MHenderson / maximal-room-squares

Generate maximal partial Room squares.

Generating Maximal Partial Room Squares in R

Matthew Henderson

• I: greedy1
• II: greedy2
• References

Two different greedy procedures for building maximal partial Room squares in R inspired by Meszka and Rosa (2021).

I: greedy1

greedy1 visits all cells in order placing into the next cell the first available pair such that the conditions of being a partial Room square will not be violated.

R <- greedy1(6)
plot_room_square_labs(R)

In this plot colour represents the order in which cells were filled. The cells were filled in order from lightest to darkest.

# is R a maximal partial Room square?
is_maximal_proom(R)
#> [1] TRUE

A few examples of maximal partial Room squares constructed with greedy1

II: greedy2

greedy2 iterates through all pairs in order placing the next pair in the first available cell such that the conditions of being a partial Room square are not violated.

R <- greedy2(8)
plot_room_square_labs(R)

Again colour represents order of filling, proceeding from lightest to darkest.

# is R a maximal partial Room square?
is_maximal_proom(R)
#> [1] TRUE

A few examples of maximal partial Room squares constructed with greedy2

References

Meszka, Mariusz, and Alexander Rosa. 2021. “Maximal Partial Room Squares.” Journal of Combinatorial Designs 29 (7): 482–501. https://doi.org/10.1002/jcd.21777.