# Square chunk my matrix

Your challenge is to write a function/program that takes a matrix of integers m and a number n as input and:

• Splits m into n by n chunks

• Replaces each chunk with the most common value in that chunk (In case of a tie, any of the tied values is fine).

• Outputs the resulting matrix.

Note: You can take either the size of a single chunk, or the number of chunks to a side.

Example:

0 1 0 1
0 0 1 1
0 0 0 0
0 0 1 1,
2


Divide into chunks:

0 1|0 1
0 0|1 1
---+---
0 0|0 0
0 0|1 1


Take the most common value in each sub-matrix

0|1
-+-
0|0


So

0 1
0 0


is the result!

Note: You can assume that there will always be an integer amount of chunks with integer size.

Input will always be square.

# Testcases

These are formatted as taking the size of a single chunk.

0 1 2 1 2 1
2 2 1 0 2 2
2 1 2 0 1 0
0 0 1 0 3 2
3 0 2 0 3 1
1 0 3 2 0 1,
3 =>
2 1
0 0
(The 1 is a tie, any of 012 are fine)

0 1 2 1 2 1
2 2 1 0 2 2
2 1 2 0 1 0
0 0 1 0 3 2
3 0 2 0 3 1
1 0 3 2 0 1,
2 =>
2 1 2
0 0 3
0 2 1
(The 3 is a tie, any of 0123 are fine)

1,
1 =>
1
(kinda obvious edgecase)


# Scoring

This is , shortest wins!

• Can we take the matrix transposed? – caird coinheringaahing Jun 16 at 11:28
• How does that help? It's the same thing... – A username Jun 16 at 11:28
• Is the matrix guaranteed to be square? – Arnauld Jun 16 at 11:38
• Can we take the width and height of the matrix as input too – StackMeter Jun 16 at 11:43
• "You can take either the size of a single chunk, or the number of chunks to a side." but can we take both? – Adám Jun 16 at 11:46

# MATL, 11 bytes

thZCtvXM[]e


### How it works

th     % Implicit input: number n. Horizontally concatenate with itself to give [n n]
ZC     % Implicit input: matrix m. Im2col: arrange each [n n] block as a column of
% length n*n
tv     % Vertically concatenate with itself. This makes columns twice as long without
% affecting their mode. This is needed in case the previous result had a single
% row (n=1), which would cause the subsequent mode function to compute the mode
% of that row, instead of the mode of each column
XM     % Mode. This gives the mode of each column (the input has at least 2 rows)
[]e    % Reshape as a square matrix. Implicit display


# APL (Dyalog Unicode), 40 38 bytes (SBCS)

Anonymous tacit infix function taking chunk size as left argument and the input matrix as right argument.

{(∪⊃⍨∘⊃∘⍒⊢∘≢⌸)∘,¨↑(⊂⊂¨⊂[1]∘⍵)(≢⍵)⍴⍺↑1}


Try it online!

{}dfn; ⍺ is chunk size and ⍵ is matrix:
2 and
⎡0,1,0,1⎤
⎢0,0,1,1⎥
⎢0,0,0,0⎥
⎣0,0,1,1⎦

⍺↑1 take "chunk size" elements from 1, padding with zeros
[1,0]

(≢⍵)⍴ cyclically reshape that to the number of rows in the matrix
[1,0,1,0]

() apply the following tacit prefix function:

⊂[1]∘⍵ use the argument to partition the matrix vertically
 ⎡0,1,0,1⎤ ⎡0,0,0,0⎤
[⎣0,0,1,1⎦,⎣0,0,1,1⎦]

⊂⊂¨ use the entire argument to partition each of those horizontally
 ⎡0,1⎤ ⎡0,1⎤ ⎡0,0⎤ ⎡0,0⎤
[[⎣0,0⎦,⎣1,1⎦],[⎣0,0⎦,⎣1,1⎦]]

↑ mix into a matrix
⎡ ⎡0,1⎤ ⎡0,1⎤ ⎤
⎢ ⎣0,0⎦,⎣1,1⎦ ⎥
⎢ ⎡0,0⎤ ⎡0,0⎤ ⎥
⎣ ⎣0,0⎦,⎣1,1⎦ ⎦

