up vote
10
down vote

favorite

_{Topically related.}

Objective: Given a matrix of positive integers $M$, output the smallest centrosymmetric matrix which contains $M$ (this matrix may contain non-positive integers as well).

A centrosymmetric matrix is a square matrix with rotational symmetry of order 2â€”i.e. it remains the same matrix after rotating it twice. For example, a centrosymmetric matrix has the top-left element the same as the bottom-right, and the element above the center the same as the one below the center. A useful visualization can be found here.

More formally, given a matrix $M$, produce a square matrix $N$ such that $N$ is centrosymmetric and $Msubseteq N$, and there is no other square matrix $K$ such that $dim K<dim N$.

$A$ is a subset of $B$ (notation: $Asubseteq B$) if and only if each value $A_i,j$ appears at index $B_i+i^prime,j+j^prime$ for some pair of integers $(i^prime, j^prime)$.

Note: some matrices have multiple solutions (e.g. [[3,3],[1,2]] being solved as [[2,1,0],[3,3,3],[0,1,2]] or [[3,3,3],[1,2,1],[3,3,3]]); you must output at least one of the valid solutions.

Test cases

input
example output

[[1, 2, 3],
 [4, 5, 6]]
[[1, 2, 3, 0],
 [4, 5, 6, 0],
 [0, 6, 5, 4],
 [0, 3, 2, 1]]

[[9]]
[[9]]

[[9, 10]]
[[9, 10],
 [10, 9]]

[[100, 200, 300]]
[[100, 200, 300],
 [ 0, 0, 0],
 [300, 200, 100]]

[[1, 2, 3],
 [4, 5, 4]]
[[1, 2, 3],
 [4, 5, 4]
 [3, 2, 1]]

[[1, 2, 3],
 [5, 6, 5],
 [3, 2, 1]]
[[1, 2, 3],
 [5, 6, 5],
 [3, 2, 1]]

[[4, 5, 4],
 [1, 2, 3]]
[[3, 2, 1],
 [4, 5, 4],
 [1, 2, 3]]

[[1, 1, 1, 1, 1, 1, 1, 1, 1, 1],
 [1, 1, 1, 9, 9, 9, 9, 9, 9, 9],
 [1, 1, 1, 9, 9, 9, 9, 9, 9, 9],
 [9, 9, 9, 9, 9, 9, 9, 9, 9, 9],
 [9, 9, 9, 9, 9, 9, 9, 9, 9, 9],
 [9, 9, 9, 9, 9, 9, 9, 9, 9, 9],
 [9, 9, 9, 9, 9, 9, 9, 9, 9, 9],
 [9, 9, 9, 9, 9, 9, 9, 9, 9, 9],
 [9, 9, 9, 9, 9, 9, 9, 9, 9, 9],
 [9, 9, 9, 9, 9, 9, 9, 9, 9, 1]]
[[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 9],
 [1, 1, 1, 9, 9, 9, 9, 9, 9, 9, 9, 9],
 [1, 1, 1, 9, 9, 9, 9, 9, 9, 9, 9, 9],
 [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],
 [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],
 [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],
 [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],
 [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],
 [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],
 [9, 9, 9, 9, 9, 9, 9, 9, 9, 1, 1, 1],
 [9, 9, 9, 9, 9, 9, 9, 9, 9, 1, 1, 1],
 [9, 9, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]]

edited yesterday

asked yesterday

Conor O'Brien

27.7k260155

Why do Centrosymmetric matrices have to be square?
â€“Â W W
yesterday

@WW in a general sense, I don't suppose it has to be. For this question, however, they must be square by definition
â€“Â Conor O'Brien
yesterday

I was wondering why you made that choice
â€“Â W W
yesterday

2

@WW it was a simplification I thought to be useful for clarity
â€“Â Conor O'Brien
yesterday

add a commentÂ |Â

up vote
10
down vote

favorite

_{Topically related.}

Objective: Given a matrix of positive integers $M$, output the smallest centrosymmetric matrix which contains $M$ (this matrix may contain non-positive integers as well).

More formally, given a matrix $M$, produce a square matrix $N$ such that $N$ is centrosymmetric and $Msubseteq N$, and there is no other square matrix $K$ such that $dim K<dim N$.

$A$ is a subset of $B$ (notation: $Asubseteq B$) if and only if each value $A_i,j$ appears at index $B_i+i^prime,j+j^prime$ for some pair of integers $(i^prime, j^prime)$.

Note: some matrices have multiple solutions (e.g. [[3,3],[1,2]] being solved as [[2,1,0],[3,3,3],[0,1,2]] or [[3,3,3],[1,2,1],[3,3,3]]); you must output at least one of the valid solutions.

