In this paper, we consider tilings by trominoes and the parity of the number of tilings. We mostly consider reptilings and tilings of related shapes by the L tromino.

You are given a problem related to tiling a 2 x n board with two types of shapes: a 2 x 1 domino and an L shaped tromino. The shapes can be rotated as needed to fit into the tiling of the board. The task is to find out how many different ways you can completely cover the 2 …

Nov 30, 2023 · Given three arrays height[], width[], and length[] of size n, where height[i], width[i], and length[i] represent the dimensions of a box. The task is to create a stack of boxes that is as tall as possible, but we can only stack a box on top of …

Jul 24, 2020 · We present a characterization of this tiling problem with pegs using flow networks and show that (i) there exists a linear-time parsimonious reduction to the maximum-flow problem, and (ii) counting the number of such tilings can be done in linear-time.

Mar 18, 2020 · I am trying to solve this tromino tiling problem for n x n board. Given Missing square co-ordinate (MS) x and y in n x n board, we have to fill the rest of the board with 'L' shaped tile. I have managed to get the output for 2 x 2 board. But, I am stuck with the output for board sizes 4 x 4, 8 x 8...and so on.

Oct 12, 2017 · Deciding the existence of a tiling with L-trominoes for an arbitrary region in general is NP-complete, nonetheless, we identify restrictions to the problem where it either remains NP-complete or has a polynomial time algorithm.

You have two types of tiles: a 2 x 1 domino shape and a tromino shape. You may rotate these shapes. Given an integer n, return the number of ways to tile an 2 x n board. Since the answer may be very large, return it modulo 10 9 + 7. In a tiling, every square must be covered by a tile.

Dec 21, 2018 · In this work we study tilings of regions in the square lattice with L-shaped trominoes (a polyomino of three cells) called an L-Tromino or simply tromino in this work. A cell in \ (\mathbb {Z}^2\) is a subset \ ( [a,a+1]\times [b,b+1]\) and a region is any finite union of connected cells.

The answer is: type 2 (horizontal domino) and type 4 (Gamma-shaped trimino). For the former, the rest of tiles will fill up a 2 x (N-1) board except for the last upper grid, and by definition, there are T_down(N-1) ways to do this.

In this work we study tilings of regions in the square lattice with L-shaped trominoes (a polyomino of three cells) called an L-Tromino or simply tromino in this work. A cell in Z2 is a subset [a; a+1] [b; b+1] and a region is any nite union of connected cells.