How do you rotate a two dimensional array

Question

Inspired by Raymond Chen s post  say you have a 4x4 two dimensional array  write a function that rotates it 90 degrees  Raymond links to a solution in pseudo code  but I d like to see some real world stuff    1  2  3  4   5  6  7  8   9  0  1  2   3  4  5  6    Becomes    3  9  5  1   4  0  6  2   5  1  7  3   6  2  8  4    Update  Nick s answer is the most straightforward  but is there a way to do it better than n 2  What if the matrix was 10000x10000

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dagorym  Aw  man  I had been hanging onto this as a good  I m bored  what can I ponder  puzzle  I came up with my in-place transposition code  but got here to find yours pretty much identical to mine   ah  well  Here it is in Ruby   require  pp  n   10 a      n times   a  lt  lt   1  n  to a    pp a  0 upto n 2-1  do  i    i upto n-i-2  do  j      tmp               a i  j      a i  j            a n-j-1  i      a n-j-1  i        a n-i-1  n-j-1      a n-i-1  n-j-1    a j  n-i-1      a j  n-i-1        tmp   end end  pp a

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Whilst rotating the data in place might be necessary  perhaps to update the physically stored representation   it becomes simpler and possibly more performant to add a layer of indirection onto the array access  perhaps an interface   interface IReadableMatrix       int GetValue int x  int y       If your Matrix already implements this interface  then it can be rotated via a decorator class like this   class RotatedMatrix   IReadableMatrix       private readonly IReadableMatrix  baseMatrix       public RotatedMatrix IReadableMatrix baseMatrix                 baseMatrix   baseMatrix             int GetValue int x  int y                   transpose x and y dimensions         return  baseMatrix y  x             Rotating  90 -90 180 degrees  flipping horizontally vertically and scaling can all be achieved in this fashion as well   Performance would need to be measured in your specific scenario   However the O n 2  operation has now been replaced with an O 1  call   It s a virtual method call which is slower than direct array access  so it depends upon how frequently the rotated array is used after rotation   If it s used once  then this approach would definitely win   If it s rotated then used in a long-running system for days  then in-place rotation might perform better   It also depends whether you can accept the up-front cost   As with all performance issues  measure  measure  measure

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Here is a C  static generic method that does the work for you  Variables are well-named  so you can easily catch the idea of the algorythm   private static T    Rotate180  lt T gt   T    matrix        var height   matrix GetLength  0       var width   matrix GetLength  1       var answer   new T height  width        for  int y   0  y  lt  height   2  y                  int topY   y          int bottomY   height - 1 - y          for  int topX   0  topX  lt  width  topX                          var bottomX   width - topX - 1              answer topY  topX    matrix bottomY  bottomX               answer bottomY  bottomX    matrix topY  topX                        if  height   2    0          return answer       var centerY   height   2      for  int leftX   0  leftX  lt  Mathf CeilToInt width   2f   leftX                  var rightX   width - 1 - leftX          answer centerY  leftX    matrix centerY  rightX           answer centerY  rightX    matrix centerY  leftX              return answer

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From a linear point of view  consider the matrices       1 2 3        0 0 1 A   4 5 6    B   0 1 0     7 8 9        1 0 0   Now take A transpose       1 4 7 A    2 5 8      3 6 9   And consider the action of A  on B  or B on A   Respectively         7 4 1          3 6 9 A B   8 5 2    BA    2 5 8       9 6 3          1 4 7   This is expandable for any n x n matrix  And applying this concept quickly in code   void swapInSpace int   mat  int r1  int c1  int r2  int c2        mat r1  c1     mat r2  c2       mat r2  c2     mat r1  c1       mat r1  c1     mat r2  c2      void transpose int   mat  int size        for  int i   0  i  lt  size  i                  for  int j    i   1   j  lt  size  j                          swapInSpace mat  i  j  j  i                      void rotate int   mat  int size          Get transpose     transpose mat  size          Swap columns     for  int i   0  i  lt  size   2  i                  for  int j   0  j  lt  size  j                          swapInSpace mat  i  j  size -  i   1   j

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Time - O N   Space - O 1   public void rotate int     matrix        int n   matrix length      for  int i   0  i  lt  n   2  i              int last   n - 1 - i          for  int j   i  j  lt  last  j                  int top   matrix i  j               matrix i  j    matrix last - j  i               matrix last - j  i    matrix last  last - j               matrix last  last - j    matrix j  last               matrix j  last    top

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Here it is in Java   public static void rotateInPlace int     m        for int layer   0  layer  lt  m length 2  layer             int first   layer          int last   m length - 1 - first          for int i   first  i  lt  last  i                  int offset   i - first              int top   m first  i               m first  i    m last - offset  first               m last - offset  first    m last  last - offset               m last  last - offset    m i  last               m i  last    top

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transpose is a standard method of Ruby s Array class  thus     irb irb main  001 0 gt  m     1  2  3  4    5  6  7  8    9  0  1  2    3  4  5  6     gt    1  2  3  4    5  6  7  8    9  0  1  2    3  4  5  6    irb main  002 0 gt  m reverse transpose   gt    3  9  5  1    4  0  6  2    5  1  7  3    6  2  8  4     The implementation is an n 2 transposition function written in C  You can see it here  http   www ruby-doc org core-1 9 3 Array html method-i-transpose by choosing  click to toggle source  beside  transpose    I recall better than O n 2  solutions  but only for specially constructed matrices  such as sparse matrices

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This is simple C code to rotate an array 90degrees  Hope this helps     include  lt stdio h gt   void main    int arr 3  4         85  2  85   4                       85  6   7  85                       9  85  11  12     int arr1 4  3    int i   0  j   0   for i 0 i lt 4 i     int k   2   k    number of columns in the new array arr1 - 1  for j 0 j lt 3 j     arr1 i  j  arr k  i   k--       int l  m  for l 0 l lt 4 l     for m 0 m lt 3 m     printf   d    arr1 l  m      printf   n         end main

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Based on the plethora of other answers  I came up with this in C         lt param name  rotation  gt The number of rotations  if negative  the  lt see cref  Matrix TValue    gt  is rotated counterclockwise       otherwise  it s rotated clockwise   A single  positive  rotation is equivalent to 90   or -270    a single  negative  rotation is      equivalent to -90   or 270    Matrices may be rotated by 90    180    or 270   only  or multiples thereof   lt  param gt       lt returns gt  lt  returns gt  public Matrix lt TValue gt  Rotate int rotation        var result   default Matrix lt TValue gt           This normalizes the requested rotation  for instance  if 10 is specified  the rotation is actually just  -2 or  -180    but all        correspond to the same rotation       var d   rotation ToDouble     4d      d   d -  int d       var degree    d - 1d    4d         This gets the type of rotation to make  there are a total of four unique rotations possible  0    90    180    and 270           Each correspond to 0  1  2  and 3  respectively  or 0  -1  -2  and -3  if in the other direction   Since       1 is equivalent to -3 and so forth  we combine both cases into one       switch  degree                case -3          case  1              degree   3              break          case -2          case  2              degree   2              break          case -1          case  3              degree   1              break          case -4          case  0          case  4              degree   0              break            switch  degree                  The rotation is 0   -180           case 0          case 2              result   new TValue Rows  Columns               break            The rotation is  -90           case 1          case 3              result   new TValue Columns  Rows               break             for  uint i   0  i  lt  Columns    i                for  uint j   0  j  lt  Rows    j                        switch  degree                                  If rotation is 0                   case 0                      result  values j  i     values j  i                       break                    If rotation is -90                   case 1                        Transpose  then reverse each column OR reverse each row  then transpose                     result  values i  j     values j  Columns - i - 1                       break                    If rotation is  -180                   case 2                        Reverse each column  then reverse each row                     result  values  Rows - 1  - j   Columns - 1  - i     values j  i                       break                    If rotation is  90                   case 3                        Transpose  then reverse each row                     result  values i  j     values Rows - j - 1  i                       break                                    return result      Where  values corresponds to a private two-dimensional array defined by Matrix lt TValue gt   in the form of        result   new TValue Columns  Rows  is possible via implicit operator overload and converts the two-dimensional array to Matrix lt TValue gt   The two properties Columns and Rows are public properties that get the number of columns and rows of the current instance   public uint Columns        gt   uint  values 0  Length   public uint Rows        gt   uint  values Length    Assuming  of course  that you prefer to work with unsigned indices  -   All of this allows you to specify how many times it should be rotated and whether it should be rotated left  if less than zero  or right  if greater than zero   You can improve this to check for rotation in actual degrees  but then you d want to throw an exception if the value isn t a multiple of 90  With that input  you could change the method accordingly   public Matrix lt TValue gt  Rotate int rotation        var  rotation    double rotation   90d       if   rotation - Math Floor  rotation   gt  0                throw new NotSupportedException  A matrix may only be rotated by multiples of 90                rotation    int  rotation              Since a degree is more accurately expressed by double than int  but a matrix can only rotate in multiples of 90  it is far more intuitive to make the argument correspond to something else that can be accurately represented by the data structure used  int is perfect because it can tell you how many times to rotate it up to a certain unit  90  as well as the direction  double may very well be able to tell you that also  but it also includes values that aren t supported by this operation  which is inherently counter-intuitive

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For i   0 to X do        For j    0 to X do                graphic j  i     graphic2 X-i  j   X is the size of the array the graphic is in

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Javascript solution for NxN matrix with runtime O N 2  and memory O 1     function rotate90 matrix       var length   matrix length     for var row   0  row  lt   length   2   row           for var col   row  col  lt    length - 1 - row   col             var tmpVal   matrix row  col           for var i   0  i  lt  4  i               var rowSwap   col            var colSwap    length - 1  - row            var poppedVal   matrix rowSwap  colSwap             matrix rowSwap  colSwap    tmpVal            tmpVal   poppedVal            col   colSwap            row   rowSwap