Test cases

input
example output

[[1, 2, 3],
 [4, 5, 6]]
[[1, 2, 3, 0],
 [4, 5, 6, 0],
 [0, 6, 5, 4],
 [0, 3, 2, 1]]

[[9]]
[[9]]

[[9, 10]]
[[9, 10],
 [10, 9]]

[[100, 200, 300]]
[[100, 200, 300],
 [ 0, 0, 0],
 [300, 200, 100]]

[[1, 2, 3],
 [4, 5, 4]]
[[1, 2, 3],
 [4, 5, 4]
 [3, 2, 1]]

[[1, 2, 3],
 [5, 6, 5],
 [3, 2, 1]]
[[1, 2, 3],
 [5, 6, 5],
 [3, 2, 1]]

[[4, 5, 4],
 [1, 2, 3]]
[[3, 2, 1],
 [4, 5, 4],
 [1, 2, 3]]

[[1, 1, 1, 1, 1, 1, 1, 1, 1, 1],
 [1, 1, 1, 9, 9, 9, 9, 9, 9, 9],
 [1, 1, 1, 9, 9, 9, 9, 9, 9, 9],
 [9, 9, 9, 9, 9, 9, 9, 9, 9, 9],
 [9, 9, 9, 9, 9, 9, 9, 9, 9, 9],
 [9, 9, 9, 9, 9, 9, 9, 9, 9, 9],
 [9, 9, 9, 9, 9, 9, 9, 9, 9, 9],
 [9, 9, 9, 9, 9, 9, 9, 9, 9, 9],
 [9, 9, 9, 9, 9, 9, 9, 9, 9, 9],
 [9, 9, 9, 9, 9, 9, 9, 9, 9, 1]]
[[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 9],
 [1, 1, 1, 9, 9, 9, 9, 9, 9, 9, 9, 9],
 [1, 1, 1, 9, 9, 9, 9, 9, 9, 9, 9, 9],
 [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],
 [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],
 [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],
 [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],
 [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],
 [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],
 [9, 9, 9, 9, 9, 9, 9, 9, 9, 1, 1, 1],
 [9, 9, 9, 9, 9, 9, 9, 9, 9, 1, 1, 1],
 [9, 9, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]]

edited yesterday

asked yesterday

Conor O'Brien

27.7k260155

Why do Centrosymmetric matrices have to be square?
â€“Â W W
yesterday

@WW in a general sense, I don't suppose it has to be. For this question, however, they must be square by definition
â€“Â Conor O'Brien
yesterday

I was wondering why you made that choice
â€“Â W W
yesterday

2

@WW it was a simplification I thought to be useful for clarity
â€“Â Conor O'Brien
yesterday

add a commentÂ |Â

up vote
10
down vote

favorite

_{Topically related.}

Objective: Given a matrix of positive integers $M$, output the smallest centrosymmetric matrix which contains $M$ (this matrix may contain non-positive integers as well).

More formally, given a matrix $M$, produce a square matrix $N$ such that $N$ is centrosymmetric and $Msubseteq N$, and there is no other square matrix $K$ such that $dim K<dim N$.

$A$ is a subset of $B$ (notation: $Asubseteq B$) if and only if each value $A_i,j$ appears at index $B_i+i^prime,j+j^prime$ for some pair of integers $(i^prime, j^prime)$.

Note: some matrices have multiple solutions (e.g. [[3,3],[1,2]] being solved as [[2,1,0],[3,3,3],[0,1,2]] or [[3,3,3],[1,2,1],[3,3,3]]); you must output at least one of the valid solutions.

Test cases

input
example output

[[1, 2, 3],
 [4, 5, 6]]
[[1, 2, 3, 0],
 [4, 5, 6, 0],
 [0, 6, 5, 4],
 [0, 3, 2, 1]]

[[9]]
[[9]]

[[9, 10]]
[[9, 10],
 [10, 9]]

[[100, 200, 300]]
[[100, 200, 300],
 [ 0, 0, 0],
 [300, 200, 100]]

[[1, 2, 3],
 [4, 5, 4]]
[[1, 2, 3],
 [4, 5, 4]
 [3, 2, 1]]

[[1, 2, 3],
 [5, 6, 5],
 [3, 2, 1]]
[[1, 2, 3],
 [5, 6, 5],
 [3, 2, 1]]

[[4, 5, 4],
 [1, 2, 3]]
[[3, 2, 1],
 [4, 5, 4],
 [1, 2, 3]]

