GCJ 2013 - Fair And Square

Below is the problem statement for 'Fair And Square' from 'Google Code Jam - 2013':


Problem
-------

Little John likes palindromes, and thinks them to be fair (which is a fancy word for nice). A palindrome is just an integer that reads the same backwards and forwards - so 6, 11 and 121 are all palindromes, while 10, 12, 223 and 2244 are not (even though 010=10, we don't consider leading zeroes when determining whether a number is a palindrome).

He recently became interested in squares as well, and formed the definition of a fair and square number - it is a number that is a palindrome and the square of a palindrome at the same time. For instance, 1, 9 and 121 are fair and square (being palindromes and squares, respectively, of 1, 3 and 11), while 16, 22 and 676 are not fair and square: 16 is not a palindrome, 22 is not a square, and while 676 is a palindrome and a square number, it is the square of 26, which is not a palindrome.

Now he wants to search for bigger fair and square numbers. Your task is, given an interval Little John is searching through, to tell him how many fair and square numbers are there in the interval, so he knows when he has found them all.

Solving this problem
--------------------

Usually, Google Code Jam problems have 1 Small input and 1 Large input. This problem has 1 Small input and 2 Large inputs. Once you have solved the Small input, you will be able to download any of the two Large inputs. As usual, you will be able to retry the Small input (with a time penalty), while you will get only one chance at each of the Large inputs.

Input
-----

The first line of the input gives the number of test cases, T. T lines follow. Each line contains two integers, A and B - the endpoints of the interval Little John is looking at.

Output
------

For each test case, output one line containing "Case #x: y", where x is the case number (starting from 1) and y is the number of fair and square numbers greater than or equal to A and smaller than or equal to B.

Limits
------

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

1 ≤ T ≤ 100.
1 ≤ A ≤ B ≤ 1000.

First large dataset
-------------------

1 ≤ T ≤ 10000.
1 ≤ A ≤ B ≤ 1014.

Second large dataset
--------------------

1 ≤ T ≤ 1000.
1 ≤ A ≤ B ≤ 10100.

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

3
1 4
10 120
100 1000

Output
------

Case #1: 2
Case #2: 0
Case #3: 2


The above problem statement says that given 2 numbers (min and max), we have to find the number of 'Fair and Square' numbers in that range (min --> max). For a number to be "Fair And Square", it should be a perfect square, a palindrome and it's square root should also be a palindrome. For Example: 4 is a palindrome and a perfect square. It's Square-Root 2 is also a palindrome. So, 4 is a "Fair And Square" number.

My idea was to find the Minimum and Maximum 'Perfect Squares' in that range, find Square Roots for those numbers and loop between these 2 square-roots, to find the number of 'Fair and Square' numbers in the given range. When looping between these Square-roots, the square-root is first checked if it is a palindrome or not. If it is a palindrome, it's square is calculated and a check is done to find out, if it is a palindrome or not. If it is a palindrome, the square number is a 'Fair And Square' number.

For the 'Small Input Dataset' of the above problem statement, the logic described above works without any problems and finishes pretty fast. But for large datasets, better algorithms or infrastructure is needed, for the programs to finish within the timeline. So, I decided on using external libraries to handle BIG numbers and also a Off-Heap-Memory framework/library, which persists Java's Map datastructure to disk (which would also help me to avoid Java's OutOfMemory problems). For handling big/large numbers, I decided to use the JScience library, which has "LargeInteger" and convenient methods to find "Square Roots" or do other math. For the Off-Heap-Memory (Disk based storage), there were a couple of options like Berkeley DB, HSQLDB, MapDB, etc...I decided on using MapDB, after I checked it's performance stats and found that to be good enough. Also, it was easy to get started. I used a Maven based project. So, the POM.xml for this project is as below:

NOTE: If you are not using Maven, you can download these libraries seperately and use them for the below listed Java program.



