# Block-sorting rows and columns in a 2D array

Given a 2D array of integers, let's sort its rows and columns in blocks. This means that you only have to sort a given row or column, but applying the transformations needed for sorting it to every other row or column in the 2D array.

### Rules

• Input will be a 2D array of integers and a 1-indexed integer. This integer will represent the row to be sorted if the number is positive, or the column to be sorted if the number is negative (or the other way round you want). Example: Given a 4x3 (rows x columns) array you can sort the second column with a -2 argument or the third row with a 3 argument. This second argument will never be zero and its absolute value will never be greater than the corresponding dimension of the array.
• Output will be also a 2D array of integers with the needed transformations applied to sort the given row or column. Alternatively you can just write the array to STDOUT.
• The output array will have the specified row or column sorted in ascending order. Just note that when you need to swap two numbers in a row, the whole columns where the numbers lay will be swapped. And when you need to swap two numbers in a column, the whole rows where the numbers lay will be swapped.
• In the case in which the same number appears several times in the row/column to be sorted, there will be several solutions possible according to the way you swap the values, just do accordingly with the rest of rows/columns to be swapped.

## Examples

Positive indices for rows and negative indices for columns

[5  8  7  6                                  [1  3  2  4
1  3  2  4   order by -3 (3rd column)  -->   9  6  3  0
9  6  3  0]                                  5  8  7  6]

[5  8  7  6                                  [9  6  3  0
1  3  2  4   order by -4 (4th column)  -->   1  3  2  4
9  6  3  0]                                  5  8  7  6]

[5  8  7  6                                  [5  7  8  6
1  3  2  4     order by 2 (2nd row)  -->     1  2  3  4
9  6  3  0]                                  9  3  6  0]

[5  8  7  6                                  [6  7  8  5
1  3  2  4     order by 3 (3rd row)  -->     4  2  3  1
9  6  3  0]                                  0  3  6  9]

[1  2                                    [1  2     [3  2
3  2]   order by -2 (2nd column)  -->    3  2] or  1  2]  (both are valid)

[7  5  9  7                                  [5  7  7  9     [5  7  7  9
1  3  2  4     order by 1 (1st row)  -->     3  1  4  2  or  3  4  1  2
9  6  3  0]                                  6  9  0  3]     6  0  9  3]


This is , so may the shortest code for each language win!

• This comes from the sandbox. – Charlie Sep 12 '18 at 13:45
• Can we change the integer representation? negative for rows and positive for columns? – Luis felipe De jesus Munoz Sep 12 '18 at 14:22
• @LuisfelipeDejesusMunoz yes, that is stated in the question. – Charlie Sep 12 '18 at 14:23
• Can a row/column contain duplicated numbers? – Kevin Cruijssen Sep 12 '18 at 15:00
• @KevinCruijssen yes, see last examples and last point of the rules. – Charlie Sep 12 '18 at 15:01

# R, 55 bytes

function(x,n)if(n>0,x[,+x[n,]],x[+x[,-n],])
+=order


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Reassigns the + operator (actually a function in R) to the order function, which returns the indices of a vector from smallest to largest. Then it's just array manipulation.

# R, 55 bytes

f=function(m,i)"if"(i<0,t(f(t(m),-i)),m[,order(m[i,])])


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Alternative to ngm's answer; a recursive function which was inspired by DimChtz's answer

## Matlab, 7362 47 bytes

@(m,i){sortrows(m,-i) sortrows(m',i)'}{(i>0)+1}


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-11 bytes thanks to @Giuseppe.

-15 bytes thanks to @LuisMendo.

# Japt, 18 17 bytes

negative for rows and positive for columns

>0?VñgUÉ:ßUa Vy)y


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• This fails when U is negative - the previous 17 byte version works, though. – Shaggy Sep 12 '18 at 15:27
• @Shaggy My bad, I though it would work anyway, didnt check at all – Luis felipe De jesus Munoz Sep 12 '18 at 15:33
• Not a bad idea, though, passing a function as the first argument of ß that automatically gets applied to U. It could create issues with trying to pass literal strings, but post a suggestion to the GitHub repo anyway for further investigation. – Shaggy Sep 12 '18 at 15:35

# 05AB1E, 2524 14 bytes

diø}Σ¹Ä<è}¹diø


Whopping -10 bytes thanks to @Emigna.