[[1, 1, 1, 1, 1, 1, 1, 1, 1, 1],
 [1, 1, 1, 9, 9, 9, 9, 9, 9, 9],
 [1, 1, 1, 9, 9, 9, 9, 9, 9, 9],
 [9, 9, 9, 9, 9, 9, 9, 9, 9, 9],
 [9, 9, 9, 9, 9, 9, 9, 9, 9, 9],
 [9, 9, 9, 9, 9, 9, 9, 9, 9, 9],
 [9, 9, 9, 9, 9, 9, 9, 9, 9, 9],
 [9, 9, 9, 9, 9, 9, 9, 9, 9, 9],
 [9, 9, 9, 9, 9, 9, 9, 9, 9, 9],
 [9, 9, 9, 9, 9, 9, 9, 9, 9, 1]]
[[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 9],
 [1, 1, 1, 9, 9, 9, 9, 9, 9, 9, 9, 9],
 [1, 1, 1, 9, 9, 9, 9, 9, 9, 9, 9, 9],
 [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],
 [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],
 [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],
 [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],
 [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],
 [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],
 [9, 9, 9, 9, 9, 9, 9, 9, 9, 1, 1, 1],
 [9, 9, 9, 9, 9, 9, 9, 9, 9, 1, 1, 1],
 [9, 9, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]]

edited yesterday

asked yesterday

Conor O'Brien

27.7k260155

_{Topically related.}

Objective: Given a matrix of positive integers $M$, output the smallest centrosymmetric matrix which contains $M$ (this matrix may contain non-positive integers as well).

More formally, given a matrix $M$, produce a square matrix $N$ such that $N$ is centrosymmetric and $Msubseteq N$, and there is no other square matrix $K$ such that $dim K<dim N$.

$A$ is a subset of $B$ (notation: $Asubseteq B$) if and only if each value $A_i,j$ appears at index $B_i+i^prime,j+j^prime$ for some pair of integers $(i^prime, j^prime)$.

Note: some matrices have multiple solutions (e.g. [[3,3],[1,2]] being solved as [[2,1,0],[3,3,3],[0,1,2]] or [[3,3,3],[1,2,1],[3,3,3]]); you must output at least one of the valid solutions.

Test cases

input
example output

[[1, 2, 3],
 [4, 5, 6]]
[[1, 2, 3, 0],
 [4, 5, 6, 0],
 [0, 6, 5, 4],
 [0, 3, 2, 1]]

[[9]]
[[9]]

[[9, 10]]
[[9, 10],
 [10, 9]]

[[100, 200, 300]]
[[100, 200, 300],
 [ 0, 0, 0],
 [300, 200, 100]]

[[1, 2, 3],
 [4, 5, 4]]
[[1, 2, 3],
 [4, 5, 4]
 [3, 2, 1]]

[[1, 2, 3],
 [5, 6, 5],
 [3, 2, 1]]
[[1, 2, 3],
 [5, 6, 5],
 [3, 2, 1]]

[[4, 5, 4],
 [1, 2, 3]]
[[3, 2, 1],
 [4, 5, 4],
 [1, 2, 3]]

[[1, 1, 1, 1, 1, 1, 1, 1, 1, 1],
 [1, 1, 1, 9, 9, 9, 9, 9, 9, 9],
 [1, 1, 1, 9, 9, 9, 9, 9, 9, 9],
 [9, 9, 9, 9, 9, 9, 9, 9, 9, 9],
 [9, 9, 9, 9, 9, 9, 9, 9, 9, 9],
 [9, 9, 9, 9, 9, 9, 9, 9, 9, 9],
 [9, 9, 9, 9, 9, 9, 9, 9, 9, 9],
 [9, 9, 9, 9, 9, 9, 9, 9, 9, 9],
 [9, 9, 9, 9, 9, 9, 9, 9, 9, 9],
 [9, 9, 9, 9, 9, 9, 9, 9, 9, 1]]
[[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 9],
 [1, 1, 1, 9, 9, 9, 9, 9, 9, 9, 9, 9],
 [1, 1, 1, 9, 9, 9, 9, 9, 9, 9, 9, 9],
 [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],
 [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],
 [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],
 [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],
 [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],
 [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],
 [9, 9, 9, 9, 9, 9, 9, 9, 9, 1, 1, 1],
 [9, 9, 9, 9, 9, 9, 9, 9, 9, 1, 1, 1],
 [9, 9, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]]

edited yesterday

asked yesterday

Conor O'Brien

27.7k260155

edited yesterday

asked yesterday

Conor O'Brien

27.7k260155

asked yesterday

Conor O'Brien

27.7k260155

asked yesterday

Conor O'Brien

27.7k260155

Why do Centrosymmetric matrices have to be square?
â€“Â W W
yesterday

@WW in a general sense, I don't suppose it has to be. For this question, however, they must be square by definition
â€“Â Conor O'Brien
yesterday

I was wondering why you made that choice
â€“Â W W
yesterday

2

@WW it was a simplification I thought to be useful for clarity
â€“Â Conor O'Brien
yesterday

add a commentÂ |Â

Why do Centrosymmetric matrices have to be square?
â€“Â W W
yesterday

@WW in a general sense, I don't suppose it has to be. For this question, however, they must be square by definition
â€“Â Conor O'Brien
yesterday

