Whose neighbours are hostile?

Clash Royale CLAN TAG#URR8PPP

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Introduction

For the purposes of this challenge, we will define the neighbours of an element $E$ in a square matrix $A$ (such that $E=A_i,j$) as all the entries of $A$ that are immediately adjacent diagonally, horizontally or vertically to $E$ (i.e. they "surround" $E$, without wrapping around).

For pedants, a formal definition of the neighbours of $A_i,:j$ for an $ntimes n$ matix $A$ is (0-indexed):
$$N_i,:j=A_a,:bmid(a,b)in E_i,:j:cap:([0,:n):cap:BbbZ)^2$$
where
$$E_i,:j=i-1,:i,:i+1times j-1,:j,:j+1 text \ i,:j$$

Let's say that the element at index $i,:j$ lives in hostility if it is coprime to all its neighbours (that is, $gcd(A_i,:j,:n)=1:forall:nin N_i,:j$). Sadly, this poor entry can't borrow even a cup of sugar from its rude nearby residents...

Task

Enough stories: Given a square matrix $M$ of positive integers, output one of the following:

• A flat list of elements (deduplicated or not) indicating all entries that occupy some indices $i,j$ in $M$ such that the neighbours $N_i,:j$ are hostile.


• A boolean matrix with $1$s at positions where the neighbours are hostile and $0$ otherwise (you can choose any other consistent values in place of $0$ and $1$).


• The list of pairs of indices $i,:j$ that represent hostile neighbourhoods.

Reference Implementation in Physica – supports Python syntax as well for I/O. You can take input and provide output through any standard method and in any reasonable format, while taking note that these loopholes are forbidden by default. This is code-golf, so the shortest code in bytes (in every language) wins!

Example

Consider the following matrix:

$$left(beginmatrix
64 & 10 & 14 \
27 & 22 & 32 \
53 & 58 & 36 \
endmatrixright)$$

The corresponding neighbours of each element are:

i j – E -> Neighbours | All coprime to E?
 |
0 0 – 64 -> 10; 27; 22 | False
0 1 – 10 -> 64; 14; 27; 22; 32 | False
0 2 – 14 -> 10; 22; 32 | False
1 0 – 27 -> 64; 10; 22; 53; 58 | True
1 1 – 22 -> 64; 10; 14; 27; 32; 53; 58; 36 | False
1 2 – 32 -> 10; 14; 22; 58; 36 | False
2 0 – 53 -> 27; 22; 58 | True
2 1 – 58 -> 27; 22; 32; 53; 36 | False
2 2 – 36 -> 22; 32; 58 | False

And thus the output must be one of the following:

• 27; 53


• 0; 0; 0; 1; 0; 0; 1; 0; 0


• (1; 0); (2; 0)

Test cases

Input –> Version 1 | Version 2 | Version 3

[[36, 94], [24, 69]] ->
 
 [[0, 0], [0, 0]]
 
[[38, 77, 11], [17, 51, 32], [66, 78, 19]] –>
 [38, 19]
 [[1, 0, 0], [0, 0, 0], [0, 0, 1]]
 [(0, 0), (2, 2)]
[[64, 10, 14], [27, 22, 32], [53, 58, 36]] ->
 [27, 53]
 [[0, 0, 0], [1, 0, 0], [1, 0, 0]]
 [(1, 0), (2, 0)]
[[9, 9, 9], [9, 3, 9], [9, 9, 9]] ->
 
 [[0, 0, 0], [0, 0, 0], [0, 0, 0]]
 
[[1, 1, 1], [1, 1, 1], [1, 1, 1]] ->
 [1, 1, 1, 1, 1, 1, 1, 1, 1] or [1]
 [[1, 1, 1], [1, 1, 1], [1, 1, 1]]
 [(0, 0), (0, 1), (0, 2), (1, 0), (1, 1), (1, 2), (2, 0), (2, 1), (2, 2)]
[[35, 85, 30, 71], [10, 54, 55, 73], [80, 78, 47, 2], [33, 68, 62, 29]] ->
 [71, 73, 47, 29]
 [[0, 0, 0, 1], [0, 0, 0, 1], [0, 0, 1, 0], [0, 0, 0, 1]]
 [(0, 3), (1, 3), (2, 2), (3, 3)]

code-golf array-manipulation arithmetic integer matrix

share|improve this question

edited 2 hours ago

asked 6 hours ago

Mr. Xcoder

30.4k758193

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Borrowing stuff from hostile neighbors? For some reason, this reminds me of Jeff Minter's game Hover Bovver...
  – Arnauld
  5 hours ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  @JonathanAllan Done, thanks!
  – Mr. Xcoder
  2 hours ago
  
  

  
  
  
  

add a comment | 

up vote
5
down vote

favorite

Introduction

For the purposes of this challenge, we will define the neighbours of an element $E$ in a square matrix $A$ (such that $E=A_i,j$) as all the entries of $A$ that are immediately adjacent diagonally, horizontally or vertically to $E$ (i.e. they "surround" $E$, without wrapping around).

