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| Time Limit: 1000MS | Memory Limit: 65536K | |
| Total Submissions: 11579 | Accepted: 4392 |
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:
| 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
大致题意：
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。
PS:输入格式保证是合法的
思路：
对于逻辑变量的每个取值，都依次枚举 判断对于每一种逻辑变量的取值情况表达式是否为真
#include<iostream> using namespace std; int cnt; char str[101]; bool step(char str[101],int tk){ cnt++; switch(str[cnt]){ case ‘p‘:return tk&1; case ‘q‘:return(tk>>1)&1; case ‘r‘:return(tk>>2)&1; case ‘s‘:return(tk>>3)&1; case ‘t‘:return(tk>>4)&1; case ‘N‘:return !step(str,tk); case ‘K‘:return step(str,tk)&step(str,tk); case ‘A‘:return step(str,tk)|step(str,tk); case ‘C‘:return !step(str,tk)|step(str,tk); case ‘E‘:return step(str,tk)==step(str,tk); } } bool judge(char str[101]){ for(int i=0;i<32;i++){ cnt=-1; if(!step(str,i)) return 0; } return 1; } int main(){ while(cin>>str){ if(str[0]==‘0‘) break; if(judge(str)) cout<<"tautology"<<endl; else cout<<"not"<<endl; } return 0; }
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原文地址：http://www.cnblogs.com/shenben/p/5646335.html