I was wondering why you made that choice
â€“Â W W
yesterday

2

@WW it was a simplification I thought to be useful for clarity
â€“Â Conor O'Brien
yesterday

Why do Centrosymmetric matrices have to be square?
â€“Â W W
yesterday

@WW in a general sense, I don't suppose it has to be. For this question, however, they must be square by definition
â€“Â Conor O'Brien
yesterday

I was wondering why you made that choice
â€“Â W W
yesterday

@WW it was a simplification I thought to be useful for clarity
â€“Â Conor O'Brien
yesterday

add a commentÂ |Â

4 Answers
4

active

oldest

votes

up vote
6
down vote

Brachylog, 12 bytes

Ã¡Â¹ÂÃ¢Â†Â”Ã¡ÂµÂÃ¢Â†Â”?aaÃ¡ÂµÂ.&Ã¢Â‰ÂœÃ¢ÂˆÂ§

Try it online!

Contrary to most Brachylog answers, this takes the input through the Output variable ., and outputs the result through the Input variable ? (confusing, I know).

Explanation

Ã¡Â¹Â We expect a square matrix
 Ã¢Â†Â”Ã¡ÂµÂÃ¢Â†Â”? When we reverse the rows and then the matrix, we get the initial matrix back
 ?a Take an adfix (prefix or suffix) of that square matrix
 aÃ¡ÂµÂ Take an adfix of each row of that adfix matrix
 . It must be the input matrix
 &Ã¢Â‰Âœ Assign values to cells which are still variables (will assign 0)
 Ã¢ÂˆÂ§ (disable implicit unification between the input and the output)

8 bytes, gives all valid matrices

Technically, this program also works:

Ã¡Â¹ÂÃ¢Â†Â”Ã¡ÂµÂÃ¢Â†Â”?aaÃ¡ÂµÂ

But this will leave as variables the cells which can take any value (they show as _XXXXX, which is an internal Prolog variable name). So technically this is even better than what is asked, but I guess it's not what the challenge asks for.

answered yesterday

Fatalize

26.2k448131

I wish Ã¢Â‰Âœ did delayed labeling...
â€“Â Erik the Outgolfer
23 hours ago

@EriktheOutgolfer Instant labeling is still useful when we need to enumerate things, so ideally we would need two different predicatesÃ¢Â€Â¦
â€“Â Fatalize
23 hours ago

add a commentÂ |Â

up vote
3
down vote

JavaScript (ES6), 192 180 177 bytes

f=(m,v=[w=0],S=c=>v.some(c))=>S(Y=>S(X=>!m[w+1-Y]&!m[0][w+1-X]&!S(y=>S(x=>(k=(m[y-Y]||0)[x-X],g=y=>((r=a[y]=a[y]||)[x]=r[x]||k|0)-k)(y)|g(w-y,x=w-x)),a=)))?a:f(m,[...v,++w])

Try it online!

Algorithm

Starting with $w=0$:

We consider a square container matrix $M$ of width $w+1$.

We consider each pair $(X,Y)$ such that the input matrix $m$ can fit within the container matrix when it's inserted at these coordinates.

Example:

$$beginalignw=2,&&(X,Y)=(0,1),&&m = pmatrix4,5,4\1,2,3endalign\
M=pmatrixcolorgray0,colorgray0,colorgray0\4,5,4\1,2,3$$

We test whether we can complete the matrix such that it's centrosymmetric.

Example:

$$M^prime=pmatrixcolorblue3,colorblue2,colorblue1\4,5,4\1,2,3$$

We increment $w$ until we find such a valid configuration.

edited yesterday

answered yesterday

Arnauld

60.3k472253

(The MathJax rendering bug has been reported in this post.)
â€“Â Arnauld
yesterday

add a commentÂ |Â

up vote
1
down vote

Python 2, 242 227 bytes

r=range
def f(m):
 w,h=len(m),len(m[0]);W=max(w,h)
 while 1:
	for x in r(1+W-w):
	 for y in r(1+W-h):
		n=[W*[0]for _ in r(W)];exec"for i in r(w):n[i+x][y:y+h]=m[i]nN=n;n=[l[::-1]for l in n[::-1]]n"*2
		if n==N:return n
	W+=1

Try it online!

edited yesterday

answered yesterday

TFeld

10.2k1832

add a commentÂ |Â

up vote
1
down vote

Jelly, 27 bytes

oZ0Ã¡Â¹Âz0oÃ¢ÂÂ¸Ã¡Â¹ÂšUÃ…Â»Ã¢Â‚Â¬Z$2Ã‚Â¡LÃƒÂÃ‚Â¡oÃ¢ÂÂ¸Ã¡Â¹ÂšU$Ã†Â‘Ã†Â‡Ã¡Â¸Â¢

Try it online!