Uses a positive integer-input to sort the rows, negative for columns.

Explanation:

di }      # If the (implicit) integer input is positive:
ø       #  Swap the rows and columns of the (implicit) matrix input
#   i.e. 3 and [[5,8,7,6],[1,3,2,4],[9,6,3,0]]
#    → [[5,1,9],[8,3,6],[7,2,3],[6,4,0]]
Σ    }    # Sort the rows of this matrix by:
¹Ä       #  Take the absolute value of the input
#   i.e. -3 → 3
<      #  Decreased by 1 to make it 0-indexed
#   i.e. 3 → 2
è     #  And index it into the current row
#   i.e. [5,8,7,6] and 2 → 7
#   i.e. [5,1,9] and 2 → 9
#  i.e. [[5,1,9],[8,3,6],[7,2,3],[6,4,0]] sorted by [9,6,3,0]
#   → [[6,4,0],[7,2,3],[8,3,6],[5,1,9]]
#  i.e. [[5,8,7,6],[1,3,2,4],[9,6,3,0]] sorted by [7,2,3]
#   → [[1,3,2,4],[9,6,3,0],[5,8,7,6]]
¹di       # And if the integer input was positive:
ø      #  Swap the rows and columns back again now that we've sorted them
#   i.e. 3 and [[6,4,0],[7,2,3],[8,3,6],[5,1,9]]
#    → [[6,7,8,5],[4,2,3,1],[0,3,6,9]]
# (And implicitly output the now sorted matrix)

• I got diø}Σ¹Ä<è]¹diø which is a subset of yours, so I'm not posting a separate answer. – Emigna Sep 12 '18 at 19:36
• @Emigna Dang, you make it look so easy.. Now that I see it I can't believe I hadn't thought about that myself, but it's ingenious at the same time.. Thanks! A whopping 10 bytes saved thanks to you. – Kevin Cruijssen Sep 12 '18 at 20:32

# JavaScript (ES6), 90 bytes

t=m=>m.map((_,x)=>m.map(r=>r[x]))
f=(m,k)=>k<0?m.sort((a,b)=>a[~k]-b[~k]):t(f(t(m),-k))


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### How?

JS has no native transposition method, so we need to define one:

t = m =>              // given a matrix m[]
m.map((_, x) =>  // for each column at position x in m[]:
m.map(r =>        //   for each row r in m[]:
r[x]            //     map this cell to r[x]
)                 //   end of map() over rows
)                   // end of map() over columns


Main function:

f = (m, k) =>         // given a matrix m[] and an integer k
k < 0 ?             // if k is negative:
m.sort((a, b) =>  //   given a pair (a, b) of matrix rows, sort them:
a[~k] - b[~k]   //     by comparing a[-k - 1] with b[-k - 1]
)                 //   end of sort
:                   // else:
t(f(t(m), -k))    //   transpose m, call f() with -k and transpose the result


Example with $k=2$:

$$M=\pmatrix{5&8&7&6\\1&3&2&4\\9&6&3&0}\rightarrow t(M)=\pmatrix{5&1&9\\8&3&6\\7&2&3\\6&4&0}\rightarrow f(t(M),-2)=\pmatrix{5&\mathbf{\color{red}1}&9\\7&\mathbf{\color{red}2}&3\\8&\mathbf{\color{red}3}&6\\6&\mathbf{\color{red}4}&0}\\f(M,2)=t(f(t(M),-2))=\pmatrix{5&7&8&6\\\mathbf{\color{red}1}&\mathbf{\color{red}2}&\mathbf{\color{red}3}&\mathbf{\color{red}4}\\9&3&6&0}$$