For pedants, a formal definition of the neighbours of $A_i,:j$ for an $ntimes n$ matix $A$ is (0-indexed):
$$N_i,:j=A_a,:bmid(a,b)in E_i,:j:cap:([0,:n):cap:BbbZ)^2$$
where
$$E_i,:j=i-1,:i,:i+1times j-1,:j,:j+1 text \ i,:j$$

Let's say that the element at index $i,:j$ lives in hostility if it is coprime to all its neighbours (that is, $gcd(A_i,:j,:n)=1:forall:nin N_i,:j$). Sadly, this poor entry can't borrow even a cup of sugar from its rude nearby residents...

Task

Enough stories: Given a square matrix $M$ of positive integers, output one of the following:

• A flat list of elements (deduplicated or not) indicating all entries that occupy some indices $i,j$ in $M$ such that the neighbours $N_i,:j$ are hostile.


• A boolean matrix with $1$s at positions where the neighbours are hostile and $0$ otherwise (you can choose any other consistent values in place of $0$ and $1$).


• The list of pairs of indices $i,:j$ that represent hostile neighbourhoods.

Reference Implementation in Physica – supports Python syntax as well for I/O. You can take input and provide output through any standard method and in any reasonable format, while taking note that these loopholes are forbidden by default. This is code-golf, so the shortest code in bytes (in every language) wins!

Example

Consider the following matrix:

$$left(beginmatrix
64 & 10 & 14 \
27 & 22 & 32 \
53 & 58 & 36 \
endmatrixright)$$

The corresponding neighbours of each element are:

i j – E -> Neighbours | All coprime to E?
 |
0 0 – 64 -> 10; 27; 22 | False
0 1 – 10 -> 64; 14; 27; 22; 32 | False
0 2 – 14 -> 10; 22; 32 | False
1 0 – 27 -> 64; 10; 22; 53; 58 | True
1 1 – 22 -> 64; 10; 14; 27; 32; 53; 58; 36 | False
1 2 – 32 -> 10; 14; 22; 58; 36 | False
2 0 – 53 -> 27; 22; 58 | True
2 1 – 58 -> 27; 22; 32; 53; 36 | False
2 2 – 36 -> 22; 32; 58 | False

And thus the output must be one of the following:

• 27; 53


• 0; 0; 0; 1; 0; 0; 1; 0; 0


• (1; 0); (2; 0)

Test cases

Input –> Version 1 | Version 2 | Version 3

[[36, 94], [24, 69]] ->
 
 [[0, 0], [0, 0]]
 
[[38, 77, 11], [17, 51, 32], [66, 78, 19]] –>
 [38, 19]
 [[1, 0, 0], [0, 0, 0], [0, 0, 1]]
 [(0, 0), (2, 2)]
[[64, 10, 14], [27, 22, 32], [53, 58, 36]] ->
 [27, 53]
 [[0, 0, 0], [1, 0, 0], [1, 0, 0]]
 [(1, 0), (2, 0)]
[[9, 9, 9], [9, 3, 9], [9, 9, 9]] ->
 
 [[0, 0, 0], [0, 0, 0], [0, 0, 0]]
 
[[1, 1, 1], [1, 1, 1], [1, 1, 1]] ->
 [1, 1, 1, 1, 1, 1, 1, 1, 1] or [1]
 [[1, 1, 1], [1, 1, 1], [1, 1, 1]]
 [(0, 0), (0, 1), (0, 2), (1, 0), (1, 1), (1, 2), (2, 0), (2, 1), (2, 2)]
[[35, 85, 30, 71], [10, 54, 55, 73], [80, 78, 47, 2], [33, 68, 62, 29]] ->
 [71, 73, 47, 29]
 [[0, 0, 0, 1], [0, 0, 0, 1], [0, 0, 1, 0], [0, 0, 0, 1]]
 [(0, 3), (1, 3), (2, 2), (3, 3)]

code-golf array-manipulation arithmetic integer matrix

share|improve this question

edited 2 hours ago

asked 6 hours ago

Mr. Xcoder

30.4k758193

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Borrowing stuff from hostile neighbors? For some reason, this reminds me of Jeff Minter's game Hover Bovver...
  – Arnauld
  5 hours ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  @JonathanAllan Done, thanks!
  – Mr. Xcoder
  2 hours ago
  
  

  
  
  
  

add a comment | 

up vote
5
down vote

favorite

up vote
5
down vote

favorite

Introduction

For the purposes of this challenge, we will define the neighbours of an element $E$ in a square matrix $A$ (such that $E=A_i,j$) as all the entries of $A$ that are immediately adjacent diagonally, horizontally or vertically to $E$ (i.e. they "surround" $E$, without wrapping around).

For pedants, a formal definition of the neighbours of $A_i,:j$ for an $ntimes n$ matix $A$ is (0-indexed):
$$N_i,:j=A_a,:bmid(a,b)in E_i,:j:cap:([0,:n):cap:BbbZ)^2$$
where
$$E_i,:j=i-1,:i,:i+1times j-1,:j,:j+1 text \ i,:j$$

Let's say that the element at index $i,:j$ lives in hostility if it is coprime to all its neighbours (that is, $gcd(A_i,:j,:n)=1:forall:nin N_i,:j$). Sadly, this poor entry can't borrow even a cup of sugar from its rude nearby residents...

Task

Enough stories: Given a square matrix $M$ of positive integers, output one of the following:

• A flat list of elements (deduplicated or not) indicating all entries that occupy some indices $i,j$ in $M$ such that the neighbours $N_i,:j$ are hostile.


