Tautology

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

 1 //类似于后缀式求值；

 2 

 3 #include<stdio.h>

 4 #include<string.h>

 5 #include<stack>

 6 using namespace std;

 7 

 8 char ss[101];

 9 stack <int> st;

10 int flag;

11 

12 void check(int p, int q, int r, int s,int t)

13 {

14     while(!st.empty())

15         st.pop();

16     int a,b;

17     int len = strlen(ss);

18     for(int i = len-1; i >= 0; i--)

19     {

20         if(ss[i] == 'p')

21             st.push(p);

22         else if(ss[i] == 'q')

23             st.push(q);

24         else if(ss[i] == 'r')

25             st.push(r);

26         else if(ss[i] == 's')

27             st.push(s);

28         else if(ss[i] == 't')

29             st.push(t);

30         else if(ss[i] == 'K')

31         {

32             a = st.top();

33             st.pop();

34             b = st.top();

35             st.pop();

36             if(a == 1 && b == 1)

37                 st.push(1);

38             else st.push(0);

39         }

40         else if(ss[i] == 'A')

41         {

42             a = st.top();

43             st.pop();

44             b = st.top();

45             st.pop();

46             if(a == 0 && b == 0)

47                 st.push(0);

48             else st.push(1);

49         }

50         else if(ss[i] == 'N')

51         {

52             a = st.top();

53             st.pop();

54             if(a == 1)

55                 st.push(0);

56             else st.push(1);

57         }

58         else if(ss[i] == 'C')

59         {

60             a = st.top();

61             st.pop();

62             b = st.top();

63             st.pop();

64             if(a == 0 && b == 1)

65                 st.push(0);

66             else st.push(1);

67         }

68         else if(ss[i] == 'E')

69         {

70             a = st.top();

71             st.pop();

72             b = st.top();

73             st.pop();

74             st.push((a && b) || (!a && !b));

75         }

76     }

77     if(st.top() != 1)

78         flag = 0;

79 }

80 int main()

81 {

82     while(~scanf("%s",ss))

83     {

84         flag = 1;

85         if(strcmp("0",ss) == 0)

86             break;

87         for(int p = 0; p < 2; p++)

88             for(int q = 0; q < 2; q++)

89                 for(int r = 0; r < 2; r++)

90                     for(int s = 0; s < 2; s++)

91                         for(int t = 0; t < 2; t++)

92                             check(p, q, r, s, t);

93         if(flag == 1)

94             printf("tautology\n");

95         else printf("not\n");

96     }

97     return 0;

98 }

View Code