# MATL, 17 bytes

y0>XH?!]w|2$XSH?!  Try it online! ### Explanation y % Implicit inputs: number n, matrix M. Duplicate from below: pushes n, M, n 0> % Greater than 0? XH % Copy into clipboard H ? % If true ! % Transpose matrix. This way, when we sort the rows it will correspond % to sorting the columns of the original M ] % End w % Swap: moves n to top | % Absolute value 2$XS    % Two-input sortrows function: sorts rows by specified column
H       % Push contents from clipboard H
?       % If true
!     %   Transpose again, to convert rows back to columns
% Implicit end
% Implicit display


# APL (Dyalog Classic), 23 bytes

{⍺<0:⍉(-⍺)∇⍉⍵⋄⍵[;⍋⍺⌷⍵]}


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# Python 2, 71 70 bytes

f=lambda m,n:n<0and sorted(m,key=lambda l:l[~n])or zip(*f(zip(*m),-n))


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If n is negative, the rows are sorted based on column n.

Otherwise the matrix is transposed, sorted the same way, and transposed back again.

# Jelly, 12 bytes

ZṠ}¡
çị@ÞA}ç


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# C# (.NET Core), 186 bytes

(x,y)=>{Func<int[][],int[][]>shift=a=> a.Select((r,i)=>a.Select(c=>c[i]).ToArray()).ToArray();return y>0?shift(shift(x).OrderBy(e=>e[y-1]).ToArray()):x.OrderBy(e=>e[-y-1]).ToArray();}


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Ungolfed:

    private static int[][] Blocksort0a(int[][] array, int sortingInstruction)
{
Func<int[][], int[][]> shift = a => a.Select((r, i) => a.Select(c => c[i]).ToArray()).ToArray();

sortingInstruction++;

array = sortingInstruction < 0 ?
shift(shift(array).OrderBy(e => e[-sortingInstruction]).ToArray())
:
array.OrderBy(e => e[sortingInstruction]).ToArray();

return null;
}


The shift function we'll use twice, so a function variable will save space. The function iterates through the horizontal dimension of the array on index, and adds every item on that index in of each horizontal array to a new output array (horizontally) - much the same as in Arnoud's JS solution.

Now the ordering is simple, order horizontal array by number-at-index (argument -1), optionally shifting the array before and after sorting.

Seen how the question talks about arrays specifically, we convert to array a few times (very, very wasteful). Feeling a bit silly to use such a verbose language in code golf hehe.

# C# (.NET Core), 142/139 138/135 bytes (and yet another -1 by Kevin)

(a,s)=>s<0?a.OrderBy(e=>e[~s]).ToArray():a.Select(f=>a[s-1].Select((v,j)=>new{v,j}).OrderBy(e=>e.v).Select(e=>f[e.j]).ToArray()).ToArray()


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Ungolfed:

    private static int[][] Blocksort0b(int[][] array, int sortingInstruction)
{
if (sortingInstruction < 0) { return array.OrderBy(e => e[-sortingInstruction - 1]).ToArray(); }
var rowIndices = array[sortingInstruction - 1].Select((value, index) => (value, index)).OrderBy(e => e.value);
var newRow = new int[array.Length];
for (var i = 0; i < array.Length; i++)
{
int horizontalIndexer = 0;
foreach (var e in rowIndices)
{
newRow[horizontalIndexer++] = array[i][e.index];
}
array[i] = newRow.ToArray();
}
return array;
}


New all-inline approach; negative answer still orders arrays by element-at-index. Otherwise, a collection of value-index-pair is created of the array-at-index and sorted by value. This effectively creates a collection of indices in order of having-to-be-added. Then for each array, the elements in the predetermined positions are selected. Quite some trimming of code and ugly, ugly, ugly **silently sobs** reuse of input parameters is involved, and there you go ... 142 bytes.

Again, the arrays argument is strictly enforced, adding quite some overhead for .ToArray() calls.

135 bytes claim, eh?! C# 7.2 inferred value-tuples would trim an additional three bytes, but tio.run doesn't allow. Therefor, this is the answer i decided to post for easy verification.