• A boolean matrix with $1$s at positions where the neighbours are hostile and $0$ otherwise (you can choose any other consistent values in place of $0$ and $1$).


• The list of pairs of indices $i,:j$ that represent hostile neighbourhoods.

Reference Implementation in Physica – supports Python syntax as well for I/O. You can take input and provide output through any standard method and in any reasonable format, while taking note that these loopholes are forbidden by default. This is code-golf, so the shortest code in bytes (in every language) wins!

Example

Consider the following matrix:

$$left(beginmatrix
64 & 10 & 14 \
27 & 22 & 32 \
53 & 58 & 36 \
endmatrixright)$$

The corresponding neighbours of each element are:

i j – E -> Neighbours | All coprime to E?
 |
0 0 – 64 -> 10; 27; 22 | False
0 1 – 10 -> 64; 14; 27; 22; 32 | False
0 2 – 14 -> 10; 22; 32 | False
1 0 – 27 -> 64; 10; 22; 53; 58 | True
1 1 – 22 -> 64; 10; 14; 27; 32; 53; 58; 36 | False
1 2 – 32 -> 10; 14; 22; 58; 36 | False
2 0 – 53 -> 27; 22; 58 | True
2 1 – 58 -> 27; 22; 32; 53; 36 | False
2 2 – 36 -> 22; 32; 58 | False

And thus the output must be one of the following:

• 27; 53


• 0; 0; 0; 1; 0; 0; 1; 0; 0


• (1; 0); (2; 0)

Test cases

Input –> Version 1 | Version 2 | Version 3

[[36, 94], [24, 69]] ->
 
 [[0, 0], [0, 0]]
 
[[38, 77, 11], [17, 51, 32], [66, 78, 19]] –>
 [38, 19]
 [[1, 0, 0], [0, 0, 0], [0, 0, 1]]
 [(0, 0), (2, 2)]
[[64, 10, 14], [27, 22, 32], [53, 58, 36]] ->
 [27, 53]
 [[0, 0, 0], [1, 0, 0], [1, 0, 0]]
 [(1, 0), (2, 0)]
[[9, 9, 9], [9, 3, 9], [9, 9, 9]] ->
 
 [[0, 0, 0], [0, 0, 0], [0, 0, 0]]
 
[[1, 1, 1], [1, 1, 1], [1, 1, 1]] ->
 [1, 1, 1, 1, 1, 1, 1, 1, 1] or [1]
 [[1, 1, 1], [1, 1, 1], [1, 1, 1]]
 [(0, 0), (0, 1), (0, 2), (1, 0), (1, 1), (1, 2), (2, 0), (2, 1), (2, 2)]
[[35, 85, 30, 71], [10, 54, 55, 73], [80, 78, 47, 2], [33, 68, 62, 29]] ->
 [71, 73, 47, 29]
 [[0, 0, 0, 1], [0, 0, 0, 1], [0, 0, 1, 0], [0, 0, 0, 1]]
 [(0, 3), (1, 3), (2, 2), (3, 3)]

code-golf array-manipulation arithmetic integer matrix

share|improve this question

edited 2 hours ago

asked 6 hours ago

Mr. Xcoder

30.4k758193

Introduction

For the purposes of this challenge, we will define the neighbours of an element $E$ in a square matrix $A$ (such that $E=A_i,j$) as all the entries of $A$ that are immediately adjacent diagonally, horizontally or vertically to $E$ (i.e. they "surround" $E$, without wrapping around).

For pedants, a formal definition of the neighbours of $A_i,:j$ for an $ntimes n$ matix $A$ is (0-indexed):
$$N_i,:j=A_a,:bmid(a,b)in E_i,:j:cap:([0,:n):cap:BbbZ)^2$$
where
$$E_i,:j=i-1,:i,:i+1times j-1,:j,:j+1 text \ i,:j$$

Let's say that the element at index $i,:j$ lives in hostility if it is coprime to all its neighbours (that is, $gcd(A_i,:j,:n)=1:forall:nin N_i,:j$). Sadly, this poor entry can't borrow even a cup of sugar from its rude nearby residents...

Task

Enough stories: Given a square matrix $M$ of positive integers, output one of the following:

• A flat list of elements (deduplicated or not) indicating all entries that occupy some indices $i,j$ in $M$ such that the neighbours $N_i,:j$ are hostile.


• A boolean matrix with $1$s at positions where the neighbours are hostile and $0$ otherwise (you can choose any other consistent values in place of $0$ and $1$).


• The list of pairs of indices $i,:j$ that represent hostile neighbourhoods.

Reference Implementation in Physica – supports Python syntax as well for I/O. You can take input and provide output through any standard method and in any reasonable format, while taking note that these loopholes are forbidden by default. This is code-golf, so the shortest code in bytes (in every language) wins!

