1490 - Cantor
Time Limit : 5 Second
Memory Limit : 128 MB
Submission: 3
Solved: 2
- Description
The ternary expansion of a number is that number written in base 3. A number can have more than one ternary expansion. A ternary expansion is indicated with a subscript 3. For example, 1 = 13 = 0.222...3, and 0.875 = 0.212121...3.
The Cantor set is defined as the real numbers between 0 and 1 inclusive that have a ternary expansion that does not contain a 1. If a number has more than one ternary expansion, it is enough for a single one to not contain a 1.
For example, 0 = 0.000...3 and 1 = 0.222...3, so they are in the Cantor set. But 0.875 = 0.212121...3 and this is its only ternary expansion, so it is not in the Cantor set.
Your task is to determine whether a given number is in the Cantor set.- Input
- The input consists of several test cases.
Each test case consists of a single line containing a number x written in decimal notation, with 0 <= x <= 1, and having at most 6 digits after the decimal point.
The last line of input is END. This is not a test case. - Output
- For each test case, output MEMBER if x is in the Cantor set, and NON-MEMBER if x is not in the Cantor set.
- sample input
-
0 1 0.875 END
- sample output
-
MEMBER MEMBER NON-MEMBER
- hint
- source
- waterloo 3 October, 2009