• Nice answer. There are a few small things to golf. (a,s)=> can be a currying a=>s=>. (s<0)? doesn't need the parenthesis, and -s-1 can be ~s. Try it online: 137 bytes – Kevin Cruijssen Sep 12 '18 at 20:55
• Sweet! I never would've through of letting the function return yet another function to save a character, i am pleasantly surprised. Thanks! Also a strong case of blatantly overlooking the not operator and parenthesis. I updated the not and parentheses, but will leave you all the honour for the function-returning-function. – Barodus Sep 12 '18 at 21:48

# Java (OpenJDK 8), 326 bytes

(a,b)->{int l=a.length,w=a.length,k,m,t,i;if(b>0){for(i=0;i<w;i++){for(k=1;k<(w-i);k++){if(a[b-1][k-1]>a[b-1][k]){for(m=0;m<l;m++){t=a[m][k];a[m][k]=a[m][k-1];a[m][k-1]=t;}}}}}else{b*=-1;for(i=0;i<l;i++){for(k=1;k<(l-i);k++){if(a[k-1][b-1]>a[k][b-1]){for(m=0;m<w;m++){t=a[k][m];a[k][m]=a[k-1][m];a[k-1][m]=t;}}}}}return a;}


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Well guys, this question was very frustrating for me, and I posted my answer KNOWING I was forgetting something, luckily we have legends like Kevin Cruijssen out here to help us out :)

# Java (OpenJDK 8), 281 bytes

a->b->{int l=a.length,w=a.length,k,m,t,i;if(b>0)for(i=0;i<w;i++)for(k=0;++k<w-i;)for(m=0;a[b-1][k-1]>a[b-1][k]&m<l;a[m][k]=a[m][k-1],a[m++][k-1]=t)t=a[m][k];else for(b*=-1,i=0;i<l;i++)for(k=0;++k<l-i;)for(m=0;a[k-1][b-1]>a[k][b-1]&m<w;a[k][m]=a[k-1][m],a[k-1][m++]=t)t=a[k][m];}


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• I haven't looked at the actual algorithm yet, but you can save 35 bytes by removing all the brackets and putting everything inside the loops (including the inner if-statement). Try it online: 291 byte EDIT: Here with space indentations so you can more clearly see the changes I did. – Kevin Cruijssen Sep 12 '18 at 20:44
• @KevinCruijssen I knew I was missing something – X1M4L Sep 12 '18 at 20:49
• In addition, you can make it a currying input a->b-> instead of (a,b)-> and remove the return-statement, since you are modifying the input-array. 281 bytes Still a nice answer, though. +1 from me. I did the challenge in 05AB1E, but wouldn't even have tried it in Java this time. ;) – Kevin Cruijssen Sep 12 '18 at 20:50
• 270 bytes – ceilingcat Nov 18 '19 at 9:42