Example

Consider the following matrix:

$$left(beginmatrix
64 & 10 & 14 \
27 & 22 & 32 \
53 & 58 & 36 \
endmatrixright)$$

The corresponding neighbours of each element are:

i j – E -> Neighbours | All coprime to E?
 |
0 0 – 64 -> 10; 27; 22 | False
0 1 – 10 -> 64; 14; 27; 22; 32 | False
0 2 – 14 -> 10; 22; 32 | False
1 0 – 27 -> 64; 10; 22; 53; 58 | True
1 1 – 22 -> 64; 10; 14; 27; 32; 53; 58; 36 | False
1 2 – 32 -> 10; 14; 22; 58; 36 | False
2 0 – 53 -> 27; 22; 58 | True
2 1 – 58 -> 27; 22; 32; 53; 36 | False
2 2 – 36 -> 22; 32; 58 | False

And thus the output must be one of the following:

• 27; 53


• 0; 0; 0; 1; 0; 0; 1; 0; 0


• (1; 0); (2; 0)

Test cases

Input –> Version 1 | Version 2 | Version 3

[[36, 94], [24, 69]] ->
 
 [[0, 0], [0, 0]]
 
[[38, 77, 11], [17, 51, 32], [66, 78, 19]] –>
 [38, 19]
 [[1, 0, 0], [0, 0, 0], [0, 0, 1]]
 [(0, 0), (2, 2)]
[[64, 10, 14], [27, 22, 32], [53, 58, 36]] ->
 [27, 53]
 [[0, 0, 0], [1, 0, 0], [1, 0, 0]]
 [(1, 0), (2, 0)]
[[9, 9, 9], [9, 3, 9], [9, 9, 9]] ->
 
 [[0, 0, 0], [0, 0, 0], [0, 0, 0]]
 
[[1, 1, 1], [1, 1, 1], [1, 1, 1]] ->
 [1, 1, 1, 1, 1, 1, 1, 1, 1] or [1]
 [[1, 1, 1], [1, 1, 1], [1, 1, 1]]
 [(0, 0), (0, 1), (0, 2), (1, 0), (1, 1), (1, 2), (2, 0), (2, 1), (2, 2)]
[[35, 85, 30, 71], [10, 54, 55, 73], [80, 78, 47, 2], [33, 68, 62, 29]] ->
 [71, 73, 47, 29]
 [[0, 0, 0, 1], [0, 0, 0, 1], [0, 0, 1, 0], [0, 0, 0, 1]]
 [(0, 3), (1, 3), (2, 2), (3, 3)]

code-golf array-manipulation arithmetic integer matrix

code-golf array-manipulation arithmetic integer matrix

share|improve this question

edited 2 hours ago

asked 6 hours ago

Mr. Xcoder

30.4k758193

share|improve this question

edited 2 hours ago

asked 6 hours ago

Mr. Xcoder

30.4k758193

share|improve this question

share|improve this question

edited 2 hours ago

edited 2 hours ago

edited 2 hours ago

asked 6 hours ago

Mr. Xcoder

30.4k758193

asked 6 hours ago

Mr. Xcoder

30.4k758193

asked 6 hours ago

Mr. Xcoder

30.4k758193

30.4k758193

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Borrowing stuff from hostile neighbors? For some reason, this reminds me of Jeff Minter's game Hover Bovver...
  – Arnauld
  5 hours ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  @JonathanAllan Done, thanks!
  – Mr. Xcoder
  2 hours ago
  
  

  
  
  
  

add a comment | 

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Borrowing stuff from hostile neighbors? For some reason, this reminds me of Jeff Minter's game Hover Bovver...
  – Arnauld
  5 hours ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  @JonathanAllan Done, thanks!
  – Mr. Xcoder
  2 hours ago
  
  

  
  
  
  

Borrowing stuff from hostile neighbors? For some reason, this reminds me of Jeff Minter's game Hover Bovver...
– Arnauld
5 hours ago

Borrowing stuff from hostile neighbors? For some reason, this reminds me of Jeff Minter's game Hover Bovver...
– Arnauld
5 hours ago

1

1

@JonathanAllan Done, thanks!
– Mr. Xcoder
2 hours ago

@JonathanAllan Done, thanks!
– Mr. Xcoder
2 hours ago

add a comment | 

4 Answers
4

active

oldest

votes

up vote
1
down vote

JavaScript (ES6), 121 bytes

Returns a matrix of Boolean values, where false means hostile.

m=>m.map((r,y)=>r.map((v,x)=>[...'12221000'].some((k,j,a)=>(g=(a,b)=>b?g(b,a%b):a>1)(v,(m[y+~-k]||0)[x+~-a[j+2&7]]||1))))

Try it online!

How?

The method used to isolate the 8 neighbors of each cell is similar to the one I described here.

Commented

m => // m = input matrix
 m.map((r, y) => // for each row r at position y in m:
 r.map((v, x) => // for each value v at position x in r:
 [...'12221000'] // we consider all 8 neighbors
 .some((k, j, a) => // for each k at position j in this array a:
 ( g = (a, b) => // g is a function which takes 2 integers a and b
 b ? // and recursively determines whether they are
 g(b, a % b) // coprime to each other
 : // (returns false if they are, true if they're not)
 a > 1 //
 )( // initial call to g() with:
 v, // the value of the current cell
 (m[y + ~-k] || 0) // and the value of the current neighbor
 [x + ~-a[j + 2 & 7]] //
 || 1 // or 1 if this neighbor is undefined
 )))) // (to make sure it's coprime with v)

share|improve this answer

edited 1 hour ago

answered 6 hours ago

Arnauld

64.2k580270

add a comment | 

up vote
1
down vote

APL (Dyalog), 17 bytes

1=⊢∨(×/∘,↓)⌺3 3÷⊢

Try it online! (credits to ngn for translating the test cases to APL)

Brief explanation

(×/∘,↓)⌺3 3 gets the product of each element with its neighbours.