Newlines added to actual output over TIO for clarity.

answered 13 hours ago

Erik the Outgolfer

29.1k42697

add a commentÂ |Â

Your Answer

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Name

4 Answers
4

active

oldest

votes

4 Answers
4

active

oldest

votes

up vote
6
down vote

Brachylog, 12 bytes

Ã¡Â¹ÂÃ¢Â†Â”Ã¡ÂµÂÃ¢Â†Â”?aaÃ¡ÂµÂ.&Ã¢Â‰ÂœÃ¢ÂˆÂ§

Try it online!

Contrary to most Brachylog answers, this takes the input through the Output variable ., and outputs the result through the Input variable ? (confusing, I know).

Explanation

Ã¡Â¹Â We expect a square matrix
 Ã¢Â†Â”Ã¡ÂµÂÃ¢Â†Â”? When we reverse the rows and then the matrix, we get the initial matrix back
 ?a Take an adfix (prefix or suffix) of that square matrix
 aÃ¡ÂµÂ Take an adfix of each row of that adfix matrix
 . It must be the input matrix
 &Ã¢Â‰Âœ Assign values to cells which are still variables (will assign 0)
 Ã¢ÂˆÂ§ (disable implicit unification between the input and the output)

8 bytes, gives all valid matrices

Technically, this program also works:

Ã¡Â¹ÂÃ¢Â†Â”Ã¡ÂµÂÃ¢Â†Â”?aaÃ¡ÂµÂ

answered yesterday

Fatalize

26.2k448131

I wish Ã¢Â‰Âœ did delayed labeling...
â€“Â Erik the Outgolfer
23 hours ago

@EriktheOutgolfer Instant labeling is still useful when we need to enumerate things, so ideally we would need two different predicatesÃ¢Â€Â¦
â€“Â Fatalize
23 hours ago

add a commentÂ |Â

up vote
6
down vote

Brachylog, 12 bytes

Ã¡Â¹ÂÃ¢Â†Â”Ã¡ÂµÂÃ¢Â†Â”?aaÃ¡ÂµÂ.&Ã¢Â‰ÂœÃ¢ÂˆÂ§

Try it online!

Contrary to most Brachylog answers, this takes the input through the Output variable ., and outputs the result through the Input variable ? (confusing, I know).

Explanation

Ã¡Â¹Â We expect a square matrix
 Ã¢Â†Â”Ã¡ÂµÂÃ¢Â†Â”? When we reverse the rows and then the matrix, we get the initial matrix back
 ?a Take an adfix (prefix or suffix) of that square matrix
 aÃ¡ÂµÂ Take an adfix of each row of that adfix matrix
 . It must be the input matrix
 &Ã¢Â‰Âœ Assign values to cells which are still variables (will assign 0)
 Ã¢ÂˆÂ§ (disable implicit unification between the input and the output)

8 bytes, gives all valid matrices

Technically, this program also works:

Ã¡Â¹ÂÃ¢Â†Â”Ã¡ÂµÂÃ¢Â†Â”?aaÃ¡ÂµÂ

answered yesterday

Fatalize

26.2k448131

I wish Ã¢Â‰Âœ did delayed labeling...
â€“Â Erik the Outgolfer
23 hours ago

@EriktheOutgolfer Instant labeling is still useful when we need to enumerate things, so ideally we would need two different predicatesÃ¢Â€Â¦
â€“Â Fatalize
23 hours ago

add a commentÂ |Â

up vote
6
down vote

Brachylog, 12 bytes

Ã¡Â¹ÂÃ¢Â†Â”Ã¡ÂµÂÃ¢Â†Â”?aaÃ¡ÂµÂ.&Ã¢Â‰ÂœÃ¢ÂˆÂ§

Try it online!

Contrary to most Brachylog answers, this takes the input through the Output variable ., and outputs the result through the Input variable ? (confusing, I know).

Explanation

Ã¡Â¹Â We expect a square matrix
 Ã¢Â†Â”Ã¡ÂµÂÃ¢Â†Â”? When we reverse the rows and then the matrix, we get the initial matrix back
 ?a Take an adfix (prefix or suffix) of that square matrix
 aÃ¡ÂµÂ Take an adfix of each row of that adfix matrix
 . It must be the input matrix
 &Ã¢Â‰Âœ Assign values to cells which are still variables (will assign 0)
 Ã¢ÂˆÂ§ (disable implicit unification between the input and the output)

8 bytes, gives all valid matrices

Technically, this program also works:

Ã¡Â¹ÂÃ¢Â†Â”Ã¡ÂµÂÃ¢Â†Â”?aaÃ¡ÂµÂ

answered yesterday

Fatalize

26.2k448131

Brachylog, 12 bytes

Ã¡Â¹ÂÃ¢Â†Â”Ã¡ÂµÂÃ¢Â†Â”?aaÃ¡ÂµÂ.&Ã¢Â‰ÂœÃ¢ÂˆÂ§

Try it online!