()∘,¨ for each element, ravel (flatten) it and then apply the following tacit prefix function:
⎡ [0,1,0,0],[0,1,1,1] ⎤
⎣ [0,0,0,0],[0,0,1,1] ⎦

⊢∘≢⌸ for each unique element, count the indices it occurs at
⎡ [3,1],[1,3] ⎤
⎣ [4] ,[2,2] ⎦

∪… with the unique elements…
⎡ [0,1],[0,1] ⎤
⎣ [0] ,[0,1] ⎦

∘⊃∘⍒ get the index of the largest count (lit. first element of the permutation vector that would sort the counts descending), then…
⎡1,2⎤
⎣1,1⎦

⊃⍨ use that to pick from the list of unique elements
⎡0,1⎤
⎣0,0⎦

# J, 23 bytes

(0{~.\:1#.=)@,;.3~2 2&$ Try it online! J's u;.3 is pretty handy for this. It splits a matrix into rectangles. You just need to give the size of the rectangles and the offset between rectangles. So for 3x3-tiles the input would be [[3 3],[3 3]]. That is handled by 2 2&$ (if we can take width and height of a tile as input, that would be ;.~ for -2 bytes). For each tile ;.3~ we flatten the tile , and sort \: the unique values ~. by their occurences 1#.= and take the first one 0{.

# Japt-h, 17 bytes

2Æ=yòV)ËËc ü ñÊÌÌ


Try it

2Æ=yòV)ËËc ü ñÊÌÌ     :Implicit input of 2D-array U and integer V
2Æ                    :Map the range [0,2)
=                   :Reassign to U
y                  :  Transpose
òV                :  Partition rows to length V
)               :End reassignment
Ë              :Map
Ë             :  Map
c            :    Flatten
ü          :    Group & sort by value
ñ        :    Sort by
Ê       :      Length
Ì      :    Last element
Ì     :    Last element
:Implicit output of last element in the range


# Jelly, 13 bytes

Zs€Zs€ẎF€ÆṃḢ€


Try it online!

## How it works

Zs€Zs€ẎF€ÆṃḢ€ - Main link. Takes M on the left and n on the right
Z             - Transpose M
s€           - Slice each row into n pieces
Z          - Transpose
s€        - Split each group of columns into n pieces
Ẏ       - Flatten into a list of n x n matrices
F€     - Flatten each matrix
ÆṃḢ€ - Get the first mode of each

• when the footer is longer than the 13 byte answer – Unrelated String Jun 16 at 11:32
• These are also 13 bytes, if you can think of anywhere to go with them – Unrelated String Jun 16 at 12:04

# Jelly, 12 bytes

sZ€FÆṃḢƊ⁹ÐƤ€


Try it online!

After several 13s, I found a 12. A dyadic link taking the grid as a list of lists of integers on the left side and the size of the split on the right.

## Explanation

s            | Split into sublists of the length specified by the right argument
Z€          | Transpose each
Ɗ⁹ÐƤ€ | For each sublist, do the following for each non-overlapping infix of the length specified by the original right argument:
F         | - Flatten
Æṃ       | - Mode


# R, 130124121116 111 bytes

-5 bytes and another 3 thanks to @Dominic

function(M,n,k=dim(M))array(Map(function(x)el(names(sort(-table(x))):0),split(M,t(a<-(row(M)-1)%/%n)*k+a)),k/n)


Try it online!

Longer approach than @Dominic's, but I thought it's worth a try.

Builds matrix mask t(a<-(row(M)-1)%/%n)*dim(M)+a used then in split, for example for matrix $$\6\times6\$$ and $$\n=2\$$:

     [,1] [,2] [,3] [,4] [,5] [,6]
[1,]    0    0    6    6   12   12
[2,]    0    0    6    6   12   12
[3,]    1    1    7    7   13   13
[4,]    1    1    7    7   13   13
[5,]    2    2    8    8   14   14
[6,]    2    2    8    8   14   14