Then I divide by the argument ÷⊢, so that each entry in the matrix has been mapped to the product of its neighbors.

Finally I take the gcd of the argument with this matrix ⊢∨, and check for equality with 1, 1=

Note, as with ngn's answer, this fails for some inputs due to a bug in the interpreter.

share|improve this answer

answered 29 mins ago

H.PWiz

9,68921249

add a comment | 

up vote
0
down vote

APL (Dyalog Classic), 23 22 bytes

-1 byte thanks to @H.PWiz

∧/1=1↓∨∘⊃⍨1⌈4⌽,⍵⌺3 3

Try it online!

doesn't support matrices smaller than 3x3 due to a bug in the interpreter

share|improve this answer

edited 25 mins ago

answered 5 hours ago

ngn

6,19812256

• 
  
  
  

  
  

  
  
  
  
  
  

  
  @H.PWiz that's very smart, do you wanna post it as your own?
  – ngn
  41 mins ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Sure, you can also use (⊃∨⊢) -> ∨∘⊂⍨ I think
  – H.PWiz
  40 mins ago
  

  
  
  
  

add a comment | 

up vote
0
down vote

Jelly, 24 bytes

^{Hmm, seems long.}

ỊẠ€T
ŒJ_€`Ç€ḟ"J$ịFg"FÇịF

A monadic Link accepting a list of lists of positive integers which returns a list of each of the values which are in hostile neighbourhoods (version 1 with no de-duplication).

Try it online! Or see a test-suite.

How?

ỊẠ€T - Link 1: indices of items which only contain "insignificant" values: list of lists
Ị - insignificant (vectorises) -- 1 if (-1<=value<=1) else 0 
 € - for €ach:
 Ạ - all?
 T - truthy indices

ŒJ_€`Ç€ḟ"J$ịFg"FÇịF - Main Link: list of lists of positive integers, M
Ã…Â’J - multi-dimensional indices
 ` - use as right argument as well as left...
 € - for €ach:
 _ - subtract (vectorises)
 € - for €ach:
 Ç - call last Link (1) as a monad
 $ - last two links as a monad:
 J - range of length -> [1,2,3,...,n(elements)]
 " - zip with:
 ḟ - filter discard (remove the index of the item itself)
 F - flatten M
 ị - index into (vectorises) -- getting a list of lists of neighbours
 F - flatten M
 " - zip with:
 g - greatest common divisor
 Ç - call last Link (1) as a monad
 F - flatten M
 ị - index into

share|improve this answer

edited 21 mins ago

answered 41 mins ago

Jonathan Allan

48.3k534159

add a comment | 

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4 Answers
4

active

oldest

votes

4 Answers
4

active

oldest

votes

active

oldest

votes

active

oldest

votes

up vote
1
down vote

JavaScript (ES6), 121 bytes

Returns a matrix of Boolean values, where false means hostile.

m=>m.map((r,y)=>r.map((v,x)=>[...'12221000'].some((k,j,a)=>(g=(a,b)=>b?g(b,a%b):a>1)(v,(m[y+~-k]||0)[x+~-a[j+2&7]]||1))))

Try it online!

How?

The method used to isolate the 8 neighbors of each cell is similar to the one I described here.

Commented

m => // m = input matrix
 m.map((r, y) => // for each row r at position y in m:
 r.map((v, x) => // for each value v at position x in r:
 [...'12221000'] // we consider all 8 neighbors
 .some((k, j, a) => // for each k at position j in this array a:
 ( g = (a, b) => // g is a function which takes 2 integers a and b
 b ? // and recursively determines whether they are
 g(b, a % b) // coprime to each other
 : // (returns false if they are, true if they're not)
 a > 1 //
 )( // initial call to g() with:
 v, // the value of the current cell
 (m[y + ~-k] || 0) // and the value of the current neighbor
 [x + ~-a[j + 2 & 7]] //
 || 1 // or 1 if this neighbor is undefined
 )))) // (to make sure it's coprime with v)

share|improve this answer

edited 1 hour ago

answered 6 hours ago

Arnauld

64.2k580270

add a comment | 

up vote
1
down vote

JavaScript (ES6), 121 bytes

Returns a matrix of Boolean values, where false means hostile.

m=>m.map((r,y)=>r.map((v,x)=>[...'12221000'].some((k,j,a)=>(g=(a,b)=>b?g(b,a%b):a>1)(v,(m[y+~-k]||0)[x+~-a[j+2&7]]||1))))

Try it online!

How?

The method used to isolate the 8 neighbors of each cell is similar to the one I described here.

Commented

m => // m = input matrix
 m.map((r, y) => // for each row r at position y in m:
 r.map((v, x) => // for each value v at position x in r:
 [...'12221000'] // we consider all 8 neighbors
 .some((k, j, a) => // for each k at position j in this array a:
 ( g = (a, b) => // g is a function which takes 2 integers a and b
 b ? // and recursively determines whether they are
 g(b, a % b) // coprime to each other
 : // (returns false if they are, true if they're not)
 a > 1 //
 )( // initial call to g() with:
 v, // the value of the current cell
 (m[y + ~-k] || 0) // and the value of the current neighbor
 [x + ~-a[j + 2 & 7]] //
 || 1 // or 1 if this neighbor is undefined
 )))) // (to make sure it's coprime with v)

share|improve this answer

edited 1 hour ago

answered 6 hours ago

Arnauld

64.2k580270

add a comment | 

up vote
1
down vote

up vote
1
down vote

JavaScript (ES6), 121 bytes

Returns a matrix of Boolean values, where false means hostile.

m=>m.map((r,y)=>r.map((v,x)=>[...'12221000'].some((k,j,a)=>(g=(a,b)=>b?g(b,a%b):a>1)(v,(m[y+~-k]||0)[x+~-a[j+2&7]]||1))))

Try it online!