Contrary to most Brachylog answers, this takes the input through the Output variable ., and outputs the result through the Input variable ? (confusing, I know).

Explanation

Ã¡Â¹Â We expect a square matrix
 Ã¢Â†Â”Ã¡ÂµÂÃ¢Â†Â”? When we reverse the rows and then the matrix, we get the initial matrix back
 ?a Take an adfix (prefix or suffix) of that square matrix
 aÃ¡ÂµÂ Take an adfix of each row of that adfix matrix
 . It must be the input matrix
 &Ã¢Â‰Âœ Assign values to cells which are still variables (will assign 0)
 Ã¢ÂˆÂ§ (disable implicit unification between the input and the output)

8 bytes, gives all valid matrices

Technically, this program also works:

Ã¡Â¹ÂÃ¢Â†Â”Ã¡ÂµÂÃ¢Â†Â”?aaÃ¡ÂµÂ

answered yesterday

Fatalize

26.2k448131

answered yesterday

Fatalize

26.2k448131

answered yesterday

Fatalize

26.2k448131

answered yesterday

Fatalize

26.2k448131

I wish Ã¢Â‰Âœ did delayed labeling...
â€“Â Erik the Outgolfer
23 hours ago

@EriktheOutgolfer Instant labeling is still useful when we need to enumerate things, so ideally we would need two different predicatesÃ¢Â€Â¦
â€“Â Fatalize
23 hours ago

add a commentÂ |Â

I wish Ã¢Â‰Âœ did delayed labeling...
â€“Â Erik the Outgolfer
23 hours ago

@EriktheOutgolfer Instant labeling is still useful when we need to enumerate things, so ideally we would need two different predicatesÃ¢Â€Â¦
â€“Â Fatalize
23 hours ago

I wish Ã¢Â‰Âœ did delayed labeling...
â€“Â Erik the Outgolfer
23 hours ago

@EriktheOutgolfer Instant labeling is still useful when we need to enumerate things, so ideally we would need two different predicatesÃ¢Â€Â¦
â€“Â Fatalize
23 hours ago

add a commentÂ |Â

up vote
3
down vote

JavaScript (ES6), 192 180 177 bytes

f=(m,v=[w=0],S=c=>v.some(c))=>S(Y=>S(X=>!m[w+1-Y]&!m[0][w+1-X]&!S(y=>S(x=>(k=(m[y-Y]||0)[x-X],g=y=>((r=a[y]=a[y]||)[x]=r[x]||k|0)-k)(y)|g(w-y,x=w-x)),a=)))?a:f(m,[...v,++w])

Try it online!

Algorithm

Starting with $w=0$:

We consider a square container matrix $M$ of width $w+1$.

We consider each pair $(X,Y)$ such that the input matrix $m$ can fit within the container matrix when it's inserted at these coordinates.

Example:

$$beginalignw=2,&&(X,Y)=(0,1),&&m = pmatrix4,5,4\1,2,3endalign\
M=pmatrixcolorgray0,colorgray0,colorgray0\4,5,4\1,2,3$$

We test whether we can complete the matrix such that it's centrosymmetric.

Example:

$$M^prime=pmatrixcolorblue3,colorblue2,colorblue1\4,5,4\1,2,3$$

We increment $w$ until we find such a valid configuration.

edited yesterday

answered yesterday

Arnauld

60.3k472253

(The MathJax rendering bug has been reported in this post.)
â€“Â Arnauld
yesterday

add a commentÂ |Â

up vote
3
down vote

JavaScript (ES6), 192 180 177 bytes

f=(m,v=[w=0],S=c=>v.some(c))=>S(Y=>S(X=>!m[w+1-Y]&!m[0][w+1-X]&!S(y=>S(x=>(k=(m[y-Y]||0)[x-X],g=y=>((r=a[y]=a[y]||)[x]=r[x]||k|0)-k)(y)|g(w-y,x=w-x)),a=)))?a:f(m,[...v,++w])

Try it online!

Algorithm

Starting with $w=0$:

We consider a square container matrix $M$ of width $w+1$.

We consider each pair $(X,Y)$ such that the input matrix $m$ can fit within the container matrix when it's inserted at these coordinates.

Example:

$$beginalignw=2,&&(X,Y)=(0,1),&&m = pmatrix4,5,4\1,2,3endalign\
M=pmatrixcolorgray0,colorgray0,colorgray0\4,5,4\1,2,3$$

We test whether we can complete the matrix such that it's centrosymmetric.