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Python   rotated   list zip  original   -1      and counterclockwise   rotated ccw   list zip  original     -1    How this works   zip  original  will swap axes of 2d arrays by stacking corresponding items from lists into new lists   The   operator tells the function to distribute the contained lists into arguments    gt  gt  gt  list zip    1 2 3   4 5 6   7 8 9       1 4 7   2 5 8   3 6 9     The    -1  statement reverses array elements  please see Extended Slices or this question     gt  gt  gt    1 2 3   4 5 6   7 8 9     -1    7 8 9   4 5 6   1 2 3     Finally  combining the two will result in the rotation transformation   The change in placement of    -1  will reverse lists in different levels of the matrix

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JavaScript solution to rotate matrix by 90 degrees in place   function rotateBy90 m      var length   m length      for each layer of the matrix   for  var first   0  first  lt  length  gt  gt  1  first          var last   length - 1 - first      for  var i   first  i  lt  last  i            var top   m first  i     store top       m first  i    m last - i  first     top   left       m last - i  first    m last  last - i     left   bottom       m last  last - i    m i  last     bottom   right       m i  last    top    right   top             return m

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PHP Solution for clockwise  amp  counterclockwise   aMatrix   array      array  1  2  3        array  4  5  6        array  7  8  9           function CounterClockwise   aMatrix          iCount    count   aMatrix         aReturn   array        for   y   0   y  lt   iCount     y                 for   x   0   x  lt   iCount     x                          aReturn   iCount -  x - 1     y      aMatrix   y     x                        return  aReturn     function Clockwise   aMatrix          iCount    count   aMatrix         aReturn   array        for   y   0   y  lt   iCount     y                 for   x   0   x  lt   iCount     x                          aReturn   x     iCount -  y - 1      aMatrix   y     x                        return  aReturn     function printMatrix   aMatrix          iCount   count   aMatrix        for   x   0   x  lt   iCount     x                 for   y   0   y  lt   iCount     y                         echo  aMatrix   x     y                echo                        echo   n           printMatrix   aMatrix    echo   n    aNewMatrix   CounterClockwise   aMatrix    printMatrix   aNewMatrix    echo   n    aNewMatrix   Clockwise   aMatrix    printMatrix   aNewMatrix

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I was able to do this with a single loop  The time complexity seems like O K  where K is all items of the array   Here s how I did it in JavaScript   First off  we represent the n 2 matrix with a single array  Then  iterate through it like this          Rotates matrix 90 degrees clockwise     param arr  the source array     param n  the array side  array is square n 2      function rotate  arr  n      var rotated       indexes         for  var i   0  i  lt  arr length  i          if  i  lt  n        indexes i    i   n    n - 1      else       indexes i    indexes i - n  - 1      rotated indexes i     arr i        return rotated     Basically  we transform the source array indexes    0 1 2 3 4 5 6 7 8      2 5 8 1 4 7 0 3 6   Then  using this transformed indexes array  we place the actual values in the final rotated array   Here are some test cases     n 3 rotate     1  2  3    4  5  6    7  8  9   3      result   7  4  1   8  5  2   9  6  3      n 4 rotate     1   2   3   4    5   6   7   8    9   10  11  12    13  14  15  16   4      result   13   9   5   1   14  10   6   2   15  11   7   3   16  12   8   4      n 5 rotate     1   2   3   4   5    6   7   8   9   10    11  12  13  14  15    16  17  18  19  20    21  22  23  24  25   5      result   21  16  11   6   1    22  17  12   7   2    23  18  13   8   3    24  19  14   9   4    25  20  15  10   5

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Here is my attempt for matrix 90 deg rotation which is a 2 step solution in C  First transpose the matrix in place and then swap the cols    define ROWS        5  define COLS        5  void print matrix b int B   COLS   int rows  int cols         for  int i   0  i  lt   rows  i              for  int j   0  j  lt  cols  j                  printf   d    B i  j                      printf   n             void swap columns int B   COLS   int l  int r  int rows        int tmp      for  int i   0  i  lt   rows  i              tmp   B i  l           B i  l    B i  r           B i  r    tmp            void matrix 2d rotation int B   COLS   int rows  int cols        int tmp         Transpose the matrix first     for  int i   0  i  lt   rows  i              for  int j   i  j  lt  cols  j                  tmp   B i  j               B i  j    B j  i               B j  i    tmp                         Swap the first and last col and continue until        the middle      for  int i   0  i  lt   cols   2   i            swap columns B  i  cols - i  rows        int  tmain int argc   TCHAR  argv          int B ROWS  COLS                          1  2  3  4  5                           6  7  8  9  10                              11  12  13  14  15                              16  17  18  19  20                              21  22  23  24  25                                  matrix 2d rotation B  ROWS - 1  COLS - 1        print matrix b B  ROWS - 1  COLS -1       return 0

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The O 1  memory algorithm    rotate the outer-most data  then you can get below result    3  9  5  1   4  6  7  2   5  0  1  3   6  2  8  4     To do this rotation  we know       dest j  n-1-i    src i  j    Observe below           a 0 0  -  a 0 3          a 0 3  -  a 3 3          a 3 3  -  a 3 0          a 3 0  -  a 0 0   Therefore it s a circle  you can rotate N elements in one loop  Do this N-1 loop then you can rotate the outer-most elements    Now you can the inner is a same question for 2X2     Therefore we can conclude it like below   function rotate array  N        Rotate outer-most data     rotate a new array with N-2 or you can do the similar action following step1

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For Novice programmers  in plain C      Borland stuff       include lt iostream h gt   include lt conio h gt   int main         clrscr         int arr 10  10             2d array that holds input elements      int result 10  10         holds result      int m n                   rows and columns of arr         int x y                   rows and columns of result          int i j                   loop variables     int t                     temporary   holds data while conversion      cout lt  lt  Enter no  of rows and columns of array         cin gt  gt m gt  gt n      cout lt  lt   nEnter elements of array   n n       for i   0  i  lt  m  i                  for j   0  j lt n   j                        cin gt  gt arr i  j              input array elements from user                        rotating matrix by  90 degrees      x   n                          for non-square matrix     y   m             for i   0  i  lt  x  i           t   m-1                         to create required array bounds        for j   0  j  lt  y  j                       result i  j    arr t  i             t--                      print result     cout lt  lt   nRotated matrix is   n n      for i   0  i  lt  x  i                for j   0  j  lt  y  j                          cout lt  lt result i  j  lt  lt                      cout lt  lt   n            getch       return 0

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Here is a recursive PHP way    m   array                 m 0    array  a    b    c                 m 1    array  d    e    f                 m 2    array  g    h    i                 newMatrix   array                 function rotateMatrix  m   i   0   amp  newMatrix                                foreach   m as  chunk                         newChunk      chunk  i                                      newMatrix     array reverse  newChunk                    i                     if   i  lt  count  m                         rotateMatrix  m   i   newMatrix                                                rotateMatrix  m  0   newMatrix               echo   lt pre gt                var dump  newMatrix               echo   lt pre gt

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Here s my Ruby version  note the values aren t displayed the same  but it still rotates as described    def rotate matrix    result        4 times    x      result x           4 times    y        result x  y    matrix y  3 - x               result end  matrix      matrix 0     1 2 3 4  matrix 1     5 6 7 8  matrix 2     9 0 1 2  matrix 3     3 4 5 6   def print matrix matrix    4 times    y      4 times    x        print    matrix x  y               puts        end  print matrix matrix  puts    print matrix rotate matrix     The output   1 5 9 3  2 6 0 4  3 7 1 5  4 8 2 6   4 3 2 1  8 7 6 5  2 1 0 9  6 5 4 3

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include  lt iostream gt   include  lt iomanip gt   using namespace std  const int SIZE 3  void print int a   SIZE  int   void rotate int a   SIZE  int    void main         int a SIZE  SIZE    11 22 33   44 55 66   77 88 99        cout lt  lt  the array befor rotate n        print a SIZE       rotate  a SIZE       cout lt  lt  the array after rotate n       print a SIZE       cout lt  lt endl      void print int a   SIZE  int SIZE        int i j      for i 0 i lt SIZE i           for j 0 j lt SIZE j              cout lt  lt a i  j  lt  lt setw 4      void rotate int a   SIZE  int SIZE        int temp 3  3  i j      for i 0 i lt SIZE i           for j 0 j lt SIZE 2 5 j                        temp i  j   a i  j              a i  j   a j  SIZE-i-1               a j  SIZE-i-1   temp i  j

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Here it is in C   int    array   new int 4 4          1 2 3 4          5 6 7 8          9 0 1 2          3 4 5 6       int    rotated   RotateMatrix array  4    static int    RotateMatrix int    matrix  int n        int    ret   new int n  n        for  int i   0  i  lt  n    i            for  int j   0  j  lt  n    j                ret i  j    matrix n - j - 1  i                        return ret

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public static void rotateMatrix int    matrix                  C   to rotate an N N matrix in place         int n   matrix GetLength 0           int layers    n   2          int temp  temp2           for  int i   0  i  lt  layers  i       for a 5   5 matrix  layers will be 2  since at layer three there would be only one element   2 2   and we do not need to rotate it with itself                        int offset   0              while  offset  lt  n - 2   i - 1                                   top right  lt - top left                  temp   matrix i   offset  n - i - 1     top right value when offset is zero                 matrix i   offset  n - i - 1    matrix i  i   offset                         bottom right  lt - top right                  temp2   matrix n - i - 1  n - i - 1 - offset     bottom right value when offset is zero                 matrix n - i - 1  n - i - 1 - offset    temp                       bottom left  lt - bottom right                  temp   matrix n - i - 1 - offset  i                   matrix n - i - 1 - offset  i    temp2                       top left  lt - bottom left                  matrix i  i   offset    temp                    offset

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PHP    lt  php      a   array array 1 2 3 4  array 5 6 7 8  array 9 0 1 2  array 3 4 5 6     b   array      result  while count  a  gt 0         b count  a 0  -1      array shift  a 0        if  count  a 0    0                 array shift  a             From PHP5 6  Array transposition can be performed with a sleak array map   call   In other words  columns are converted to rows   Code   Demo    array          1  2  3  4        5  6  7  8        9  0  1  2        3  4  5  6      transposed   array map null      array      transposed          1  5  9  3        2  6  0  4        3  7  1  5        4  8  2  6

