| 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.
- 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.
| 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 "); 106 } 107 else printf("not "); 108 clr(str,0); 109 } 110 return 0; 111 }