Example:

$$M^prime=pmatrixcolorblue3,colorblue2,colorblue1\4,5,4\1,2,3$$

We increment $w$ until we find such a valid configuration.

edited yesterday

answered yesterday

Arnauld

60.3k472253

(The MathJax rendering bug has been reported in this post.)
â€“Â Arnauld
yesterday

add a commentÂ |Â

up vote
3
down vote

JavaScript (ES6), 192 180 177 bytes

f=(m,v=[w=0],S=c=>v.some(c))=>S(Y=>S(X=>!m[w+1-Y]&!m[0][w+1-X]&!S(y=>S(x=>(k=(m[y-Y]||0)[x-X],g=y=>((r=a[y]=a[y]||)[x]=r[x]||k|0)-k)(y)|g(w-y,x=w-x)),a=)))?a:f(m,[...v,++w])

Try it online!

Algorithm

Starting with $w=0$:

We consider a square container matrix $M$ of width $w+1$.

We consider each pair $(X,Y)$ such that the input matrix $m$ can fit within the container matrix when it's inserted at these coordinates.

Example:

$$beginalignw=2,&&(X,Y)=(0,1),&&m = pmatrix4,5,4\1,2,3endalign\
M=pmatrixcolorgray0,colorgray0,colorgray0\4,5,4\1,2,3$$

We test whether we can complete the matrix such that it's centrosymmetric.

Example:

$$M^prime=pmatrixcolorblue3,colorblue2,colorblue1\4,5,4\1,2,3$$

We increment $w$ until we find such a valid configuration.

edited yesterday

answered yesterday

Arnauld

60.3k472253

JavaScript (ES6), 192 180 177 bytes

f=(m,v=[w=0],S=c=>v.some(c))=>S(Y=>S(X=>!m[w+1-Y]&!m[0][w+1-X]&!S(y=>S(x=>(k=(m[y-Y]||0)[x-X],g=y=>((r=a[y]=a[y]||)[x]=r[x]||k|0)-k)(y)|g(w-y,x=w-x)),a=)))?a:f(m,[...v,++w])

Try it online!

Algorithm

Starting with $w=0$:

We consider a square container matrix $M$ of width $w+1$.

We consider each pair $(X,Y)$ such that the input matrix $m$ can fit within the container matrix when it's inserted at these coordinates.

Example:

$$beginalignw=2,&&(X,Y)=(0,1),&&m = pmatrix4,5,4\1,2,3endalign\
M=pmatrixcolorgray0,colorgray0,colorgray0\4,5,4\1,2,3$$

We test whether we can complete the matrix such that it's centrosymmetric.

Example:

$$M^prime=pmatrixcolorblue3,colorblue2,colorblue1\4,5,4\1,2,3$$

We increment $w$ until we find such a valid configuration.

edited yesterday

answered yesterday

Arnauld

60.3k472253

edited yesterday

answered yesterday

Arnauld

60.3k472253

answered yesterday

Arnauld

60.3k472253

answered yesterday

Arnauld

60.3k472253

(The MathJax rendering bug has been reported in this post.)
â€“Â Arnauld
yesterday

add a commentÂ |Â

(The MathJax rendering bug has been reported in this post.)
â€“Â Arnauld
yesterday

(The MathJax rendering bug has been reported in this post.)
â€“Â Arnauld
yesterday

add a commentÂ |Â

up vote
1
down vote

Python 2, 242 227 bytes

r=range
def f(m):
 w,h=len(m),len(m[0]);W=max(w,h)
 while 1:
	for x in r(1+W-w):
	 for y in r(1+W-h):
		n=[W*[0]for _ in r(W)];exec"for i in r(w):n[i+x][y:y+h]=m[i]nN=n;n=[l[::-1]for l in n[::-1]]n"*2
		if n==N:return n
	W+=1

Try it online!

edited yesterday

answered yesterday

TFeld

10.2k1832

add a commentÂ |Â

up vote
1
down vote

Python 2, 242 227 bytes

r=range
def f(m):
 w,h=len(m),len(m[0]);W=max(w,h)
 while 1:
	for x in r(1+W-w):
	 for y in r(1+W-h):
		n=[W*[0]for _ in r(W)];exec"for i in r(w):n[i+x][y:y+h]=m[i]nN=n;n=[l[::-1]for l in n[::-1]]n"*2
		if n==N:return n
	W+=1

Try it online!

edited yesterday

answered yesterday

TFeld

10.2k1832

add a commentÂ |Â

up vote
1
down vote

Python 2, 242 227 bytes

r=range
def f(m):
 w,h=len(m),len(m[0]);W=max(w,h)
 while 1:
	for x in r(1+W-w):
	 for y in r(1+W-h):
		n=[W*[0]for _ in r(W)];exec"for i in r(w):n[i+x][y:y+h]=m[i]nN=n;n=[l[::-1]for l in n[::-1]]n"*2
		if n==N:return n
	W+=1

