13
\$\begingroup\$

Challenge

Imagine a hexagonal grid as shown below. Let's call such a grid has size \$n\$ if it has \$n\$ dots on one side. The following is one of size 3:

 - - - - - - - - - - - - - - - - - - -

Then, pick as many dots as possible on the grid so that no two dots are adjacent. For size 3, the maximum is 7 dots:

 - * - * - * * - - * - - - - - - * - - or * - * - * * - - * - - - - - * - * - *

Your task is to output such a grid. For a size-\$n\$ hexagon, the output must contain exactly A002061(n) = \$n^2-n+1\$ non-adjacent dots. The corresponding maximal pattern can be found in this image linked on the OEIS sequence (imagine this: dissect all the hexagons there into triangles, remove one outermost layer of triangles, and pick the centers of original hexagons). The corresponding ASCII-art output must look like the following, modulo rotation/reflection:

n = 1 * n = 2 * - - - * * - n = 3 (following or alternative shown above) * - * - - - - * - * - * - - - - * - * n = 4 * - - * - - * - - - * - - * - * - - * - - * - * - - * - - - * - - * - - * n = 5 - * - - * * - - * - - - - * - - * - - * - - * - - * * - - * - - * - - - * - - * - - * - - * - - * - * - - * - - - * - - * n = 6 - * - - * - * - - * - - * - - * - - * - - - * - - * - - * - * - - * - - * - - * - - * - - * - - * - - * - - * - - * - - * - * - - * - - * - - - * - - * - - * - - * - - * - * - - * - n = 7 * - - * - - * - - * - - * - - - * - - * - - * - * - - * - - * - - * - - * - - * - - * - - - * - - * - - * - - * - * - - * - - * - - * - - * - * - - * - - * - - * - - - * - - * - - * - - * - - * - - * - - * - * - - * - - * - - - * - - * - - * - - * - - * n = 8 - * - - * - - * * - - * - - * - - - - * - - * - - * - - * - - * - - * - - * * - - * - - * - - * - - - - * - - * - - * - - * - - * - - * - - * - - * - - * * - - * - - * - - * - - * - - - * - - * - - * - - * - - * - - * - - * - - * - - * - * - - * - - * - - * - - - * - - * - - * - - * - - * - - * - - * - * - - * - - * - - - * - - * - - * n = 9 - * - - * - - * - * - - * - - * - - * - - * - - * - - * - - - * - - * - - * - - * - * - - * - - * - - * - - * - - * - - * - - * - - * - - - * - - * - - * - - * - - * - * - - * - - * - - * - - * - - * - - * - - * - - * - - * - - * - - * - - * - - * - - * - - * - - * - * - - * - - * - - * - - * - - - * - - * - - * - - * - - * - - * - - * - - * - - * - * - - * - - * - - * - - - * - - * - - * - - * - - * - - * - - * - * - - * - - * - n = 10 * - - * - - * - - * - - * - - * - - * - - - * - - * - - * - - * - * - - * - - * - - * - - * - - * - - * - - * - - * - - - * - - * - - * - - * - - * - * - - * - - * - - * - - * - - * - - * - - * - - * - - * - - * - - - * - - * - - * - - * - - * - - * - * - - * - - * - - * - - * - - * - - * - * - - * - - * - - * - - * - - * - - - * - - * - - * - - * - - * - - * - - * - - * - - * - - * - - * - * - - * - - * - - * - - * - - - * - - * - - * - - * - - * - - * - - * - - * - - * - * - - * - - * - - * - - - * - - * - - * - - * - - * - - * - - *

I/O and rules

You can use any two distinct non-whitespace chars for marked and unmarked dots respectively. Trailing spaces on each line and leading/trailing whitespaces are allowed. Outputting a list of lines, and outputting integer charcodes instead of the corresponding chars are also allowed.

Standard rules apply. The shortest code in bytes wins.

Improve this question
\$\endgroup\$

4 Answers 4

Reset to default
5
\$\begingroup\$

Charcoal, 33 bytes

ＮθＧ↙↘→→↗↖θ⎇﹪賓⟲∧ＬＶoIＧ；”“⟲∧⦄≧Σ¶ζ；

Try it online! Link is to verbose version of code. Explanation: After reading in n, the code simply draws a hexagon using one of two fill patterns depending on whether n is a multiple of 3; if it is, the fill pattern has the * one - in from the corner, otherwise it has the * in the top left corner.

Improve this answer
\$\endgroup\$
4
\$\begingroup\$

Python 3.8 (pre-release), 92 bytes

f=lambda n,i=0:[l:=' '*(n-i)+('- * - '*n)[n%3%2+i<<1:][:n+i<<1]]+(n>i+1and[*f(n,i+1),l]or[])

Try it online!

Improve this answer
\$\endgroup\$
3
\$\begingroup\$

Haskell, 84 bytes

f n=[[" * - -"!!mod(i+gcd 3n)6|i<-[1,3..2*y]++[4*y..2*y+4*n-4]]|y<-abs<$>[1-n..n-1]]

Try it online!

Improve this answer
\$\endgroup\$
2
\$\begingroup\$

Jelly,  27  26 bytes

3ḍ6_BṙN€ṁ"Ḥ’rƊK€ṭ"Ḷ⁶ẋƊṚŒḄY

A full program that accepts a positive integer and prints using 0 as * and 1 as -.

Try it online! Or see a few with * and - in place of 0 and 1.

How?

3ḍ6_BṙN€ṁ"Ḥ’rƊK€ṭ"Ḷ⁶ẋƊṚŒḄY - Main Link: positive integer, n 3ḍ - three divides (n)? -> 1 if n is a multiple of three else 0 6 - six _ - subtract -> 5 if n is a multiple of three else 6 B - to binary -> 101 (i.e. "-*-") ...else 110 (i.e. "--*") N€ - negate each (of implicit [1..n]) -> [-1,-2,...,-n] ṙ - rotate (110 or 101) left by (each of those) -> Patterns (one for each row of bottom half of a hexagon) Ɗ - last three links as a monad, f(n): Ḥ - double -> 2n ’ - decrement -> 2n-1 r - (2n-1) inclusive range (n) -> [2n-1..n] " - zip (Patterns) and (range) applying, f(Pattern, i): ṁ - mould like -> resized rows using repetition K€ - join each with space characters -> Rows Ɗ - last three links as a monad, f(n): Ḷ - lowered range -> [0..n-1] ⁶ - space character ẋ - repeat -> leading spaces for bottom half " - zip (Rows) and (leading spaces) applying, f(row, spaces): ṭ - tack (row) to (spaces) Ṛ - reverse -> top of the hexagon ŒḄ - bounce -> whole hexagon Y - join with newline characters - implicit, smashing print
Improve this answer
\$\endgroup\$

Start asking to get answers

Find the answer to your question by asking.

Ask question

Explore related questions

See similar questions with these tags.