GNY07H - Tiling a Grid With Dominoes
We wish to tile a grid 4 units high and N units long with rectangles (dominoes) 2 units by one unit (in either orientation). For example, the figure shows the five different ways that a grid 4 units high and 2 units wide may be tiled.
Write a program that takes as input the width, W, of the grid and outputs the number of different ways to tile a 4-by-W grid.
The first line of input contains a single integer N, (1 ≤ N ≤ 1000) which is the number of datasets that follow.
Each dataset contains a single decimal integer, the width, W, of the grid for this problem instance.
For each problem instance, there is one line of output: The problem instance number as a decimal integer (start counting at one), a single space and the number of tilings of a 4-by-W grid. The values of W will be chosen so the count will fit in a 32-bit integer.
Input: 3 2 3 7 Output: 1 5 2 11 3 781
|Added by:||Marco Gallotta|
|Cluster:||Cube (Intel Pentium G860 3GHz)|
|Languages:||All except: ERL JS NODEJS PERL 6 SCM chicken VB.net|
|Resource:||ACM Greater New York Regionals 2007|
Very nice problem!! Learnt a lot! (hint: how can you start the series? Write all combinations of dominos by which you can start(and continue), and the answer will start to present itself)!
Awesome problem. Enjoyed solving it :)
Tried after M3TILE. Almost similar. Could not get it straight though! :P
good one :)
Ravi Shankar Mondal:
100th green light :)
Shouldn't input 3 give 5 + 2*5 - 1 = 14 as each tiling (except last) for input 2 can be widened by adding a column to the left or to the right.
my 50th on SPOJ :)
for n=0 ans=1
what is the range of W??Last edit: 2013-05-13 23:37:40