poj 3295 -- Tautology

Tautology
Time Limit: 1000MS   Memory Limit: 65536K
Total Submissions: 9075   Accepted: 3474

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

说是构造法。。哎！参考别人的思路，学习了一下。。。 http://blog.csdn.net/lyy289065406/article/details/6642766

  1 /*======================================================================
  2  *           Author :   kevin
  3  *         Filename :   Tautology.cpp
  4  *       Creat time :   2014-05-19 20:35
  5  *      Description :
  6  ========================================================================*/
  7 #include <iostream>
  8 #include <algorithm>
  9 #include <cstdio>
 10 #include <cstring>
 11 #include <queue>
 12 #include <cmath>
 13 #include <stack>
 14 #define clr(a,b) memset(a,b,sizeof(a))
 15 #define M 115
 16 using namespace std;
 17 char str[M];
 18 stack<int>st;
 19 int p,q,r,s,t,len;
 20 bool judgevalue(char c)
 21 {
 22     if(c == 'p')       st.push(p);
 23     else if(c == 'q')  st.push(q);
 24     else if(c == 'r')  st.push(r);
 25     else if(c == 's')  st.push(s);
 26     else if(c == 't')  st.push(t);
 27     else return false;
 28     return true;
 29 }
 30 void opera(char c)
 31 {
 32     if(c == 'K'){
 33         int x = st.top();
 34         st.pop();
 35         int y = st.top();
 36         st.pop();
 37         st.push(x && y);
 38     }
 39     else if(c == 'A'){
 40         int x = st.top();
 41         st.pop();
 42         int y = st.top();
 43         st.pop();
 44         st.push(x || y);
 45     }
 46     else if(c == 'C'){
 47         int x = st.top();
 48         st.pop();
 49         int y = st.top();
 50         st.pop();
 51         st.push((!x)||y);
 52     }
 53     else if(c == 'E'){
 54         int x = st.top();
 55         st.pop();
 56         int y = st.top();
 57         st.pop();
 58         st.push(x == y);
 59     }
 60     else if(c == 'N'){
 61         int x = st.top();
 62         st.pop();
 63         st.push(!x);
 64     }
 65     return;
 66 }
 67 bool slove()
 68 {
 69     bool flag = true;
 70     for(p = 0; p < 2; p++){
 71         for(q = 0; q < 2; q++){
 72             for(r = 0; r < 2; r++){
 73                 for(s = 0; s < 2; s++){
 74                     for(t = 0; t < 2; t++){
 75                         for(int ii = len-1; ii >= 0 ; ii--){
 76                             if(!judgevalue(str[ii])){
 77                                 opera(str[ii]);
 78                             }
 79                         }
 80                         int ans = st.top();
 81                         st.pop();
 82                         if(!ans){
 83                             flag = false;
 84                             break;
 85                         }
 86                     }
 87                     if(!flag) break;
 88                 }
 89                 if(!flag) break;
 90             }
 91             if(!flag) break;
 92         }
 93         if(!flag) break;
 94     }
 95     if(flag) return true;
 96     return false;
 97 }
 98 int main(int argc,char *argv[])
 99 {
100     while(scanf("%s",str)!=EOF){
101         getchar();
102         if(str[0] == '0') break;
103         len = strlen(str);
104         if(slove()){
105             printf("tautology\n");
106         }
107         else printf("not\n");
108         clr(str,0);
109     }
110     return 0;
111 }
View Code

 

 

posted @ 2014-05-19 21:39  ZeroCode_1337  阅读(241)  评论(0)  编辑  收藏  举报