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PHP   array unshift  array  null    array   call user func array  array map    array     If you need to rotate rectangular two-dimension array on 90 degree  add the following line before or after  depending on the rotation direction you need  the code above    array   array reverse  array

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Based on the community wiki algorithm and this SO answer for transposing arrays  here is a Swift 4 version to rotate some 2D array 90 degrees counter-clockwise  This assumes matrix is a 2D array   func rotate matrix    Int    - gt    Int         let transposedPoints   transpose input  matrix      let rotatedPoints   transposedPoints map  Array  0 reversed          return rotatedPoints     fileprivate func transpose lt T gt  input    T    - gt    T         if input isEmpty   return   T           let count   input 0  count     var out     T   repeating   T     count  count      for outer in input           for  index  inner  in outer enumerated                 out index  append inner                       return out

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Implementation of dimple s  90 pseudocode  e g  transpose then reverse each row  in JavaScript   function rotate90 a        transpose from http   www codesuck com 2012 02 transpose-javascript-array-in-one-line html   a   Object keys a 0   map function  c    return a map function  r    return r c                row reverse   for  i in a       a i    a i  reverse          return a

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It is not possible to do it quicker than O n 2  for in place rotation  for the reason that if we want to rotate the matrix  we have to touch all the n 2 element at least once  no matter what algorithm you are implementing

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This solution doesn t care square or rectangle dimension  you can rotate 4x5 or 5x4 or even 4x4  it doesn t care the size as well  Note that this implementation creates a new array every time you call rotate90 method  it doesn t mutate the original array at all   public static void main String   args        int     a   new int                              1  2  3  4                           5  6  7  8                           9  0  1  2                           3  4  5  6                           7  8  9  0                             int     rotate180   rotate90 rotate90 a        print rotate180      static int     rotate90 int     a        int     ret   new int a 0  length  a length       for  int i   0  i  lt  a length  i              for  int j   0  j  lt  a i  length  j                  ret j  a length - i - 1    a i  j                       return ret     static void print int     array        for  int i   0  i  lt  array length  i              System out print               for  int j   0  j  lt  array i  length  j                  System out print array i  j                System out print                         System out println

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My C  example code for the great Algorithm sent by  dimple      Author  Dudi     http   www tutorialspoint com compile csharp online php PID 0Bw CjBb95KQMYm5qU3VjVGNuZFU     using System IO  using System   class Program       static void Main                 Console WriteLine  Rotating this matrix by 90  degree              int    values new int 3 3   1 2 3    4 5 6    7 8 9              int    values new int 4 4   101 102 103  104    105 106  107 108    109  110  111  112    113  114  115  116             print2dArray ref values           transpose2dArray ref values             print2dArray ref values           reverse2dArray ref values           Console WriteLine  Output             print2dArray ref values              static void print2dArray ref int    matrix           int  nLen   matrix GetLength 0           int  mLen   matrix GetLength 1               for int n 0  n lt nLen  n                 for int m 0  m lt mLen  m                     Console Write matrix n m     t                              Console WriteLine                              Console WriteLine               static void transpose2dArray ref int    matrix           int  nLen   matrix GetLength 0           int  mLen   matrix GetLength 1               for int n 0  n lt nLen  n                 for int m 0  m lt mLen  m                     if n gt m                       int tmp   matrix n m                       matrix n m    matrix m n                       matrix m n    tmp                                                       static void reverse2dArray ref int    matrix           int  nLen   matrix GetLength 0           int  mLen   matrix GetLength 1           for int n 0  n lt nLen  n                 for int m 0  m lt mLen 2  m                                     int tmp   matrix n m                   matrix n m    matrix n  mLen-1-m                   matrix n mLen-1-m    tmp                                      Rotating this matrix by 90  degree                                                                                                                                               1       2       3                                                                                                                                                                4       5       6                                                                                                                                                                7       8       9                                                                                                                                                                 Output                                                                                                                                                                           7       4       1                                                                                                                                                                8       5       2                                                                                                                                                                9       6       3

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here is my In Place implementation in C  void rotateRight int matrix   SIZE   int length         int layer   0       for  int layer   0  layer  lt  length   2    layer             int first   layer          int last   length - 1 - layer           for  int i   first  i  lt  last    i                 int topline   matrix first  i               int rightcol   matrix i  last               int bottomline   matrix last  length - layer - 1 - i               int leftcol   matrix length - layer - 1 - i  first                matrix first  i    leftcol              matrix i  last    topline              matrix last  length - layer - 1 - i    rightcol              matrix length - layer - 1 - i  first    bottomline

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Nick s answer would work for an NxM array too with only a small modification  as opposed to an NxN    string    orig   new string n  m   string    rot   new string m  n         for   int i 0  i  lt  n  i       for   int j 0  j  lt  m  j         rot j  n - i - 1    orig i  j     One way to think about this is that you have moved the center of the axis  0 0  from the top left corner to the top right corner   You re simply transposing from one to the other

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All the current solutions have O n 2  overhead as scratch space  this excludes those filthy OOP cheaters    Here s a solution with O 1  memory usage  rotating the matrix in-place 90 degress right  Screw extensibility  this sucker runs fast    include  lt algorithm gt   include  lt cstddef gt      Rotates an NxN matrix of type T 90 degrees to the right  template  lt typename T  size t N gt  void rotate matrix T   amp matrix  N  N         for size t i   0  i  lt  N    i          for size t j   0  j  lt    N-i     j              std  swap matrix i  j   matrix j  i        DISCLAIMER  I didn t actually test this  Let s play whack-a-bug

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Try My library AbacusUtil    Test public void test 42519   throws Exception       final IntMatrix matrix   IntMatrix range 0  16  reshape 4        N println          original                                matrix println           print out             0  1  2  3             4  5  6  7             8  9  10  11             12  13  14  15       N println          rotate 90                               matrix rotate90   println           print out             12  8  4  0             13  9  5  1             14  10  6  2             15  11  7  3       N println          rotate 180                              matrix rotate180   println           print out             15  14  13  12             11  10  9  8             7  6  5  4             3  2  1  0       N println          rotate 270                               matrix rotate270   println           print out             3  7  11  15             2  6  10  14             1  5  9  13             0  4  8  12       N println          transpose                                matrix transpose   println           print out             0  4  8  12             1  5  9  13             2  6  10  14             3  7  11  15       final IntMatrix bigMatrix   IntMatrix range 0  10000 0000  reshape 10000           It take about 2 seconds to rotate 10000 X 10000 matrix      Profiler run 1  2  3   sequential      - gt  bigMatrix rotate90    printResult            Want faster  Go parallel  1 second to rotate 10000 X 10000 matrix      final int     a   bigMatrix array        final int     c   new int a 0  length  a length       final int n   a length      final int threadNum   4       Profiler run 1  2  3   parallel      - gt            IntStream range 0  n  parallel threadNum  forEach i - gt                for  int j   0  j  lt  n  j                      c i  j    a n - j - 1  i                                    printResult

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There are a lot of answers already  and I found two claiming O 1  time complexity  The real O 1  algorithm is to leave the array storage untouched  and change how you index its elements  The goal here is that it does not consume additional memory  nor does it require additional time to iterate the data   Rotations of 90  -90 and 180 degrees are simple transformations which can be performed as long as you know how many rows and columns are in your 2D array  To rotate any vector by 90 degrees  swap the axes and negate the Y axis  For -90 degree  swap the axes and negate the X axis  For 180 degrees  negate both axes without swapping   Further transformations are possible  such as mirroring horizontally and or vertically by negating the axes independently   This can be done through e g  an accessor method  The examples below are JavaScript functions  but the concepts apply equally to all languages    x000D   x000D      Get an array element in column row order x000D   var getArray2d   function a  x  y    x000D     return a y  x   x000D      x000D   x000D     demo x000D   var arr     x000D      5  4  6   x000D      1  7  9   x000D      -2  11  0   x000D      8  21  -3   x000D      3  -1  2  x000D      x000D   x000D   var newarr       x000D   arr 0  forEach      gt  newarr push new Array arr length     x000D   x000D   for  var i   0  i  lt  newarr length  i      x000D     for  var j   0  j  lt  newarr 0  length  j      x000D       newarr i  j    getArray2d arr  i  j   x000D       x000D     x000D   console log newarr   x000D   x000D   x000D     x000D   x000D     Get an array element rotated 90 degrees clockwise x000D  function getArray2dCW a  x  y    x000D    var t   x  x000D    x   y  x000D    y   a length - t - 1  x000D    return a y  x   x000D    x000D   x000D    demo x000D  var arr     x000D     5  4  6   x000D     1  7  9   x000D     -2  11  0   x000D     8  21  -3   x000D     3  -1  2  x000D     x000D   x000D  var newarr       x000D  arr 0  forEach      gt  newarr push new Array arr length     x000D   x000D  for  var i   0  i  lt  newarr 0  length  i      x000D    for  var j   0  j  lt  newarr length  j      x000D      newarr j  i    getArray2dCW arr  i  j   x000D      x000D    x000D  console log newarr   x000D   x000D   x000D     x000D   x000D     Get an array element rotated 90 degrees counter-clockwise x000D  function getArray2dCCW a  x  y    x000D    var t   x  x000D    x   a 0  length - y - 1  x000D    y   t  x000D    return a y  x   x000D    x000D   x000D    demo x000D  var arr     x000D     5  4  6   x000D     1  7  9   x000D     -2  11  0   x000D     8  21  -3   x000D     3  -1  2  x000D     x000D   x000D  var newarr       x000D  arr 0  forEach      gt  newarr push new Array arr length     x000D   x000D  for  var i   0  i  lt  newarr 0  length  i      x000D    for  var j   0  j  lt  newarr length  j      x000D      newarr j  i    getArray2dCCW arr  i  j   x000D      x000D    x000D  console log newarr   x000D   x000D   x000D     x000D   x000D     Get an array element rotated 180 degrees x000D  function getArray2d180 a  x  y    x000D    x   a 0  length - x - 1  x000D    y   a length - y - 1  x000D    return a y  x   x000D    x000D   x000D    demo x000D  var arr     x000D     5  4  6   x000D     1  7  9   x000D     -2  11  0   x000D     8  21  -3   x000D     3  -1  2  x000D     x000D   x000D  var newarr       x000D  arr forEach      gt  newarr push new Array arr 0  length     x000D   x000D  for  var i   0  i  lt  newarr 0  length  i      x000D    for  var j   0  j  lt  newarr length  j      x000D      newarr j  i    getArray2d180 arr  i  j   x000D      x000D    x000D  console log newarr   x000D   x000D   x000D    This code assumes an array of nested arrays  where each inner array is a row   The method allows you to read  or write  elements  even in random order  as if the array has been rotated or transformed  Now just pick the right function to call  probably by reference  and away you go   The concept can be extended to apply transformations additively  and non-destructively  through the accessor methods  Including arbitrary angle rotations and scaling