How?

The method used to isolate the 8 neighbors of each cell is similar to the one I described here.

Commented

m => // m = input matrix
 m.map((r, y) => // for each row r at position y in m:
 r.map((v, x) => // for each value v at position x in r:
 [...'12221000'] // we consider all 8 neighbors
 .some((k, j, a) => // for each k at position j in this array a:
 ( g = (a, b) => // g is a function which takes 2 integers a and b
 b ? // and recursively determines whether they are
 g(b, a % b) // coprime to each other
 : // (returns false if they are, true if they're not)
 a > 1 //
 )( // initial call to g() with:
 v, // the value of the current cell
 (m[y + ~-k] || 0) // and the value of the current neighbor
 [x + ~-a[j + 2 & 7]] //
 || 1 // or 1 if this neighbor is undefined
 )))) // (to make sure it's coprime with v)

share|improve this answer

edited 1 hour ago

answered 6 hours ago

Arnauld

64.2k580270

JavaScript (ES6), 121 bytes

Returns a matrix of Boolean values, where false means hostile.

m=>m.map((r,y)=>r.map((v,x)=>[...'12221000'].some((k,j,a)=>(g=(a,b)=>b?g(b,a%b):a>1)(v,(m[y+~-k]||0)[x+~-a[j+2&7]]||1))))

Try it online!

How?

The method used to isolate the 8 neighbors of each cell is similar to the one I described here.

Commented

m => // m = input matrix
 m.map((r, y) => // for each row r at position y in m:
 r.map((v, x) => // for each value v at position x in r:
 [...'12221000'] // we consider all 8 neighbors
 .some((k, j, a) => // for each k at position j in this array a:
 ( g = (a, b) => // g is a function which takes 2 integers a and b
 b ? // and recursively determines whether they are
 g(b, a % b) // coprime to each other
 : // (returns false if they are, true if they're not)
 a > 1 //
 )( // initial call to g() with:
 v, // the value of the current cell
 (m[y + ~-k] || 0) // and the value of the current neighbor
 [x + ~-a[j + 2 & 7]] //
 || 1 // or 1 if this neighbor is undefined
 )))) // (to make sure it's coprime with v)

share|improve this answer

edited 1 hour ago

answered 6 hours ago

Arnauld

64.2k580270

share|improve this answer

share|improve this answer

edited 1 hour ago

edited 1 hour ago

edited 1 hour ago

answered 6 hours ago

Arnauld

64.2k580270

answered 6 hours ago

Arnauld

64.2k580270

answered 6 hours ago

Arnauld

64.2k580270

64.2k580270

add a comment | 

add a comment | 

up vote
1
down vote

APL (Dyalog), 17 bytes

1=⊢∨(×/∘,↓)⌺3 3÷⊢

Try it online! (credits to ngn for translating the test cases to APL)

Brief explanation

(×/∘,↓)⌺3 3 gets the product of each element with its neighbours.

Then I divide by the argument ÷⊢, so that each entry in the matrix has been mapped to the product of its neighbors.

Finally I take the gcd of the argument with this matrix ⊢∨, and check for equality with 1, 1=

Note, as with ngn's answer, this fails for some inputs due to a bug in the interpreter.

share|improve this answer

answered 29 mins ago

H.PWiz

9,68921249

add a comment | 

up vote
1
down vote

APL (Dyalog), 17 bytes

1=⊢∨(×/∘,↓)⌺3 3÷⊢

Try it online! (credits to ngn for translating the test cases to APL)

Brief explanation

(×/∘,↓)⌺3 3 gets the product of each element with its neighbours.

Then I divide by the argument ÷⊢, so that each entry in the matrix has been mapped to the product of its neighbors.

Finally I take the gcd of the argument with this matrix ⊢∨, and check for equality with 1, 1=

Note, as with ngn's answer, this fails for some inputs due to a bug in the interpreter.

share|improve this answer

answered 29 mins ago

H.PWiz

9,68921249

add a comment | 

up vote
1
down vote

up vote
1
down vote

APL (Dyalog), 17 bytes

1=⊢∨(×/∘,↓)⌺3 3÷⊢

Try it online! (credits to ngn for translating the test cases to APL)

Brief explanation

(×/∘,↓)⌺3 3 gets the product of each element with its neighbours.

Then I divide by the argument ÷⊢, so that each entry in the matrix has been mapped to the product of its neighbors.

Finally I take the gcd of the argument with this matrix ⊢∨, and check for equality with 1, 1=

Note, as with ngn's answer, this fails for some inputs due to a bug in the interpreter.

share|improve this answer

answered 29 mins ago

H.PWiz

9,68921249

APL (Dyalog), 17 bytes

1=⊢∨(×/∘,↓)⌺3 3÷⊢

Try it online! (credits to ngn for translating the test cases to APL)

Brief explanation

(×/∘,↓)⌺3 3 gets the product of each element with its neighbours.

