# Rotating a 2D Matrix

Let's say I have the following (2D) matrix:

[[1,  2,  3,  4 ],
[5,  6,  7,  8 ],
[9,  10, 11, 12],
[13, 14, 15, 16]]


Rotate the matrix counterclockwise R times (not in 90 degree increments, just by 1 number each time),

1  2  3  4             2 3   4  8         3   4   8  12
5  6  7  8    -->      1 7  11 12   -->   2  11  10  16
9  10 11 12            5 6  10 16         1   7   6  15
13 14 15 16            9 13 14 15         5   9  13  14


Completed example:

Input:

2
[[1,  2,  3,  4 ],
[5,  6,  7,  8 ],
[9,  10, 11, 12],
[13, 14, 15, 16]]


Output:

[[3,  4,  8, 12],
[2, 11, 10, 16],
[1,  7,  6, 15],
[5,  9, 13, 14]]


(weird spaces are to align the numbers in nice columns)

The outer "ring" of the matrix rotates 2 counterclockwise, and the inner right rotates 2 also. In this matrix, there are only two rings.

An example with 1 "ring":

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


Should output:

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


Your challenge is to take in a matrix and an integer R, and output the translated version after R rotations.

Rotation of a 4x5 matrix is represented by the following figure: Constraints:

• 2 ≤ M, N ≤ 100, where M and N are the dimensions of the matrix. It is guaranteed that the minimum of M and N will be even.
• 1 ≤ R ≤ 80, where r is number of rotations.
• The matrix will only ever contain positive integers.
• Values are not always distinct.
• The input should always be as a 2D array (if you can't take runtime input as a 2D array, then you just have to find another way to get input).

Another test case, with non-distinct values:

1
[[1, 1],
[2, 2],
[3, 3]]


Outputs:

[[1, 2],
[1, 3],
[2, 3]]


This is , so the shortest answer wins!

• Related Mar 3, 2017 at 19:36
• Related. Mar 3, 2017 at 20:17
• Related. Mar 4, 2017 at 15:18
• @ceasedtoturncounterclockwis Your name is very ironic for this challenge... Mar 5, 2017 at 2:48
• [[3, 4, 8, 12], [2, 11, 10, 16], [1, 7, 6, 16], [5, 9, 13, 14]] the 16 is suddenly duplicated I guess it should be: [[3, 4, 8, 12], [2, 11, 10, 16], [1, 7, 6, 15], [5, 9, 13, 14]]? Mar 10, 2017 at 14:56