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short normal 4  4      8 4 7 5   3 4 5 7   9 5 5 6   3 3 3 3     short rotated 4  4    for  int r   0  r  lt  4    r      for  int c   0  c  lt  4    c          rotated r  c    normal c  3-r           Simple C   method  tho there would be a big memory overhead in a big array

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A common method to rotate a 2D array clockwise or anticlockwise   clockwise rotate  first reverse up to down  then swap the symmetry 1 2 3     7 8 9     7 4 1 4 5 6    gt  4 5 6    gt  8 5 2 7 8 9     1 2 3     9 6 3      void rotate vector lt vector lt int gt   gt   amp matrix        reverse matrix begin    matrix end         for  int i   0  i  lt  matrix size      i            for  int j   i   1  j  lt  matrix i  size      j              swap matrix i  j   matrix j  i              anticlockwise rotate  first reverse left to right  then swap the symmetry 1 2 3     3 2 1     3 6 9 4 5 6    gt  6 5 4    gt  2 5 8 7 8 9     9 8 7     1 4 7      void anti rotate vector lt vector lt int gt   gt   amp matrix        for  auto vi   matrix  reverse vi begin    vi end         for  int i   0  i  lt  matrix size      i            for  int j   i   1  j  lt  matrix i  size      j              swap matrix i  j   matrix j  i

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I   d like to add a little more detail  In this answer  key concepts are repeated  the pace is slow and intentionally repetitive  The solution provided here is not the most syntactically compact  it is however  intended for those who wish to learn what matrix rotation is and the resulting implementation  Firstly  what is a matrix  For the purposes of this answer  a matrix is just a grid where the width and height are the same  Note  the width and height of a matrix can be different  but for simplicity  this tutorial considers only matrices with equal width and height  square matrices   And yes  matrices is the plural of matrix  Example matrices are  2  2  3  3 or 5  5  Or  more generally  N  N  A 2  2 matrix will have 4 squares because 2  2 4  A 5  5 matrix will have 25 squares because 5  5 25  Each square is called an element or entry  We   ll represent each element with a period     in the diagrams below  2  2 matrix          3  3 matrix                    4  4 matrix                                  So  what does it mean to rotate a matrix  Let   s take a 2  2 matrix and put some numbers in each element so the rotation can be observed  0 1 2 3  Rotating this by 90 degrees gives us  2 0 3 1  We literally turned the whole matrix once to the right just like turning the steering wheel of a car  It may help to think of    tipping    the matrix onto its right side  We want to write a function  in Python  that takes a matrix and rotates in once to the right  The function signature will be  def rotate matrix         Algorithm goes here   The matrix will be defined using a two-dimensional array  matrix          0 1        2 3     Therefore the first index position accesses the row  The second index position accesses the column  matrix row  column   We   ll define a utility function to print a matrix  def print matrix matrix       for row in matrix          print row  One method of rotating a matrix is to do it a layer at a time  But what is a layer   Think of an onion  Just like the layers of an onion  as each layer is removed  we move towards the center  Other analogies is a Matryoshka doll or a game of pass-the-parcel  The width and height of a matrix dictate the number of layers in that matrix   Let   s use different symbols for each layer  A 2  2 matrix has 1 layer          A 3  3 matrix has 2 layers         x          A 4  4 matrix has 2 layers           x x     x x            A 5  5 matrix has 3 layers             x x x     x O x     x x x              A 6  6 matrix has 3 layers               x x x x     x O O x     x O O x     x x x x                A 7  7 matrix has 4 layers                 x x x x x     x O O O x     x O - O x     x O O O x     x x x x x                  You may notice that incrementing the width and height of a matrix by one  does not always increase the number of layers  Taking the above matrices and tabulating the layers and dimensions  we see the number of layers increases once for every two increments of width and height   ----- --------    N  N   Layers    ----- --------    1  1        1     2  2        1     3  3        2     4  4        2     5  5        3     6  6        3     7  7        4    ----- --------   However  not all layers need rotating  A 1  1 matrix is the same before and after rotation  The central 1  1 layer is always the same before and after rotation no matter how large the overall matrix   ----- -------- ------------------    N  N   Layers   Rotatable Layers    ----- -------- ------------------    1  1        1                  0     2  2        1                  1     3  3        2                  1     4  4        2                  2     5  5        3                  2     6  6        3                  3     7  7        4                  3    ----- -------- ------------------   Given N  N matrix  how can we programmatically determine the number of layers we need to rotate  If we divide the width or height by two and ignore the remainder we get the following results   ----- -------- ------------------ ---------    N  N   Layers   Rotatable Layers     N 2      ----- -------- ------------------ ---------    1  1        1                  0   1 2   0     2  2        1                  1   2 2   1     3  3        2                  1   3 2   1     4  4        2                  2   4 2   2     5  5        3                  2   5 2   2     6  6        3                  3   6 2   3     7  7        4                  3   7 2   3    ----- -------- ------------------ ---------   Notice how N 2 matches the number of layers that need to be rotated  Sometimes the number of rotatable layers is one less the total number of layers in the matrix  This occurs when the innermost layer is formed of only one element  i e  a 1  1 matrix  and therefore need not be rotated  It simply gets ignored  We will undoubtedly need this information in our function to rotate a matrix  so let   s add it now  def rotate matrix       size   len matrix        Rotatable layers only      layer count   size   2  Now we know what layers are and how to determine the number of layers that actually need rotating  how do we isolate a single layer so we can rotate it  Firstly  we inspect a matrix from the outermost layer  inwards  to the innermost layer  A 5  5 matrix has three layers in total and two layers that need rotating              x x x     x O x     x x x              Let   s look at columns first  The position of the columns defining the outermost layer  assuming we count from 0  are 0 and 4   -------- -----------    Column   0 1 2 3 4    -------- -----------                                      x x x                  x O x                  x x x                             -------- -----------   0 and 4 are also the positions of the rows for the outermost layer   ----- -----------    Row                ----- -----------      0                   1     x x x         2     x O x         3     x x x         4                ----- -----------   This will always be the case since the width and height are the same  Therefore we can define the column and row positions of a layer with just two values  rather than four   Moving inwards to the second layer  the position of the columns are 1 and 3  And  yes  you guessed it  it   s the same for rows  It   s important to understand we had to both increment and decrement the row and column positions when moving inwards to the next layer   ----------- --------- --------- ---------      Layer      Rows     Columns   Rotate     ----------- --------- --------- ---------    Outermost   0 and 4   0 and 4   Yes         Inner       1 and 3   1 and 3   Yes         Innermost   2         2         No         ----------- --------- --------- ---------   So  to inspect each layer  we want a loop with both increasing and decreasing counters that represent moving inwards  starting from the outermost layer  We   ll call this our    layer loop     def rotate matrix       size   len matrix      layer count   size   2      for layer in range 0  layer count           first   layer         last   size - first - 1         print  Layer  d  first   d  last   d     layer  first  last     5x5 matrix matrix           0  1  2  3  4         5  6  6  8  9        10 11 12 13 14        15 16 17 18 19        20 21 22 23 24     rotate matrix   The code above loops through the  row and column  positions of any layers that need rotating  Layer 0  first  0  last  4 Layer 1  first  1  last  3  We now have a loop providing the positions of the rows and columns of each layer  The variables first and last identify the index position of the first and last rows and columns  Referring back to our row and column tables   -------- -----------    Column   0 1 2 3 4    -------- -----------                                      x x x                  x O x                  x x x                             -------- -----------    ----- -----------    Row                ----- -----------      0                   1     x x x         2     x O x         3     x x x         4                ----- -----------   So we can navigate through the layers of a matrix  Now we need a way of navigating within a layer so we can move elements around that layer  Note  elements never    jump    from one layer to another  but they do move within their respective layers  Rotating each element in a layer rotates the entire layer  Rotating all layers in a matrix rotates the entire matrix  This sentence is very important  so please try your best to understand it before moving on  Now  we need a way of actually moving elements  i e  rotate each element  and subsequently the layer  and ultimately the  matrix  For simplicity  we   ll revert to a 3x3 matrix     that has one rotatable layer  0 1 2 3 4 5 6 7 8  Our layer loop provides the indexes of the first and last columns  as well as first and last rows   ----- -------    Col   0 1 2    ----- -------          0 1 2           3 4 5           6 7 8    ----- -------    ----- -------    Row            ----- -------      0   0 1 2       1   3 4 5       2   6 7 8    ----- -------   Because our matrices are always square  we need just two variables  first and last  since index positions are the same for rows and columns  def rotate matrix       size   len matrix      layer count   size   2        Our layer loop i 0  i 1  i 2     for layer in range 0  layer count            first   layer         last   size - first - 1                    We want to move within a layer here   The variables first and last can easily be used to reference the four corners of a matrix  This is because the corners themselves can be defined using various permutations of first and last  with no subtraction  addition or offset of those variables    --------------- ------------------- -------------    Corner          Position            3x3 Values     --------------- ------------------- -------------    top left         first  first        0 0            top right        first  last         0 2            bottom right     last  last          2 2            bottom left      last  first         2 0           --------------- ------------------- -------------   For this reason  we start our rotation at the outer four corners     we   ll rotate those first  Let   s highlight them with      1   3 4 5   7    We want to swap each   with the   to the right of it  So let   s go ahead a print out our corners defined using only various permutations of first and last  def rotate matrix       size   len matrix      layer count   size   2     for layer in range 0  layer count            first   layer         last   size - first - 1          top left    first  first          top right    first  last          bottom right    last  last          bottom left    last  first           print  top left   s     top left          print  top right   s     top right          print  bottom right   s     bottom right          print  bottom left   s     bottom left   matrix      0  1  2    3  4  5    6  7  8     rotate matrix   Output should be  top left   0  0  top right   0  2  bottom right   2  2  bottom left   2  0   Now we could quite easily swap each of the corners from within our layer loop  def rotate matrix       size   len matrix      layer count   size   2     for layer in range 0  layer count                    first   layer         last   size - first - 1          top left   matrix first  first          top right   matrix first  last          bottom right   matrix last  last          bottom left   matrix last  first             bottom left - gt  top left         matrix first  first    bottom left           top left - gt  top right         matrix first  last    top left           top right - gt  bottom right         matrix last  last    top right           bottom right - gt  bottom left         matrix last  first    bottom right   print matrix matrix  print  ---------  rotate matrix  print matrix matrix   Matrix before rotating corners   0  1  2   3  4  5   6  7  8   Matrix after rotating corners   6  1  0   3  4  5   8  7  2   Great  We have successfully rotated each corner of the matrix  But  we haven   t rotated the elements in the middle of each layer  Clearly we need a way of iterating within a layer  The problem is  the only loop in our function so far  our layer loop   moves to the next layer on each iteration  Since our matrix has only one rotatable layer  the layer loop exits after rotating only the corners  Let   s look at what happens with a larger  5  5 matrix  where two layers need rotating   The function code has been omitted  but it remains the same as above  matrix      0  1  2  3  4    5  6  7  8  9    10  11  12  13  14    15  16  17  18  19    20  21  22  23  24    print matrix matrix  print  --------------------  rotate matrix  print matrix matrix   The output is   20   1   2   3   0    5  16   7   6   9   10  11  12  13  14   15  18  17   8  19   24  21  22  23   4   It shouldn   t be a surprise that the corners of the outermost layer have been rotated  but  you may also notice the corners of the next layer  inwards  have also been rotated  This makes sense  We   ve written code to navigate through layers and also to rotate the corners of each layer  This feels like progress  but unfortunately we must take a step back  It   s just no good moving onto the next layer until the previous  outer  layer has been fully rotated  That is  until each element in the layer has been rotated  Rotating only the corners won   t do  Take a deep breath  We need another loop  A nested loop no less  The new  nested loop  will use the first and last variables  plus an offset to navigate within a layer  We   ll call this new loop our    element loop     The element loop will visit each element along the top row  each element down the right side  each element along the bottom row and each element up the left side   Moving forwards along the top row requires the column index to be incremented  Moving down the right side requires the row index to be incremented  Moving backwards along the bottom requires the column index to be decremented  Moving up the left side requires the row index to be decremented   This sounds complex  but it   s made easy because the number of times we increment and decrement to achieve the above remains the same along all four sides of the matrix  For example   Move 1 element across the top row  Move 1 element down the right side  Move 1 element backwards along the bottom row  Move 1 element up the left side   This means we can use a single variable in combination with the first and last variables to move within a layer  It may help to note that moving across the top row and down the right side both require incrementing  While moving backwards along the bottom and up the left side both require decrementing  def rotate matrix       size   len matrix      layer count   size   2            Move through layers  i e  layer loop       for layer in range 0  layer count                        first   layer             last   size - first - 1                Move within a single layer  i e  element loop               for element in range first  last                                offset   element - first                     element  increments column  across right                  top    first  element                     element  increments row  move down                  right side    element  last                     last-offset  decrements column  across left                  bottom    last  last-offset                     last-offset  decrements row  move up                  left side    last-offset  first                   print  top   s     top                  print  right side   s     right side                  print  bottom   s     bottom                  print  left side   s     left side   Now we simply need to assign the top to the right side  right side to the bottom  bottom to the left side  and left side to the top  Putting this all together we get  def rotate matrix       size   len matrix      layer count   size   2      for layer in range 0  layer count           first   layer         last   size - first - 1          for element in range first  last               offset   element - first              top   matrix first  element              right side   matrix element  last              bottom   matrix last  last-offset              left side   matrix last-offset  first               matrix first  element    left side             matrix element  last    top             matrix last  last-offset    right side             matrix last-offset  first    bottom  Given the matrix  0   1   2   3   4   5   6   7   8   Our rotate function results in  6   3   0   7   4   1   8   5   2