Then I divide by the argument ÷⊢, so that each entry in the matrix has been mapped to the product of its neighbors.

Finally I take the gcd of the argument with this matrix ⊢∨, and check for equality with 1, 1=

Note, as with ngn's answer, this fails for some inputs due to a bug in the interpreter.

share|improve this answer

answered 29 mins ago

H.PWiz

9,68921249

share|improve this answer

share|improve this answer

answered 29 mins ago

H.PWiz

9,68921249

answered 29 mins ago

H.PWiz

9,68921249

answered 29 mins ago

H.PWiz

9,68921249

9,68921249

add a comment | 

add a comment | 

up vote
0
down vote

APL (Dyalog Classic), 23 22 bytes

-1 byte thanks to @H.PWiz

∧/1=1↓∨∘⊃⍨1⌈4⌽,⍵⌺3 3

Try it online!

doesn't support matrices smaller than 3x3 due to a bug in the interpreter

share|improve this answer

edited 25 mins ago

answered 5 hours ago

ngn

6,19812256

• 
  
  
  

  
  

  
  
  
  
  
  

  
  @H.PWiz that's very smart, do you wanna post it as your own?
  – ngn
  41 mins ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Sure, you can also use (⊃∨⊢) -> ∨∘⊂⍨ I think
  – H.PWiz
  40 mins ago
  

  
  
  
  

add a comment | 

up vote
0
down vote

APL (Dyalog Classic), 23 22 bytes

-1 byte thanks to @H.PWiz

∧/1=1↓∨∘⊃⍨1⌈4⌽,⍵⌺3 3

Try it online!

doesn't support matrices smaller than 3x3 due to a bug in the interpreter

share|improve this answer

edited 25 mins ago

answered 5 hours ago

ngn

6,19812256

• 
  
  
  

  
  

  
  
  
  
  
  

  
  @H.PWiz that's very smart, do you wanna post it as your own?
  – ngn
  41 mins ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Sure, you can also use (⊃∨⊢) -> ∨∘⊂⍨ I think
  – H.PWiz
  40 mins ago
  

  
  
  
  

add a comment | 

up vote
0
down vote

up vote
0
down vote

APL (Dyalog Classic), 23 22 bytes

-1 byte thanks to @H.PWiz

∧/1=1↓∨∘⊃⍨1⌈4⌽,⍵⌺3 3

Try it online!

doesn't support matrices smaller than 3x3 due to a bug in the interpreter

share|improve this answer

edited 25 mins ago

answered 5 hours ago

ngn

6,19812256

APL (Dyalog Classic), 23 22 bytes

-1 byte thanks to @H.PWiz

∧/1=1↓∨∘⊃⍨1⌈4⌽,⍵⌺3 3

Try it online!

doesn't support matrices smaller than 3x3 due to a bug in the interpreter

share|improve this answer

edited 25 mins ago

answered 5 hours ago

ngn

6,19812256

share|improve this answer

share|improve this answer

edited 25 mins ago

edited 25 mins ago

edited 25 mins ago

answered 5 hours ago

ngn

6,19812256

answered 5 hours ago

ngn

6,19812256

answered 5 hours ago

ngn

6,19812256

6,19812256

• 
  
  
  

  
  

  
  
  
  
  
  

  
  @H.PWiz that's very smart, do you wanna post it as your own?
  – ngn
  41 mins ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Sure, you can also use (⊃∨⊢) -> ∨∘⊂⍨ I think
  – H.PWiz
  40 mins ago
  

  
  
  
  

add a comment | 

• 
  
  
  

  
  

  
  
  
  
  
  

  
  @H.PWiz that's very smart, do you wanna post it as your own?
  – ngn
  41 mins ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Sure, you can also use (⊃∨⊢) -> ∨∘⊂⍨ I think
  – H.PWiz
  40 mins ago
  

  
  
  
  

@H.PWiz that's very smart, do you wanna post it as your own?
– ngn
41 mins ago

@H.PWiz that's very smart, do you wanna post it as your own?
– ngn
41 mins ago

Sure, you can also use (⊃∨⊢) -> ∨∘⊂⍨ I think
– H.PWiz
40 mins ago

Sure, you can also use (⊃∨⊢) -> ∨∘⊂⍨ I think
– H.PWiz
40 mins ago

add a comment | 

up vote
0
down vote

Jelly, 24 bytes

^{Hmm, seems long.}

ỊẠ€T
ŒJ_€`Ç€ḟ"J$ịFg"FÇịF

A monadic Link accepting a list of lists of positive integers which returns a list of each of the values which are in hostile neighbourhoods (version 1 with no de-duplication).

Try it online! Or see a test-suite.

How?