• This may be a bit longer, but I'm glad you posted it: I tried for ages to get a split approach to work, without success. This is very neat. – Dominic van Essen Jun 17 at 9:01
• 116 bytes with a bit of cleaning... – Dominic van Essen Jun 17 at 11:05
• @DominicvanEssen, thanks, I always forget about Map... – pajonk Jun 17 at 11:23
• ...and another -3... – Dominic van Essen Jun 17 at 12:09
• @DominicvanEssen, that's nice golf for the mask matrix, thanks! I managed to shave off another two by replacing nrow with dim and further optimisation. – pajonk Jun 17 at 19:46

# K (ngn/k), 29 28 bytes

-1 byte from @Traws

{(*>#'=,/)''2(+(0N;y)#/:)/x}


Try it online!

Based off of @Shaggy's Japt answer. Takes the input matrix as x and the chunk size as y.

• 2(...)/x set up a do-reduce, seeded with x and run twice
• (+(0N;y)#/:) slice each row into y-length chunks, then transpose them
• (...)'' run the code in (...) on each chunk in the transformed matrix
• (*>#'=,/) group the flattened chunk contents, counting the number of times each distinct number appears, then sort descending and return the first value (i.e. the mode)
• I guess you could transpose after the slice, saving 1 byte – Traws Jun 28 at 20:30
• Thanks, nice catch! – coltim Jun 28 at 23:42

# JavaScript (ES6),  136  135 bytes

Expects (matrix)(chunk_size).

m=>n=>m.slice(-m.length/n).map((_,y,a)=>a.map((_,x)=>eval("for(o=K={},i=n*n;i--;)(o[v=m[y*n+i/n|0][x*n+i%n]]=-~o[v])<K?0:K=o[V=v];V")))


Try it online!

### Commented

This is a version without eval() for readability.

m => n =>                     // m[] = matrix; n = chunk size
m.slice(-m.length / n)        // get an array of m.length / n entries
.map((_, y, a) =>             // for each value at position y in this slice:
a.map((_, x) => {           //   for each value at position x in this slice:
for(                      //     chunk loop:
o =                     //       o is used to store all counts
K = {},                 //       K is used to store the highest count
i = n * n;              //       start with i = n * n
i--;                    //       stop when i = 0 / decrement it
) ( o[                    //
v = m[              //       v is the value in m[]
y * n + i / n | 0 //       at row y * n + floor(i / n)
][                  //       and column x * n + (i mod n)
x * n + i % n     //
]                   //
] = -~o[v]            //       increment o[v]
) < K ? 0               //       do nothing if it's less than K
: K = o[V = v];   //       otherwise update V to v and K to o[v]
return V                  //     implicit end of for(); return V
})                          //   end of inner map()
)                             // end of outer map()


# Python 2, 174 bytes

Quite long, very ugly, possibly the most comprehensions I've used in one statement. There is undoubtedly a better way to do this but I can't look at this thing anymore.

def f(m,n):l=len(m);r=range(0,l,n);b=l/n;print('%s '*b+'\n')*b%tuple(max(v,key=v.count)for v in[sum([x[k][j:j+n]for k in range(n)],[])for x in[m[i:i+n]for i in r]for j in r])


Try it online!

# Python 3.8 (pre-release), 96 bytes

Takes as input an integer matrix $$\ m \$$, and an integer $$\ n \$$ denoting the chunk size.

lambda m,n:[[max(x:=sum(j,()),key=x.count)for j in zip(*[zip(*i)]*n)]for i in zip(*[iter(m)]*n)]


Try it online!

Very messy use of the split into chunks golfing tip.

# Wolfram Language (Mathematica), 41 bytes

BlockMap[Commonest[Join@@#,1]&,#2,{#,#}]&


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Input [n, m]. Returns a matrix of singleton lists.

# APL (Dyalog Extended), 37 (SBCS)

Anonymous tacit infix function taking chunk count as right argument and the input matrix as right argument.

((∪⊃⍨∘⊃∘⍒⊢∘≢⌸)∘,⍤2)1 3 2 4⍉⊣⍴⍨4⍴⊢,≢⍛÷


Try it online!