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As I said in my previous post  here s some code in C  that implements an O 1  matrix rotation for any size matrix  For brevity and readability there s no error checking or range checking  The code   static void Main  string    args      int             create an arbitrary matrix     m     0  1    2  3    4  5       Matrix         create wrappers for the data     m1   new Matrix  m       m2   new Matrix  m       m3   new Matrix  m          rotate the matricies in various ways - all are O 1    m1 RotateClockwise90       m2 Rotate180       m3 RotateAnitclockwise90            output the result of transforms   System Diagnostics Trace WriteLine  m1 ToString        System Diagnostics Trace WriteLine  m2 ToString        System Diagnostics Trace WriteLine  m3 ToString         class Matrix     enum Rotation         None      Clockwise90      Clockwise180      Clockwise270        public Matrix  int     matrix          m matrix   matrix      m rotation   Rotation None             the transformation routines   public void RotateClockwise90            m rotation    Rotation     int  m rotation   1   amp  3          public void Rotate180            m rotation    Rotation     int  m rotation   2   amp  3          public void RotateAnitclockwise90            m rotation    Rotation     int  m rotation   3   amp  3              accessor property to make class look like a two dimensional array   public int this  int row  int column          get             int         value   0         switch  m rotation                case Rotation None          value   m matrix  row  column           break         case Rotation Clockwise90          value   m matrix  m matrix GetUpperBound  0  - column  row           break         case Rotation Clockwise180          value   m matrix  m matrix GetUpperBound  0  - row  m matrix GetUpperBound  1  - column           break         case Rotation Clockwise270          value   m matrix  column  m matrix GetUpperBound  1  - row           break                 return value             set             switch  m rotation                case Rotation None          m matrix  row  column    value          break         case Rotation Clockwise90          m matrix  m matrix GetUpperBound  0  - column  row    value          break         case Rotation Clockwise180          m matrix  m matrix GetUpperBound  0  - row  m matrix GetUpperBound  1  - column    value          break         case Rotation Clockwise270          m matrix  column  m matrix GetUpperBound  1  - row    value          break                           creates a string with the matrix values   public override string ToString            int       num rows   0        num columns   0       switch  m rotation            case Rotation None      case Rotation Clockwise180        num rows   m matrix GetUpperBound  0         num columns   m matrix GetUpperBound  1         break       case Rotation Clockwise90      case Rotation Clockwise270        num rows   m matrix GetUpperBound  1         num columns   m matrix GetUpperBound  0         break             StringBuilder       output   new StringBuilder          output Append             for  int row   0   row  lt   num rows     row              if  row    0                  output Append                        output Append               for  int column   0   column  lt   num columns     column                  if  column    0                      output Append                            output Append  this  row  column  ToString                     output Append                   output Append             return output ToString            int             the original matrix     m matrix     Rotation         the current view of the matrix     m rotation      OK  I ll put my hand up  it doesn t actually do any modifications to the original array when rotating  But  in an OO system that doesn t matter as long as the object looks like it s been rotated to the clients of the class  At the moment  the Matrix class uses references to the original array data so changing any value of m1 will also change m2 and m3  A small change to the constructor to create a new array and copy the values to it will sort that out

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Here is a Javascript solution   const transpose   m   gt  m 0  map  x i    gt  m map x   gt  x i      a     original matrix 123 456 789  transpose a  reverse       rotate 90 degrees counter clockwise  369 258 147  transpose a slice   reverse        rotate 90 degrees clockwise  741 852 963  transpose transpose a slice   reverse    slice   reverse       rotate 180 degrees  987 654 321

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O n 2  time and O 1  space algorithm   without any workarounds and hanky-panky stuff     Rotate by  90    Transpose Reverse each row   Rotate by -90   Method 1     Transpose Reverse each column   Method 2     Reverse each row Transpose   Rotate by  180   Method 1  Rotate by  90 twice  Method 2  Reverse each row and then reverse each column  Transpose   Rotate by -180   Method 1  Rotate by -90 twice  Method 2  Reverse each column and then reverse each row  Method 3  Rotate by  180 as they are same

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usr bin env python  original      1 2 3                 4 5 6                 7 8 9       Rotate matrix 90 degrees    for i in map None  original   -1        print str i      n    This causes the sides to be rotated 90 degrees  ie  123  top side  is now 741  left side    This Python solution works because it uses slicing with a negative step to reverse the row orders  bringing 7 to top   original      7 8 9                 4 5 6                 1 2 3      It then uses map  along with the implied identity function which is the result of map with None as first arg  along with   to unpack all elements in sequence  to regroup the columns  ie  the first elements are put in a tuple together  the 2nd elements are put in a tuple together  and so forth   You effectively get get returned the following regrouping   original     7 8 9                 4 5 6                 1 2 3

