Your browser (Unknown 0) is no longer supported. Some parts of the website may not work correctly. Please update your browser.

UPCOMING CHALLENGES:

CURRENT CHALLENGES:

Neon 2014

PAST CHALLENGES

Fluorum 2014

Oxygenium 2014

Nitrogenium 2013

Carbo 2013

Boron 2013

Beryllium 2013

Lithium 2013

Helium 2013

Hydrogenium 2013

Omega 2013

Psi 2012

Chi 2012

Phi 2012

Upsilon 2012

Tau 2012

Sigma 2012

Rho 2012

Pi 2012

Omicron 2012

Xi 2012

Nu 2011

Mu 2011

Lambda 2011

Kappa 2011

Iota 2011

Theta 2011

Eta 2011

Zeta 2011

Epsilon 2011

Delta 2011

Gamma 2011

December 2010

PrefixSet edition (2010-10)

Count tilings of a narrow but long rectangle with tiles of size 1x1 or 2x2.

A board consisting of squares arranged into N rows and M columns is given. A *tiling* of this board is a pattern of tiles that covers it. A tiling is *interesting* if:

- only tiles of size 1x1 and/or 2x2 are used;
- each tile of size 1x1 covers exactly one whole square;
- each tile of size 2x2 covers exactly four whole squares;
- each square of the board is covered by exactly one tile.

For example, the following images show a few interesting tilings of a board of size 4 rows and 3 columns:

Two interesting tilings of a board are *different* if there exists at least one square on the board that is covered with a tile of size 1x1 in one tiling and with a tile of size 2x2 in the other. For example, all tilings shown in the images above are different.

Write a function:

class Solution { public int solution(int N, int M); }

that, given two integers N and M, returns the remainder modulo 10,000,007 of the number of different interesting tilings of a board of size N rows and M columns.

For example, given N = 4 and M = 3, the function should return 11, because there are 11 different interesting tilings of a board of size 4 rows and 3 columns:

Write an ** efficient** algorithm for the following assumptions:

- N is an integer within the range [1..1,000,000];
- M is an integer within the range [1..7].

Copyright 2009–2023 by Codility Limited. All Rights Reserved. Unauthorized copying, publication or disclosure prohibited.