{}dfn; ⍺ is matrix and ⍵ is chunk size:
⎡0,1,0,1⎤
⎢0,0,1,1⎥
⎢0,0,0,0⎥
⎣0,0,1,1⎦
and 2

≢⍛÷ the matrix size divided by the chunk size
2

⊢, prepend the matrix size
[2,2]

4⍴ cyclically reshape to size 4
[2,2,2,2]

⊣⍴⍨ use that to reshape the matrix
⎡ ⎡0,1⎤ ⎡0,0⎤ ⎤
⎢ ⎣0,1⎦,⎣1,1⎦ ⎥
⎢ ⎡0,0⎤ ⎡0,0⎤ ⎥
⎣ ⎣0,0⎦,⎣1,1⎦ ⎦

1 3 2 4⍉ switch the middle two axes
⎡ ⎡0,1⎤ ⎡0,1⎤ ⎤
⎢ ⎣0,0⎦,⎣1,1⎦ ⎥
⎢ ⎡0,0⎤ ⎡0,0⎤ ⎥
⎣ ⎣0,0⎦,⎣1,1⎦ ⎦

()∘,⍤2 on each 2D leaf, ravel (flatten) it and then apply the following tacit prefix function:
⎡ [0,1,0,0],[0,1,1,1] ⎤
⎣ [0,0,0,0],[0,0,1,1] ⎦

⊢∘≢⌸ for each unique element, count the indices it occurs at
⎡ [3,1],[1,3] ⎤
⎣ [4] ,[2,2] ⎦

∪… with the unique elements…
⎡ [0,1],[0,1] ⎤
⎣ [0] ,[0,1] ⎦

∘⊃∘⍒ get the index of the largest count (lit. first element of the permutation vector that would sort the counts descending), then…
⎡1,2⎤
⎣1,1⎦

⊃⍨ use that to pick from the list of unique elements
⎡0,1⎤
⎣0,0⎦

# R, 113111 108 bytes

Edit: -2 bytes, and then -3 more bytes, thanks to pajonk

(or 105 bytes by outputting a matrix of text strings representing the integers)

function(m,n)outer(o<-0:(nrow(m)/n-1)*n,o,Vectorize(function(x,y)el(names(sort(-table(m[x+1:n,y+1:n]))):0)))


Try it online!

• -2 with el(.:0) trick converting to integer. – pajonk Jun 16 at 19:51
• @pajonk - Thanks! – Dominic van Essen Jun 16 at 20:37
• Another -3 - we don't need to select the first element from sort, as : will do that for us (with a warning). – pajonk Jun 17 at 10:19
• @pajonk - Thanks again, although I really should've noticed that myself... – Dominic van Essen Jun 17 at 11:01

# JavaScript (Node.js), 159 bytes

n=>k=>n.flatMap((e,i)=>i%k?[]:e.flatMap((h,j)=>j%k?[]:(M=n.slice(i,i+k).map(K=>K.slice(j,j+k)).flat()).sort((a,b)=>(X=Y=>M.map(Z=>z+=Z==Y,z=0)|z)(b)-X(a))[0]))


Try it online!

Golfing languages which have built-ins for occurrence count or chunks have concise programs. Mine is 159 bytes long.

# Charcoal, 54 bytes

Ｆ⪪Ｅθ⪪ιηη«≔⟦⟧ζＦＬ§ι⁰«≔⟦⟧εＦι≔⁺ε§λκε≔Ｅε№ελδ⊞ζ§ε⌕δ⌈δ»⊞υζ»Ｉυ


Try it online! Link is to verbose version of code. Explanation:

Ｆ⪪Ｅθ⪪ιηη«


Split each column into chunks of size n, then split the rows into chunks of size n and loop over the chunks.

≔⟦⟧ζ


Start collecting the results for this chunk of rows.

ＦＬ§ι⁰«


Loop over the number of chunks of columns.

≔⟦⟧εＦι≔⁺ε§λκε


Collect all of the values in this chunk of matrix into a single array.

≔Ｅε№ελδ


Get the frequencies of all the values.

⊞ζ§ε⌕δ⌈δ


Collect the value with the greatest frequency (chooses the first such value in case of a tie).

»⊞υζ


Save the results for this chunk of rows.

»Ｉυ


Output all of the results using Charcoal's default array output format.