Try it online!

edited yesterday

answered yesterday

TFeld

10.2k1832

Python 2, 242 227 bytes

r=range
def f(m):
 w,h=len(m),len(m[0]);W=max(w,h)
 while 1:
	for x in r(1+W-w):
	 for y in r(1+W-h):
		n=[W*[0]for _ in r(W)];exec"for i in r(w):n[i+x][y:y+h]=m[i]nN=n;n=[l[::-1]for l in n[::-1]]n"*2
		if n==N:return n
	W+=1

Try it online!

edited yesterday

answered yesterday

TFeld

10.2k1832

edited yesterday

answered yesterday

TFeld

10.2k1832

answered yesterday

TFeld

10.2k1832

answered yesterday

TFeld

10.2k1832

add a commentÂ |Â

up vote
1
down vote

Jelly, 27 bytes

oZ0Ã¡Â¹Âz0oÃ¢ÂÂ¸Ã¡Â¹ÂšUÃ…Â»Ã¢Â‚Â¬Z$2Ã‚Â¡LÃƒÂÃ‚Â¡oÃ¢ÂÂ¸Ã¡Â¹ÂšU$Ã†Â‘Ã†Â‡Ã¡Â¸Â¢

Try it online!

Newlines added to actual output over TIO for clarity.

answered 13 hours ago

Erik the Outgolfer

29.1k42697

add a commentÂ |Â

up vote
1
down vote

Jelly, 27 bytes

oZ0Ã¡Â¹Âz0oÃ¢ÂÂ¸Ã¡Â¹ÂšUÃ…Â»Ã¢Â‚Â¬Z$2Ã‚Â¡LÃƒÂÃ‚Â¡oÃ¢ÂÂ¸Ã¡Â¹ÂšU$Ã†Â‘Ã†Â‡Ã¡Â¸Â¢

Try it online!

Newlines added to actual output over TIO for clarity.

answered 13 hours ago

Erik the Outgolfer

29.1k42697

add a commentÂ |Â

up vote
1
down vote

Jelly, 27 bytes

oZ0Ã¡Â¹Âz0oÃ¢ÂÂ¸Ã¡Â¹ÂšUÃ…Â»Ã¢Â‚Â¬Z$2Ã‚Â¡LÃƒÂÃ‚Â¡oÃ¢ÂÂ¸Ã¡Â¹ÂšU$Ã†Â‘Ã†Â‡Ã¡Â¸Â¢

Try it online!

Newlines added to actual output over TIO for clarity.

answered 13 hours ago

Erik the Outgolfer

29.1k42697

Jelly, 27 bytes

oZ0Ã¡Â¹Âz0oÃ¢ÂÂ¸Ã¡Â¹ÂšUÃ…Â»Ã¢Â‚Â¬Z$2Ã‚Â¡LÃƒÂÃ‚Â¡oÃ¢ÂÂ¸Ã¡Â¹ÂšU$Ã†Â‘Ã†Â‡Ã¡Â¸Â¢

Try it online!

Newlines added to actual output over TIO for clarity.

answered 13 hours ago

Erik the Outgolfer

29.1k42697

answered 13 hours ago

Erik the Outgolfer

29.1k42697

answered 13 hours ago

Erik the Outgolfer

29.1k42697

answered 13 hours ago

Erik the Outgolfer

29.1k42697

add a commentÂ |Â

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Minimal Centrosymmetrization

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4 Answers 4

Brachylog, 12 bytes

Explanation

8 bytes, gives all valid matrices

JavaScript (ES6), 192 180 177 bytes

Algorithm

Python 2, 242 227 bytes

Jelly, 27 bytes

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4 Answers 4

4 Answers 4

Brachylog, 12 bytes

Explanation

8 bytes, gives all valid matrices

Brachylog, 12 bytes

Explanation

8 bytes, gives all valid matrices

Brachylog, 12 bytes

Explanation

8 bytes, gives all valid matrices

Brachylog, 12 bytes

Explanation

8 bytes, gives all valid matrices

JavaScript (ES6), 192 180 177 bytes

Algorithm

JavaScript (ES6), 192 180 177 bytes

Algorithm

JavaScript (ES6), 192 180 177 bytes

Algorithm

JavaScript (ES6), 192 180 177 bytes

Algorithm

Python 2, 242 227 bytes

Python 2, 242 227 bytes

Python 2, 242 227 bytes

Python 2, 242 227 bytes

Jelly, 27 bytes

Jelly, 27 bytes

Jelly, 27 bytes

Jelly, 27 bytes

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