ỊẠ€T - Link 1: indices of items which only contain "insignificant" values: list of lists
Ị - insignificant (vectorises) -- 1 if (-1<=value<=1) else 0 
 € - for €ach:
 Ạ - all?
 T - truthy indices

ŒJ_€`Ç€ḟ"J$ịFg"FÇịF - Main Link: list of lists of positive integers, M
Ã…Â’J - multi-dimensional indices
 ` - use as right argument as well as left...
 € - for €ach:
 _ - subtract (vectorises)
 € - for €ach:
 Ç - call last Link (1) as a monad
 $ - last two links as a monad:
 J - range of length -> [1,2,3,...,n(elements)]
 " - zip with:
 ḟ - filter discard (remove the index of the item itself)
 F - flatten M
 ị - index into (vectorises) -- getting a list of lists of neighbours
 F - flatten M
 " - zip with:
 g - greatest common divisor
 Ç - call last Link (1) as a monad
 F - flatten M
 ị - index into

share|improve this answer

edited 21 mins ago

answered 41 mins ago

Jonathan Allan

48.3k534159

add a comment | 

up vote
0
down vote

Jelly, 24 bytes

^{Hmm, seems long.}

ỊẠ€T
ŒJ_€`Ç€ḟ"J$ịFg"FÇịF

A monadic Link accepting a list of lists of positive integers which returns a list of each of the values which are in hostile neighbourhoods (version 1 with no de-duplication).

Try it online! Or see a test-suite.

How?

ỊẠ€T - Link 1: indices of items which only contain "insignificant" values: list of lists
Ị - insignificant (vectorises) -- 1 if (-1<=value<=1) else 0 
 € - for €ach:
 Ạ - all?
 T - truthy indices

ŒJ_€`Ç€ḟ"J$ịFg"FÇịF - Main Link: list of lists of positive integers, M
Ã…Â’J - multi-dimensional indices
 ` - use as right argument as well as left...
 € - for €ach:
 _ - subtract (vectorises)
 € - for €ach:
 Ç - call last Link (1) as a monad
 $ - last two links as a monad:
 J - range of length -> [1,2,3,...,n(elements)]
 " - zip with:
 ḟ - filter discard (remove the index of the item itself)
 F - flatten M
 ị - index into (vectorises) -- getting a list of lists of neighbours
 F - flatten M
 " - zip with:
 g - greatest common divisor
 Ç - call last Link (1) as a monad
 F - flatten M
 ị - index into

share|improve this answer

edited 21 mins ago

answered 41 mins ago

Jonathan Allan

48.3k534159

add a comment | 

up vote
0
down vote

up vote
0
down vote

Jelly, 24 bytes

^{Hmm, seems long.}

ỊẠ€T
ŒJ_€`Ç€ḟ"J$ịFg"FÇịF

A monadic Link accepting a list of lists of positive integers which returns a list of each of the values which are in hostile neighbourhoods (version 1 with no de-duplication).

Try it online! Or see a test-suite.

How?

ỊẠ€T - Link 1: indices of items which only contain "insignificant" values: list of lists
Ị - insignificant (vectorises) -- 1 if (-1<=value<=1) else 0 
 € - for €ach:
 Ạ - all?
 T - truthy indices

ŒJ_€`Ç€ḟ"J$ịFg"FÇịF - Main Link: list of lists of positive integers, M
Ã…Â’J - multi-dimensional indices
 ` - use as right argument as well as left...
 € - for €ach:
 _ - subtract (vectorises)
 € - for €ach:
 Ç - call last Link (1) as a monad
 $ - last two links as a monad:
 J - range of length -> [1,2,3,...,n(elements)]
 " - zip with:
 ḟ - filter discard (remove the index of the item itself)
 F - flatten M
 ị - index into (vectorises) -- getting a list of lists of neighbours
 F - flatten M
 " - zip with:
 g - greatest common divisor
 Ç - call last Link (1) as a monad
 F - flatten M
 ị - index into

share|improve this answer

edited 21 mins ago

answered 41 mins ago

Jonathan Allan

48.3k534159

Jelly, 24 bytes

^{Hmm, seems long.}

ỊẠ€T
ŒJ_€`Ç€ḟ"J$ịFg"FÇịF

A monadic Link accepting a list of lists of positive integers which returns a list of each of the values which are in hostile neighbourhoods (version 1 with no de-duplication).

Try it online! Or see a test-suite.

How?

ỊẠ€T - Link 1: indices of items which only contain "insignificant" values: list of lists
Ị - insignificant (vectorises) -- 1 if (-1<=value<=1) else 0 
 € - for €ach:
 Ạ - all?
 T - truthy indices

ŒJ_€`Ç€ḟ"J$ịFg"FÇịF - Main Link: list of lists of positive integers, M
Ã…Â’J - multi-dimensional indices
 ` - use as right argument as well as left...
 € - for €ach:
 _ - subtract (vectorises)
 € - for €ach:
 Ç - call last Link (1) as a monad
 $ - last two links as a monad:
 J - range of length -> [1,2,3,...,n(elements)]
 " - zip with:
 ḟ - filter discard (remove the index of the item itself)
 F - flatten M
 ị - index into (vectorises) -- getting a list of lists of neighbours
 F - flatten M
 " - zip with:
 g - greatest common divisor
 Ç - call last Link (1) as a monad
 F - flatten M
 ị - index into

share|improve this answer

edited 21 mins ago

answered 41 mins ago

Jonathan Allan

48.3k534159

share|improve this answer

share|improve this answer

edited 21 mins ago

edited 21 mins ago

edited 21 mins ago

answered 41 mins ago

Jonathan Allan

48.3k534159

answered 41 mins ago

Jonathan Allan

48.3k534159

answered 41 mins ago

Jonathan Allan

48.3k534159

48.3k534159

add a comment | 

add a comment | 

 

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