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.



1 5
2 11
3 781

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sleepntsheep: 2023-04-16 05:03:20

Can be solved with plug dp

sanskar_native: 2021-05-28 20:16:32

Can be solved using dp with bitmask...see William Fiset's YouTube channels for "Tilling Problem" explanation :)

distructo: 2020-12-28 09:59:59
try this after solving will be much easier

sharjeel_spoj: 2020-10-01 21:10:50

Why is it tagged #bitmasks? Can somebody point how to solve with bitmasks?
Hint: DP table size of 120 is more than enough.

zakir068: 2020-03-30 08:27:09

for w=0 ans = 1

lnxdx: 2019-10-04 15:23:36

Two ACs in two goes :/

lnxdx: 2018-11-23 17:31:55

The values of W will be chosen so the count will fit in a 32-bit integer.
About 4 billion will fit in a 32-bit unsigned integer. 2 billion for signed.

Last edit: 2018-11-23 17:32:26
ushould_study: 2018-09-13 15:07:12

how to define the size of w ? Is there any upper limit to it?
I had kept it 100 then SIGSEGV occurred.
Changed it to 1000 got AC.
How to find the upper limit of w? Anyone ?

ayusofayush: 2018-08-17 15:51:36
this link really helped me in understanding how to form recurrence ....
thanks to @cenation092

Last edit: 2018-08-17 15:52:15
karan_yadav: 2018-08-05 13:42:00

Before solving this problem solve (

Last edit: 2018-08-05 13:42:13

Added by:Marco Gallotta
Time limit:9.600s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ERL JS-RHINO NODEJS PERL6 VB.NET
Resource:ACM Greater New York Regionals 2007