# Jelly, 393836 35 bytes

ḢṚ;Ḣ€;Ṫ;Ṫ€Ṛ$,-ṙ\;"ß¹¡ FJ©ṁ¹Çy®ịFṁµ¡  Try it online! # Octave, 210 bytes function M=F(M,R);f=@(z)[-z/2:-1 !eye(!!mod(z,2)) 1:z/2];t=angle(f([x y]=size(M))'+f(y)*i);B=!!M;B(2:x-1,2:y-1)=0;d=bwdist(B,'ch');[~,I]=sortrows([d(:) t(:)]);for k=0:max(d(:));M(h)=shift(M(h=I(d(I)==k)),R);end  Try it on Octave Online! Ungolfed version: function M=F(M,R) [x y]=size(M); f=@(z)[-z/2:-1 !eye(!!mod(z,2)) 1:z/2]; t=angle(f(x)'+f(y)*i); B=!!M; B(2:x-1,2:y-1)=0; d=bwdist(B,'chessboard'); [~,I]=sortrows([d(:) t(:)]); for k=0:max(d(:)) M(h)=shift(M(h=I(d(I)==k)),R); end end R=2; M=randi(10,4,7) F(M,R)  Explanation: f=@(z)[-z/2:-1 !eye(!!mod(z,2)) 1:z/2];  A function that gets a number and generates a range that is ordered and centered for input 4 (even) generates -2 -1 1 2 for input 5(odd) generates -2.5 -1.5 0 1 2  only it should be ordered and centered f(x)'+f(y)*i  a complex matrix generated from ranges (-2,-2.5) (-2,-1.5) (-2,0) (-2,1) (-2,2) (-1,-2.5) (-1,-1.5) (-1,0) (-1,1) (-1,2) (1,-2.5) (1,-1.5) (1,0) (1,1) (1,2) (2,-2.5) (2,-1.5) (2,0) (2,1) (2,2) t=angle(f(x)'+f(y)*i);  Convert rectangular to polar coordinates and return angles so for each ring angles are sorted counteclockwise -2.25 -2.50 3.14 2.68 2.36 -1.95 -2.16 3.14 2.36 2.03 -1.19 -0.98 0.00 0.79 1.11 -0.90 -0.64 0.00 0.46 0.79 B=!!M; B(2:x-1,2:y-1)=0;  The following matrix generated 1 1 1 1 1 1 0 0 0 1 1 0 0 0 1 1 1 1 1 1 d=bwdist(B,'chessboard');  Computes the distance transform of B using chessboard distance to generate ring indices 0 0 0 0 0 0 1 1 1 0 0 1 1 1 0 0 0 0 0 0  for a 6 * 7 matrix we will have the following matrix 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 1 2 2 2 1 0 0 1 2 2 2 1 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 [~,I]=sortrows([d(:) t(:)]);  lexicographic sort first based on ring index and then by order of angle(indices of sorted elements returned)  for k=0:max(d(:)) M(h)=shift(M(h=I(d(I)==k)),R); end  and finally circular shift each ring. # Python 3, 292 288 bytes _=eval a=input().split() b,a=int(a),_("".join(a[1:]))[::-1] c=len(a) d=len(a) e=range f="int((i>=j and i+j<c-1)|2*(i>=c/2and i+d>j+c)|3*(i<c/2and i+j<d))" l=[-1,1,0,0],[0,0,1,-1] g=lambda x:[[x[i+l[_(f)]][j+l[_(f)]]for j in e(d)]for i in e(c)] print(_("g("*b+"a"+")"*b)[::-1])  Takes input with newlines removed, but leaving a space after the number of increments to rotate it by. ## Explanation: Instead of modeling the matrix as a series of concentric rings per the OP's suggestion, one can instead divide it into four regions where the elements travel either up, down, right, or left during a single rotation. This is the purpose of the long eval-ed string f: to determine which region each i,j combination falls into. Then, the result of that is looked up twice in l, giving the element that must rotate into position i,j in the next step. The function g that does all of this and forms the new matrix after a single step is then called repeatedly by evaling a generated string containing the representation of a nested function call. When I made this originally, I accidentally caused the matrix to rotate clockwise instead of counterclockwise. Rather than doing a proper fix, I added two strategically placed copies of [::-1] to reverse the matrix before and after the rotation. These could probably be golfed off to ~280 276 bytes, but I'm too lazy to do that. Also, this is a quick untested port from a slightly longer Python 2 program, so forgive me if it doesn't work quite right. Here's the Python 2 code, anyways: _=eval a=raw_input().split() b,a=int(a),_("".join(a[1:]))[::-1] c=len(a) d=len(a) e=xrange f="int((i>=j and i+j<c-1)|2*(i>=c/2and i+d>j+c)|3*(i<c/2and i+j<d))" l=[-1,1,0,0],[0,0,1,-1] g=lambda x:[[x[i+l[_(f)]][j+l[_(f)]]for j in e(d)]for i in e(c)] print _("g("*b+"a"+")"*b)[::-1]  EDIT: Golfed off 4 bytes by replacing or with | twice. and can't be helped, unfortunately. • Welcome to PPCG! Nice first post! Mar 10, 2017 at 3:27 • Funny story actually — in my high school marching band today we learned a formation where everyone moves in concentric rectangular "rings" similar to this question, and I immediately thought of this answer. Aug 9, 2017 at 21:16 # K (ngn/k), 7876 60 bytes -16 bytes from using @ngn's version {(,()){(,y),+|x}/|,/{1_{1_y,*x}':x,,*x}'0N 4#-1_*'(|+1_)\x}/  Try it online! • {...}/ use the "do" variant of / to run the function x times, seeded with y and returning the last result. (each iteration rotates each ring of the input matrix one position) • (|+1_)\x peel off the first row, rotating the remainder until there's nothing left, accumulating the results into a list • -1_*' take the first item of each (i.e. the "top-most" slice of the outer ring). drop the last item, as it's empty • 0N 4# reshape the flat list into groups of four items; each group represents one "ring" of the input matrix • {...}' for each ring... • x,,*x append a copy of the first ring slice • 1_{1_y,*x}': for each slice of the ring, append the first item of the current slice to the previous slice, dropping the first value of the result. (this has the effect of rotating the values in each ring one position) • (,()){...}/|,/ set up a /, seeded with an empty list and run over the flattened and reversed ring slices... • (,y),+|x where we prepend each ring slice to the rotated and transposed result so far # Perl, 330 328 bytes sub f{($r,$m)=@_;$h=@m=@$m;for$s(0..(($w=$#{$m})<--$h?$w:$h)/2-.5){@_=(@{$m[$s]}[@x=$s..($x=$w-$s)],(map$m[$_][$x],@y=1+$s..($y=$h-$s)-1),reverse(@{$m[$y]}[@x]),(map$m[$h-$_][$s],@y));push@_,shift for 1..$r;@{$m[$s]}[@x]=map shift,@x;$m[$_][$x]=shift for@y;@{$m[$y]}[@x]=reverse map shift,@x;$m[$h-$_][$s]=shift for@y}@$m=@m}


Ungolfed:

sub f {
my ($r,$m) = @_;

my @m = @$m; my$h = $#m; my$w = @{$m} - 1; my$c = (($w <$h ? $w :$h) + 1) / 2 - 1;

for my $s (0 ..$c) {
my $x =$w - $s; my$y = $h -$s;
my @x = $s ..$x;
my @y = $s + 1 ..$y - 1;

# One circle.
@_ = (@{$m[$s]}[@x],
(map { $m[$_][$x] } @y), reverse(@{$m[$y]}[@x]), (map {$m[$h -$_][$s] } @y)); # Circular shift. push(@_, shift(@_)) for 1 ..$r;

@{$m[$s]}[@x] = map { shift(@_) } @x;
$m[$_][$x] = shift(@_) for @y; @{$m[$y]}[@x] = reverse(map { shift(@_) } @x);$m[$h -$_][$s] = shift(@_) for @y; } @$m = @m;
}