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C code for matrix transpose  amp  rotate    -90    -180    Supports square and non-square matrices  has in-place and copy features Supports both 2D arrays and 1D pointers with logical rows cols Unit tests  see tests for examples of usage tested gcc -std c90 -Wall -pedantic  MSVC17       include  lt stdlib h gt   include  lt memory h gt   include  lt assert h gt           Matrix transpose  amp  rotate    -90    -180          Supports both 2D arrays and 1D pointers with logical rows cols         Supports square and non-square matrices  has in-place and copy features         See tests for examples of usage     tested gcc -std c90 -Wall -pedantic  MSVC17     typedef int matrix data t      matrix data type     void transpose const matrix data t  src  matrix data t  dst  int rows  int cols   void transpose inplace matrix data t  data  int n    void rotate int direction  const matrix data t  src  matrix data t  dst  int rows  int cols   void rotate inplace int direction  matrix data t  data  int n   void reverse rows matrix data t  data  int rows  int cols   void reverse cols matrix data t  data  int rows  int cols       test compare fn    int test cmp const matrix data t  lhs  const matrix data t  rhs  int rows  int cols        TESTS USAGE    void transpose test          matrix data t sq3x3 9      0 1 2 3 4 5 6 7 8      3x3 square  odd length side        matrix data t sq3x3 cpy 9       matrix data t sq3x3 2D 3  3        0 1 2     3 4 5     6 7 8        2D 3x3 square        matrix data t sq3x3 2D copy 3  3           expected test values        const matrix data t sq3x3 orig 9      0 1 2 3 4 5 6 7 8        const matrix data t sq3x3 transposed 9      0 3 6 1 4 7 2 5 8        matrix data t sq4x4 16     0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15      4x4 square  even length       const matrix data t sq4x4 orig 16      0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15        const matrix data t sq4x4 transposed 16      0 4 8 12 1 5 9 13 2 6 10 14 3 7 11 15            2x3 rectangle        const matrix data t r2x3 orig 6      0 1 2 3 4 5        const matrix data t r2x3 transposed 6      0 3 1 4 2 5        matrix data t r2x3 copy 6        matrix data t r2x3 2D 2  3       0 1 2   3 4 5         2x3 2D rectangle        matrix data t r2x3 2D t 3  2           matrix data t r3x2 6      0 1 2 3 4 5           matrix data t r3x2 copy 6          3x2 rectangle        const matrix data t r3x2 orig 6      0 1 2 3 4 5        const matrix data t r3x2 transposed 6      0 2 4 1 3 5         matrix data t r6x1 6      0 1 2 3 4 5          6x1        matrix data t r6x1 copy 6        matrix data t r1x1 1      0       1x1       matrix data t r1x1 copy 1           3x3 tests  2D array tests        transpose inplace sq3x3  3         transpose in place        assert  test cmp sq3x3  sq3x3 transposed  3  3        transpose inplace sq3x3  3         transpose again        assert  test cmp sq3x3  sq3x3 orig  3  3         transpose sq3x3  sq3x3 cpy  3  3       transpose copy 3x3       assert  test cmp sq3x3 cpy  sq3x3 transposed  3  3         transpose  matrix data t  sq3x3 2D   matrix data t  sq3x3 2D copy  3  3        2D array transpose copy        assert  test cmp  matrix data t  sq3x3 2D copy  sq3x3 transposed  3  3        transpose inplace  matrix data t  sq3x3 2D copy  3         2D array transpose in place        assert  test cmp  matrix data t  sq3x3 2D copy  sq3x3 orig  3  3            4x4 tests        transpose inplace sq4x4  4         transpose in place        assert  test cmp sq4x4  sq4x4 transposed  4 4        transpose inplace sq4x4  4         transpose again        assert  test cmp sq4x4  sq4x4 orig  3  3            2x3 3x2 tests        transpose r2x3 orig  r2x3 copy  2  3       assert  test cmp r2x3 copy  r2x3 transposed  3  2         transpose r3x2 orig  r3x2 copy  3  2       assert  test cmp r3x2 copy  r3x2 transposed  2 3            2D array        transpose  matrix data t  r2x3 2D   matrix data t  r2x3 2D t  2  3       assert  test cmp  matrix data t  r2x3 2D t  r2x3 transposed  3 2            Nx1 test  1x1 test        transpose r6x1  r6x1 copy  6  1       assert  test cmp r6x1 copy  r6x1  1  6         transpose r1x1  r1x1 copy  1  1       assert  test cmp r1x1 copy  r1x1  1  1        void rotate test             3x3 square        const matrix data t sq3x3 9      0 1 2 3 4 5 6 7 8        const matrix data t sq3x3 r90 9      6 3 0 7 4 1 8 5 2        const matrix data t sq3x3 180 9      8 7 6 5 4 3 2 1 0        const matrix data t sq3x3 l90 9      2 5 8 1 4 7 0 3 6        matrix data t sq3x3 copy 9           3x3 square  2D        matrix data t sq3x3 2D 3  3        0 1 2     3 4 5     6 7 8              4x4  2D        matrix data t sq4x4 4  4        0 1 2 3     4 5 6 7     8 9 10 11     12 13 14 15          matrix data t sq4x4 copy 4  4       const matrix data t sq4x4 r90 16      12 8 4 0 13 9 5 1 14 10 6 2 15 11 7 3        const matrix data t sq4x4 l90 16      3 7 11 15 2 6 10 14 1 5 9 13 0 4 8 12        const matrix data t sq4x4 180 16      15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0         matrix data t r6 6      0 1 2 3 4 5        rectangle with area of 6  1x6 2x3 3x2  or 6x1         matrix data t r6 copy 6       const matrix data t r1x6 r90 6      0 1 2 3 4 5        const matrix data t r1x6 l90 6      5 4 3 2 1 0        const matrix data t r1x6 180 6      5 4 3 2 1 0         const matrix data t r2x3 r90 6      3 0 4 1 5 2        const matrix data t r2x3 l90 6      2 5 1 4 0 3        const matrix data t r2x3 180 6      5 4 3 2 1 0         const matrix data t r3x2 r90 6      4 2 0 5 3 1        const matrix data t r3x2 l90 6      1 3 5 0 2 4        const matrix data t r3x2 180 6      5 4 3 2 1 0         const matrix data t r6x1 r90 6      5 4 3 2 1 0        const matrix data t r6x1 l90 6      0 1 2 3 4 5        const matrix data t r6x1 180 6      5 4 3 2 1 0            sq3x3 tests        rotate 90  sq3x3  sq3x3 copy  3  3          90        assert  test cmp sq3x3 copy  sq3x3 r90  3  3        rotate -90  sq3x3  sq3x3 copy  3  3        -90        assert  test cmp sq3x3 copy  sq3x3 l90  3  3        rotate 180  sq3x3  sq3x3 copy  3  3        180        assert  test cmp sq3x3 copy  sq3x3 180  3  3           sq3x3 in-place rotations        memcpy  sq3x3 copy  sq3x3  3   3   sizeof matrix data t        rotate inplace 90  sq3x3 copy  3       assert  test cmp sq3x3 copy  sq3x3 r90  3  3        rotate inplace -90  sq3x3 copy  3       assert  test cmp sq3x3 copy  sq3x3  3  3       back to 0 orientation        rotate inplace 180  sq3x3 copy  3       assert  test cmp sq3x3 copy  sq3x3 180  3  3        rotate inplace -180  sq3x3 copy  3       assert  test cmp sq3x3 copy  sq3x3  3  3        rotate inplace 180   matrix data t  sq3x3 2D  3     2D test        assert  test cmp  matrix data t  sq3x3 2D  sq3x3 180  3  3            sq4x4        rotate 90   matrix data t  sq4x4   matrix data t  sq4x4 copy  4  4       assert  test cmp  matrix data t  sq4x4 copy  sq4x4 r90  4  4        rotate -90   matrix data t  sq4x4   matrix data t  sq4x4 copy  4  4       assert  test cmp  matrix data t  sq4x4 copy  sq4x4 l90  4  4        rotate 180   matrix data t  sq4x4   matrix data t  sq4x4 copy  4  4       assert  test cmp  matrix data t  sq4x4 copy  sq4x4 180  4  4            r6 as 1x6        rotate 90  r6  r6 copy  1  6       assert  test cmp r6 copy  r1x6 r90  1  6        rotate -90  r6  r6 copy  1  6       assert  test cmp r6 copy  r1x6 l90  1  6        rotate 180  r6  r6 copy  1  6       assert  test cmp r6 copy  r1x6 180  1  6            r6 as 2x3        rotate 90  r6  r6 copy  2  3       assert  test cmp r6 copy  r2x3 r90  2  3        rotate -90  r6  r6 copy  2  3       assert  test cmp r6 copy  r2x3 l90  2  3        rotate 180  r6  r6 copy  2  3       assert  test cmp r6 copy  r2x3 180  2  3            r6 as 3x2        rotate 90  r6  r6 copy  3  2       assert  test cmp r6 copy  r3x2 r90  3  2        rotate -90  r6  r6 copy  3  2       assert  test cmp r6 copy  r3x2 l90  3  2        rotate 180  r6  r6 copy  3  2       assert  test cmp r6 copy  r3x2 180  3  2            r6 as 6x1        rotate 90  r6  r6 copy  6  1       assert  test cmp r6 copy  r6x1 r90  6  1        rotate -90  r6  r6 copy  6  1       assert  test cmp r6 copy  r6x1 l90  6  1        rotate 180  r6  r6 copy  6  1       assert  test cmp r6 copy  r6x1 180  6  1          test comparison fn  return 0 on match else non zero    int test cmp const matrix data t  lhs  const matrix data t  rhs  int rows  int cols         int r  c       for  r   0  r  lt  rows    r            for  c   0  c  lt  cols    c                if   lhs   r   cols  c      rhs   r   cols  c                   return -1                      return 0        Reverse values in place of each row in 2D matrix data rows  cols  or in 1D pointer with logical rows cols  A B C  - gt    C B A   D E F       F E D     void reverse rows matrix data t  data  int rows  int cols         int r  c      matrix data t temp      matrix data t  pRow   NULL       for  r   0  r  lt  rows    r            pRow    data   r   cols           for  c   0  c  lt   int  cols   2     c       explicit truncate                temp   pRow c               pRow c    pRow cols - 1 - c               pRow cols - 1 - c    temp                        Reverse values in place of each column in 2D matrix data rows  cols  or in 1D pointer with logical rows cols  A B C  - gt    D E F   D E F       A B C     void reverse cols matrix data t  data  int rows  int cols         int r  c      matrix data t temp      matrix data t  pRowA   NULL      matrix data t  pRowB   NULL       for  c   0  c  lt  cols    c            for  r   0  r  lt   int  rows   2     r       explicit truncate                pRowA   data   r   cols              pRowB   data   cols    rows - 1 - r               temp   pRowA c               pRowA c    pRowB c               pRowB c    temp                        Transpose NxM matrix to MxN matrix in O n  time    void transpose const matrix data t  src  matrix data t  dst  int N  int M         int i      for  i   0  i lt N M    i  dst  i M  N    i   M     src i         one-liner version                expanded version of one-liner   calculate XY based on array index  then convert that to YX array index     int i j x y      for  i   0  i  lt  N M    i        x   i   M      y    int  i   M       j   x   N   y      dst j    src i                            nested for loop version     using ptr arithmetic to get proper row column     this is really just dst col  row  src row  col       int r  c       for  r   0  r  lt  rows    r            for  c   0  c  lt  cols    c                 dst   c   rows  r     src   r   cols  c                                Transpose NxN matrix in place    void transpose inplace matrix data t  data  int N          int r  c      matrix data t temp       for  r   0  r  lt  N    r            for  c   r  c  lt  N    c      start at column row                                          using ptr arithmetic to get proper row column                                           this is really just                                     temp dst col  row                                       dst col  row  src row  col                                       src row  col  temp                                                     temp    data   c   N  r                data   c   N  r     data   r   N  c                data   r   N  c    temp                        Rotate 1D or 2D src matrix to dst matrix in a direction  90 180 -90  Precondition   src and dst are 2d matrices with dimensions src rows  cols  and dst cols  rows  or 1D pointers with logical rows cols    void rotate int direction  const matrix data t  src  matrix data t  dst  int rows  int cols         switch  direction        case -90          transpose src  dst  rows  cols           reverse cols dst  cols  rows           break      case 90          transpose src  dst  rows  cols           reverse rows dst  cols  rows           break      case 180      case -180             bit copy to dst  use in-place reversals            memcpy dst  src  rows cols sizeof matrix data t            reverse cols dst  cols  rows           reverse rows dst  cols  rows           break              Rotate array in a direction  Array must be NxN 2D or 1D array with logical rows cols Direction can be  90 180 -90 -180     void rotate inplace  int direction  matrix data t  data  int n         switch  direction        case -90          transpose inplace data  n           reverse cols data  n  n           break      case 90          transpose inplace data  n           reverse rows data  n  n           break      case 180      case -180          reverse cols data  n  n           reverse rows data  n  n           break

