :return 0;
}
return 1;
}
void Count(char s)
{
switch(s)
{
case 'K':
{
int x=a.top();a.pop();
int y=a.top();a.pop();
a.push(x&&y);
}
break;
case 'A':
{
int x=a.top();a.pop();
int y=a.top();a.pop();
a.push(x||y);
}
break;
case 'N':
{
int x=a.top();a.pop();
a.push(!x);
}
break;
case 'C':
{
int x=a.top();a.pop();
int y=a.top();a.pop();
a.push((!x)||y);
}
break;
case 'E':
{
int x=a.top();a.pop();
int y=a.top();a.pop();
a.push(x==y);
}
break;
}
}
bool Cal()
{
int len=str.length();
for(int i=0;i<=31;i++)
{
Bit(i);
for(int j=len-1;j>=0;j--)
{
if(!Jud(str[j]))
{
Count(str[j]);
}
}
int x=a.top();
a.pop();
if(!x)
return false;
}
return true;
}
int main()
{
while(cin>>str)
{
if(str=="0")
break;
if(Cal())
{
cout<<"tautology"<<endl;
}
else
{
cout<<"not"<<endl;
}
} }
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