# Clean, 95 bytes

import StdEnv,Data.List,Data.Func
$n#f=if(n>0)transpose id =f o sortBy(on(<)\u=u!!(abs n-1))o f  Try it online! # Kotlin, 192 bytes {m:Array<Array<Int>>,s:Int->if(s<0){m.sortBy{it[-s-1]}}else{val a=Array(m.size){c->Array(m.size){m[it][c]}} a.sortBy{it[s-1]} (0..m.size-1).map{r->(0..m.size-1).map{m[r][it]=a[it][r]}}}}  Try it online! # Ruby, 69 bytes ->a,n{f=->x{[0,x.transpose,x][n<=>0]};f[f[a].sort_by{|x|x[n.abs-1]}]}  Try it online! # Red, 190 185 bytes func[b n][t: func[a][c: length? a/1 a: to[]form a d: copy[]loop c[append/only d extract a c take a]d]d: does[if n > 0[b: t b]]d m: absolute n sort/compare b func[x y][x/(m) < y/(m)]d b]  Try it online! ## Explanation: f: func [ b n ] [ t: func [ a ] [ ; helper transpose function c: length? a/1 ; c is the length of the rows a: to-block form a ; flatten the list d: copy [] ; an empty block (list) loop c [ ; do as many times as the number of columns append/only d extract a c ; extract each c-th element (an entire column) ; and append it as a sublist to d take a ; drop the first element ] d ; return the transposed block (list of lists) ] d: does [ if n > 0 [ b: t b ] ] ; a helper function (parameterless) to transpose ; the array if positive n d ; call the function m: absolute n ; absolute n sort/compare b func[ x y ] [ x/(m) < y/(m) ]; sort the array according to the chosen column d ; transpose if positive n b ; return the array ]  My actual solution is 175 bytes long, but it doesn't work in TIO. Here it is, working normalyl in the Red console: ## Red, 175 bytes func[b n][d: does[if n > 0[c: length? b/1 a: to-block form b t: copy[]loop c[append/only t extract a c take a]b: t]]d m: absolute n sort/compare b func[x y][x/(m) < y/(m)]d b]  # VBA (Excel), 205 bytes Yay! 2nd longest byte count! I didn't completely lose :D Golfed: Sub d(a) With ActiveSheet.Sort .SortFields.Clear .SortFields.Add Key:=IIf(a<0,ActiveSheet.Columns(Abs(a)),ActiveSheet.Rows(Abs(a))) .SetRange ActiveSheet.UsedRange .Orientation=IIf(a<0,1,2) .Apply End With End Sub  This sorts all the data on the open (active) worksheet using UsedRange... which can be buggy, but should only contain cells that have been edited. UnGolfed: Sub d(a) 'Clear any Sort preferences that already exists ActiveSheet.Sort.SortFields.Clear 'Use the column if A is negative, the row if A is positive ActiveSheet.Sort.SortFields.Add Key:=IIf(a < 0, ActiveSheet.Columns(Abs(a)), ActiveSheet.Rows(Abs(a))) 'Set the area to sort ActiveSheet.Sort.SetRange ActiveSheet.UsedRange 'Orient sideways if sorting by row, vertical if by column ActiveSheet.Sort.Orientation = IIf(a < 0, xlTopToBottom, xlLeftToRight) 'Actually sort it now ActiveSheet.Sort.Apply End Sub  • If you assume that the activesheet is sheet1, then you can get this down to 169 bytes as Sub d(a) With Sheet1.Sort .SortFields.Clear .SortFields.Add IIf(a<0,Columns(Abs(a)),Rows(Abs(a))) .SetRange Sheet1.UsedRange .Orientation=(a<0)+2 .Apply End With End Sub – Taylor Scott Mar 7 '19 at 14:37 • Also, I think that you can safely assume that there are no .SortFields Defined so you can remove the .Sortfields.Clear line as well. – Taylor Scott Mar 7 '19 at 14:40 # Perl 6, 43 bytes {($!=$_>0??&[Z]!!*[])o*.sort(*[.abs-1])o$!}


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Curried function.

### Explanation

{                                         } # Block returning function composed of
o$! # 1. Apply$! (transpose or not)
o*.sort(*[.abs-1])     # 2. Sort rows by column abs(i)-1
$_>0??&[Z] # 3. If i > 0 transpose matrix !!*[] # Else identity function ($!=               )                       #    Store in \$!


# Physica, 45 bytes

Very similar to Arnauld's JS answer.

F=>n;m:n<0&&Sort[->u:u{~n};m]||Zip@F#Zip@m#-n


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### How it works?

A more elaborate and visual explanation can be found in the linked answer.

F=>n;m:           // Create a function F that takes two arguments, n and m.
n<0&&      // If n < 0 (i.e. is negative)
Sort[->u{~n};m]   // Sort the rows u of m by the result of the function u[~n].
// In short, sort by indexing from the end with n.
||    F#Zip@m#-n  // Else, apply F to Zip[m] and -n. Uses a new feature, binding.
Zip@            // And transpose the result.


# J, 32 bytes

f=.[/:({"1~<:)
g=.(f&.|:|)f@.(0<])


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Note: The g=. of the main verb doesn't count.

# J, 32 bytes

4 :'y(]/:{"1)&.(|:^:(x<0))~<:|x'


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## Clojure, 91 bytes

(fn f[A i](if(< i 0)(sort-by #(nth %(- -1 i))A)(apply map list(f(apply map list A)(- i)))))


Argh, apply map list` * 2.