And the solution to the above problem statement is as below:

Note that the below solution works for only the 'Small Data Set' and 'Large Dataset - 1', within the given timeline. For 'Large Dataset - 2', you can solve it by creating the 'Fair And Square' cache first, then download the input and solve it. A better solution would be to use a better algorithm, as described in the 'Contest Analysis' section of the GCJ 2013 Qualification Round's Dashboard.



You can also find the source code at: GCJ 2013 - Fair And Square

GCJ 2013 - Tic-Tac-Toe-Tomek

Below is the problem statement for 'Tic-Tac-Toe-Tomek' from 'Google Code Jam - 2013':


Problem
-------

Tic-Tac-Toe-Tomek is a game played on a 4 x 4 square board. The board starts empty, except that a single 'T' symbol may appear in one of the 16 squares. There are two players: X and O. They take turns to make moves, with X starting. In each move a player puts her symbol in one of the empty squares. Player X's symbol is 'X', and player O's symbol is 'O'.

After a player's move, if there is a row, column or a diagonal containing 4 of that player's symbols, or containing 3 of her symbols and the 'T' symbol, she wins and the game ends. Otherwise the game continues with the other player's move. If all of the fields are filled with symbols and nobody won, the game ends in a draw. See the sample input for examples of various winning positions.

Given a 4 x 4 board description containing 'X', 'O', 'T' and '.' characters (where '.' represents an empty square), describing the current state of a game, determine the status of the Tic-Tac-Toe-Tomek game going on. The statuses to choose from are:

"X won" (the game is over, and X won)
"O won" (the game is over, and O won)
"Draw" (the game is over, and it ended in a draw)
"Game has not completed" (the game is not over yet)
If there are empty cells, and the game is not over, you should output "Game has not completed", even if the outcome of the game is inevitable.

Input
-----

The first line of the input gives the number of test cases, T. T test cases follow. Each test case consists of 4 lines with 4 characters each, with each character being 'X', 'O', '.' or 'T' (quotes for clarity only). Each test case is followed by an empty line.

Output
------

For each test case, output one line containing "Case #x: y", where x is the case number (starting from 1) and y is one of the statuses given above. Make sure to get the statuses exactly right. When you run your code on the sample input, it should create the sample output exactly, including the "Case #1: ", the capital letter "O" rather than the number "0", and so on.

Limits
------

The game board provided will represent a valid state that was reached through play of the game Tic-Tac-Toe-Tomek as described above.

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

1 ≤ T ≤ 10.

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

1 ≤ T ≤ 1000.

Sample Input
------------
6
XXXT
....
OO..
....

XOXT
XXOO
OXOX
XXOO

XOX.
OX..
....
....

OOXX
OXXX
OX.T
O..O

XXXO
..O.
.O..
T...

OXXX
XO..
..O.
...O

Output
------

Case #1: X won
Case #2: Draw
Case #3: Game has not completed
Case #4: O won
Case #5: O won
Case #6: O won

From the above problem statement, it is clear that we have to check all the rows, columns and diagonals to determine the status of the game. Since it's a small 4*4 board, it was easy for me to build a set of constant strings, which will help my program decide the status of the game. For X to win, the possible set of winning combination strings are: XXXX, XXXT, XXTX, XTXX, TXXX. Similarly, for O to win, the possible set of winning combination strings are: OOOO, OOOT, OOTO, OTOO, TOOO. After knowing this, it was easy for me to loop through rows, columns and diagonals, to determine the status of the game.

Initially, that was the logic (above paragraph) for my solution. After I re-read the problem statement, I wrongly assumed that I have to determine the status of the game, after the next step (future). So, I changed my code to find out who's gonna make the next move (by counting the number of X's and O's - If they are equal, X moves, otherwise O moves) and tried to find the status of the game, after the next step. This was obviously wrong...So, I reverted back to my old code. Here's the solution for the above problem statement:

In the below solution, I'm parsing the input from the file and storing the String input (rows) in an String array of length 4 and passing it to the getStatusQuo method, as shown in the below code:



You can also find the source code at: GCJ 2013 - TicTacToeTomek