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C code for matrix rotation 90 degree clockwise IN PLACE for any M N matrix  void rotateInPlace int   arr size  size   int row  int column       int i  j      int temp   row gt column row column      int flipTill   row  lt  column   row   column      for i 0 i lt flipTill i             for j 0 j lt i j                 swapArrayElements arr  i  j                        temp   j 1       for i   row gt column i 0  i lt row  i                 for j row lt column temp 0  j lt column  j                     swapArrayElements arr  i  j                            for i 0 i lt column i             for j 0 j lt row 2 j                 temp   arr i  j               arr i  j    arr i  row-j-1               arr i  row-j-1    temp

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C  code to rotate  n m  2D arrays 90 deg right  using System  using System Collections Generic  using System Linq  using System Text  using System Threading Tasks   namespace MatrixProject          mattrix class      class Matrix          private int rows          private int cols          private int    matrix           public Matrix int n               this rows   n              this cols   n              this matrix   new int this rows this cols                       public Matrix int n int m               this rows   n              this cols   m               this matrix   new int this rows this cols                      public void Show                         for  var i   0  i  lt  this rows  i                                  for  var j   0  j  lt  this cols  j                          Console Write   0 3    this matrix i  j                                      Console WriteLine                                                     public void ReadElements                        for  var i   0  i  lt  this rows  i                    for  var j   0  j  lt  this cols  j                                          Console Write  element  0   1     i j                       this matrix i  j    Convert ToInt32 Console ReadLine                                                          rotate  n m  2D array by 90 deg right         public void Rotate90DegRight                             create a mirror of current matrix             int    mirror   this matrix                  create a new matrix             this matrix   new int this cols  this rows                for  int i   0  i  lt  this rows  i                                  for  int j   0  j  lt  this cols  j                                          this matrix j  this rows - i - 1    mirror i  j                                                   replace cols count with rows count             int tmp   this rows              this rows   this cols              this cols   tmp                                  class Program               static void Main string   args                        Matrix myMatrix   new Matrix 3 4               Console WriteLine  Enter matrix elements                 myMatrix ReadElements                Console WriteLine  Matrix elements are                 myMatrix Show                myMatrix Rotate90DegRight                Console WriteLine  Matrix rotated at 90 deg are                 myMatrix Show                Console ReadLine                        Result       Enter matrix elements      element 0 0  1     element 0 1  2     element 0 2  3     element 0 3  4     element 1 0  5     element 1 1  6     element 1 2  7     element 1 3  8     element 2 0  9     element 2 1  10     element 2 2  11     element 2 3  12     Matrix elements are        1  2  3  4       5  6  7  8       9 10 11 12     Matrix rotated at 90 deg are        9  5  1      10  6  2      11  7  3      12  8  4

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You can do this in 3 easy steps   1 Suppose we have a matrix     1 2 3    4 5 6    7 8 9   2 Take the transpose of the matrix     1 4 7    2 5 8    3 6 9   3 Interchange rows to get rotated matrix     3 6 9    2 5 8    1 4 7   Java source code for this   public class MyClass        public static void main String args              Demo obj   new Demo              initial matrix to rotate           int     matrix       1  2  3      4  5  6      7  8  9              int     transpose   new int 3  3      matrix to store transpose          obj display matrix                   initial matrix          obj rotate matrix  transpose         call rotate method         System out println            obj display transpose                display the rotated matix          class Demo          public void rotate int     mat  int     tran                First take the transpose of the matrix            for  int i   0  i  lt  mat length  i                  for  int j   0  j  lt  mat length  j                      tran i  j    mat j  i                                                   Interchange the rows of the transpose matrix to get rotated            matrix                     for  int i   0  j   tran length - 1  i    j  i    j--                for  int k   0  k  lt  tran length  k                      swap i  k  j  k  tran                                      public void swap int a  int b  int c  int d  int     arr            int temp   arr a  b           arr a  b    arr c  d           arr c  d    temp                    Method to display the matrix        public void display int     arr            for  int i   0  i  lt  arr length  i                  for  int j   0  j  lt  arr length  j                      System out print arr i  j                                    System out println                        Output   1 2 3  4 5 6  7 8 9   3 6 9  2 5 8  1 4 7

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Can be done recursively quite cleanly  here is my implementation in golang   rotate nxn matrix in go golang recursively in place with no additional memory  func rot90 a     int        n    len a      if n    1           return           for i    0  i  lt  n  i             a 0  i   a n-1-i  n-1    a n-1-i  n-1   a 0  i            rot90 a 1

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90-degree clockwise     temp array           left col    left col             bottom row    bottom row           reverse right col     reverse right col    reverse top row     reverse top row      temp array    void RotateClockwise90 int    arr  int lo  int hi       if  lo  gt   hi       return     for  int i lo  i lt hi  i          int j   lo hi-i      int temp     arr i  lo       arr i  lo    arr hi  i       arr hi  i    arr j  hi       arr j  hi    arr lo  j       arr lo  j    temp         RotateClockwise90 arr  lo 1  hi-1

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There are tons of good code here but I just want to show what s going on geometrically so you can understand the code logic a little better   Here is how I would approach this   first of all  do not confuse this with transposition which is very easy    the basica idea is to treat it as layers and we rotate one layer at a time    say we have a 4x4  1   2   3   4 5   6   7   8 9   10  11  12 13  14  15  16   after we rotate it clockwise by 90 we get  13  9   5   1 14  10  6   2    15  11  7   3 16  12  8   4   so let s decompose this  first we rotate the 4 corners essentially  1           4   13          16   then we rotate the following diamond which is sort of askew      2             8 9                15   and then the 2nd skewed diamond          3 5                        12     14   so that takes care of the outer edge so essentially we do that one shell at a time until   finally the middle square  or if it s odd just the final element which does not move   6   7 10  11   so now let s figure out the indices of each layer  assume we always work with the outermost layer  we are doing   0 0  - gt   0 n-1    0 n-1  - gt   n-1 n-1    n-1 n-1  - gt   n-1 0   and  n-1 0  - gt   0 0   0 1  - gt   1 n-1    1 n-2  - gt   n-1 n-2    n-1 n-2  - gt   n-2 0   and  n-2 0  - gt   0 1   0 2  - gt   2 n-2    2 n-2  - gt   n-1 n-3    n-1 n-3  - gt   n-3 0   and  n-3 0  - gt   0 2    so on and so on until we are halfway through the edge  so in general the pattern is    0 i  - gt   i n-i    i n-i  - gt   n-1 n- i 1     n-1 n- i 1   - gt   n- i 1  0   and  n- i 1  0  to  0 i

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This is my implementation  in C  O 1  memory complexity  in place rotation  90 degrees clockwise    include  lt stdio h gt    define M SIZE 5  static void initMatrix    static void printMatrix    static void rotateMatrix     static int m M SIZE  M SIZE    int main void       initMatrix        printMatrix        rotateMatrix        printMatrix         return 0     static void initMatrix        int i  j       for i   0  i  lt  M SIZE  i             for j   0  j  lt  M SIZE  j                 m i  j    M SIZE i   j   1                     static void printMatrix        int i  j       printf  Matrix n        for i   0  i  lt  M SIZE  i             for j   0  j  lt  M SIZE  j                 printf   02d    m i  j                      printf   n              printf   n       static void rotateMatrix        int r  c       for r   0  r  lt  M SIZE 2  r             for c   r  c  lt  M SIZE - r - 1  c                 int tmp   m r  c                m r  c    m M SIZE - c - 1  r               m M SIZE - c - 1  r    m M SIZE - r - 1  M SIZE - c - 1               m M SIZE - r - 1  M SIZE - c - 1    m c  M SIZE - r - 1               m c  M SIZE - r - 1    tmp

