### GCJ 2008 - Alien Numbers

Posted on July 16, 2008

'Alien Numbers' problem statement:

Problem
-------

The decimal numeral system is composed of ten digits, which we represent as "0123456789" (the digits in a system are written from lowest to highest). Imagine you have discovered an alien numeral system composed of some number of digits, which may or may not be the same as those used in decimal. For example, if the alien numeral system were represented as "oF8", then the numbers one through ten would be (F, 8, Fo, FF, F8, 8o, 8F, 88, Foo, FoF). We would like to be able to work with numbers in arbitrary alien systems. More generally, we want to be able to convert an arbitrary number that's written in one alien system into a second alien system.

Input
-----

The first line of input gives the number of cases, N. N test cases follow. Each case is a line formatted as

alien_number source_language target_language

Each language will be represented by a list of its digits, ordered from lowest to highest value. No digit will be repeated in any representation, all digits in the alien number will be present in the source language, and the first digit of the alien number will not be the lowest valued digit of the source language (in other words, the alien numbers have no leading zeroes). Each digit will either be a number 0-9, an uppercase or lowercase letter, or one of the following symbols !"#\$%&'()*+,-./:;<=>[email protected][\]^_`{|}~

Output
------

For each test case, output one line containing "Case #x: " followed by the alien number translated from the source language to the target language.

Limits
------

1 ≤ N ≤ 100.

Small dataset
-------------

1 ≤ num digits in alien_number ≤ 4,
2 ≤ num digits in source_language ≤ 16,
2 ≤ num digits in target_language ≤ 16.

Large dataset
-------------

1 ≤ alien_number (in decimal) ≤ 1000000000,
2 ≤ num digits in source_language ≤ 94,
2 ≤ num digits in target_language ≤ 94.

Sample Input
------------

4
9 0123456789 oF8
Foo oF8 0123456789
13 0123456789abcdef 01
CODE O!CDE? A?JM!.

Sample Output
-------------

Case #1: Foo
Case #2: 9
Case #3: 10011
Case #4: JAM!

There are a couple of ways you can code a solution for this, but if you know (or did some research on) number systems, you can figure out the easiest solution.

My Solution:
------------

Since the 'decimal system' is the easiest that we humans and the programming languages (Higher-Level Languages) can comprehend, I converted the 'Alien Number' (using 'Source Language' input) into a decimal number and then divided that number with the 'base of the 'Target Language' number system) . The remainder is found and if its not zero, the division has to be done repeatedly on the quotient of the previous division until the remainder is '0' and collect all the 'remainders'. Form a number from the remainders, in the reverse order....and....VOILA!

Example: (Converting '19' (decimal) to 'base 5')

19/5 = 3 ------> 4 (remainder)
3/5 = 0 - -----> 3 (remainder)

So, the decimal number 19 is equal to 34 in 'base 5'. Simple! :-)

Then I uploaded the output files and found the solution to be 'Correct'.

Here's the code for my solution:

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