Home » Problems (medium) » Tautology

Tautology

Problem code: TAUT

All submissions for this problem are available.

Write a program that checks if the given logical expression is a tautology. The logical expression is a tautology if it is always true, regardless of logical value of its variables.

Input

On the first line there is the number of expressions to check (at most 35). The expression is in a prefix notation, that means that operator precedes its arguments. The following logical operators will be used: 

C - and 
D - or
I - implies
E - if, and only if
N - not

The variables will be lowercase letters (a-z). There will be no more than 16 different letters in the expression. The length of the expression will not exceed 111 characters.

Output

For each expression write one word: YES if it is a tautology, NO in other case.

Example

Sample input:
7
IIpqDpNp
NCNpp
Iaz
NNNNNNNp
IIqrIIpqIpr
Ipp
Ezz


Sample output:
YES
YES
NO
NO
YES
YES
YES

Date:2008-12-01
Time limit:7s
Source limit:50000B
Languages:All except: PERL6


Comments

Loading Comments...

SUCCESSFUL SUBMISSIONS FOR THIS PROBLEM:

Loading Submissions...

RECENT ACTIVITY FOR THIS PROBLEM:

Loading Recent Activity...

HELP

Program should read from standard input and write to standard output.

After you submit a solution you can see your results by clicking on the [My Submissions] tab on the problem page. Below are the possible results:

  • Accepted Your program ran successfully and gave a correct answer. If there is a score for the problem, this will be displayed in parenthesis next to the checkmark.
  • Time Limit Exceeded Your program was compiled successfully, but it didn't stop before time limit. Try optimizing your approach.
  • Wrong Answer Your program compiled and ran succesfully but the output did not match the expected output.
  • Runtime Error Your code compiled and ran but encountered an error. The most common reasons are using too much memory or dividing by zero. For the specific error codes see the help section.
  • Compilation Error Your code was unable to compile. When you see this icon, click on it for more information.

If you are still having problems, see a sample solution here.