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Here is one that does the rotation in place instead of using a completely new array to hold the result   I ve left off initialization of the array and printing it out   This only works for square arrays but they can be of any size   Memory overhead is equal to the size of one element of the array so you can do the rotation of as large an array as you want   int a 4  4   int n   4  int tmp  for  int i   0  i  lt  n   2  i          for  int j   i  j  lt  n - i - 1  j                  tmp               a i  j           a i  j            a j  n-i-1           a j  n-i-1        a n-i-1  n-j-1           a n-i-1  n-j-1    a n-j-1  i           a n-j-1  i        tmp

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My version of rotation   void rotate matrix int  matrix  int size     int result size size        for  int i   0  i  lt  size    i          for  int j   0  j  lt  size    j              result  size - 1 - i    j size    matrix i size j        for  int i   0  i  lt  size size    i          matrix i    result i       In it we change last column to first row and so further  It is may be not optimal but clear for understanding

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private static int     rotate int     matrix  int n        int     rotated   new int n  n       for  int i   0  i  lt  n  i              for  int j   0  j  lt  n  j                  rotated i  j    matrix n-j-1  i                       return rotated

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Here is the Java version   public static void rightRotate int     matrix  int n        for  int layer   0  layer  lt  n   2  layer              int first   layer          int last   n - 1 - first          for  int i   first  i  lt  last  i                 int offset   i - first             int temp   matrix first  i              matrix first  i    matrix last-offset  first              matrix last-offset  first    matrix last  last-offset              matrix last  last-offset    matrix i  last              matrix i  last    temp                      the method first rotate the mostouter layer  then move to the inner layer squentially

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In Eigen  C     Eigen  Matrix2d mat  mat  lt  lt   1  2          3  4  std  cout  lt  lt  mat  lt  lt   quot  n n quot    Eigen  Matrix2d r plus 90   mat transpose   rowwise   reverse    std  cout  lt  lt  r plus 90  lt  lt   quot  n n quot    Eigen  Matrix2d r minus 90   mat transpose   colwise   reverse    std  cout  lt  lt  r minus 90  lt  lt   quot  n n quot    Eigen  Matrix2d r 180   mat colwise   reverse   rowwise   reverse        180 same as -180 std  cout  lt  lt  r 180  lt  lt   quot  n n quot    Output  1 2 3 4  3 1 4 2  2 4 1 3  4 3 2 1

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In place clock wise 90 degrees rotation using vector of vectors      include lt iostream gt    include lt vector gt    include lt algorithm gt   using namespace std     Rotate a Matrix by 90 degrees void rotateMatrix vector lt vector lt int gt   gt   amp matrix      int n matrix size       for int i 0 i lt n i         for int j i 1 j lt n j             swap matrix i  j  matrix j  i                  for int i 0 i lt n i             reverse matrix i  begin   matrix i  end                        int main        int n     cout lt  lt  enter the size of the matrix   lt  lt endl       while  cin  gt  gt  n        vector lt  vector lt int gt   gt  m        cout lt  lt  enter the elements  lt  lt endl      for  int i   0  i  lt  n  i              m push back vector lt int gt  n            for  int j   0  j  lt  n  j                scanf   d    amp m i  j                cout lt  lt  the rotated matrix is   lt  lt endl        rotateMatrix m       for  int i   0  i  lt  n  i              for  int j   0  j  lt  n  j                cout  lt  lt  m i  j   lt  lt               cout  lt  lt  endl                return 0

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here s a in-space rotate method  by java  only for square  for non-square 2d array  you will have to create new array anyway   private void rotateInSpace int     arr        int z   arr length      for  int i   0  i  lt  z   2  i              for  int j   0  j  lt   z   2   z   2   j                  int x   i  y   j              int temp   arr x  y               for  int k   0  k  lt  4  k                      int temptemp   arr y  z - x - 1                   arr y  z - x - 1    temp                  temp   temptemp                   int tempX   y                  y   z - x - 1                  x   tempX                                    code to rotate any size 2d array by creating new array   private int     rotate int     arr        int width   arr 0  length      int depth   arr length      int     re   new int width  depth       for  int i   0  i  lt  depth  i              for  int j   0  j  lt  width  j                  re j  depth - i - 1    arr i  j                       return re

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Ruby-way   transpose map  amp  reverse

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A couple of people have already put up examples which involve making a new array     A few other things to consider    a  Instead of actually moving the data  simply traverse the  rotated  array differently      b  Doing the rotation in-place can be a little trickier   You ll need a bit of scratch place  probably roughly equal to one row or column in size    There s an ancient ACM paper about doing in-place transposes  http   doi acm org 10 1145 355719 355729   but their example code is nasty goto-laden FORTRAN   Addendum   http   doi acm org 10 1145 355611 355612 is another  supposedly superior  in-place transpose algorithm

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In Java   public class Matrix      Author Shrikant Dande    private static void showMatrix int     arr int rows int col        for int i  0  i lt rows i             for int j  0  j lt col j                 System out print arr i  j                          System out println              private static void rotateMatrix int     arr int rows int col        int     tempArr   new int 4  4       for int i  0  i lt rows i             for int j  0  j lt col j                 tempArr i  j    arr rows-1-j  i               System out print tempArr i  j                          System out println             public static void main String   args        int     arr      1   2   3   4                 5   6   7   8                 9   1  2  5                 7  4  8  9        int rows   4 col   4       showMatrix arr  rows  col       System out println  ------------------------------------------------        rotateMatrix arr  rows  col

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This is an overrated interview question these days   My suggestion is  Do not let the interviewer confuse you with their crazy suggestion about solving this problem  Use the whiteboard to draw the indexing of input array then draw the indexing of output array  Samples of column indexing before and after rotation shown below   30 -- gt  00 20 -- gt  01 10 -- gt  02 00 -- gt  03  31 -- gt  10 21 -- gt  11 11 -- gt  12 01 -- gt  13   Notice the number pattern after rotation   Provided below a clean cut Java solution  It is tested  and it works    Input      M A C P      B N L D      Y E T S      I W R Z       Output      I Y B M      W E N A      R T L C      Z S D P           c   author  G A N MOHIM     Oct 3  2015    RotateArrayNintyDegree java     package rotatearray   public class RotateArrayNintyDegree        public char     rotateArrayNinetyDegree char     input            int k     k is used to generate index for output array          char     output   new char input length   input 0  length            for  int i   0  i  lt  input length  i                  k   0              for  int j   input length-1  j  gt   0  j--                    output i  k    input j  i      note how i is used as column index  and j as row                 k                                     return output             public void printArray char     charArray            for  int i   0  i  lt  charArray length  i                  for  int j   0  j  lt  charArray 0  length  j                      System out print charArray i  j                                    System out println                           public static void main String   args            char     input                        M    A    C    P                        B    N    L    D                        Y    E    T    S                        I    W    R    Z                               char     output   new char input length   input 0  length            RotateArrayNintyDegree rotationObj   new RotateArrayNintyDegree            rotationObj printArray input            System out println   n            output   rotationObj rotateArrayNinetyDegree input           rotationObj printArray output

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This a better version of it in Java  I ve made it for a matrix with a different width and height   h is here the height of the matrix after rotating w is here the width of the matrix after rotating    nbsp   public int     rotateMatrixRight int     matrix           W and H are already swapped        int w   matrix length      int h   matrix 0  length      int     ret   new int h  w       for  int i   0  i  lt  h    i            for  int j   0  j  lt  w    j                ret i  j    matrix w - j - 1  i                       return ret      public int     rotateMatrixLeft int     matrix           W and H are already swapped        int w   matrix length      int h   matrix 0  length         int     ret   new int h  w       for  int i   0  i  lt  h    i            for  int j   0  j  lt  w    j                ret i  j    matrix j  h - i - 1                       return ret      This code is based on Nick Berardi s post

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Great answers but for those who are looking for a DRY JavaScript code for this - both  90 Degrees and -90 Degrees    x000D   x000D               Input  1 2 3 x000D                      4 5 6 x000D                      7 8 9 x000D   x000D               Transpose   x000D                     1 4 7 x000D                     2 5 8 x000D                     3 6 9 x000D   x000D               Output   x000D                90 Degree  x000D                     7 4 1 x000D                     8 5 2 x000D                     9 6 3 x000D   x000D               -90 Degree  x000D                    3 6 9 x000D                    2 5 8 x000D                    1 4 7 x000D   x000D               Rotate  90 x000D           function rotate90 matrix    x000D   x000D             matrix   transpose matrix   x000D             matrix map function array    x000D               array reverse    x000D                 x000D   x000D             return matrix  x000D             x000D   x000D               Rotate -90 x000D           function counterRotate90 matrix    x000D             var result   createEmptyMatrix matrix length   x000D             matrix   transpose matrix   x000D             var counter   0  x000D   x000D             for  var i   matrix length - 1  i  gt   0  i--    x000D               result counter    matrix i   x000D               counter    x000D               x000D   x000D             return result  x000D             x000D   x000D               Create empty matrix x000D           function createEmptyMatrix len    x000D             var result   new Array    x000D             for  var i   0  i  lt  len  i      x000D               result push      x000D               x000D             return result  x000D             x000D   x000D               Transpose the matrix x000D           function transpose matrix    x000D                make empty array x000D             var len   matrix length  x000D             var result   createEmptyMatrix len   x000D   x000D             for  var i   0  i  lt  matrix length  i      x000D               for  var j   0  j  lt  matrix i  length  j      x000D                 var temp   matrix i  j   x000D                 result j  i    temp  x000D                 x000D               x000D             return result  x000D             x000D   x000D   x000D   x000D               Test Cases x000D           var array1     x000D              1  2   x000D              3  4  x000D              x000D           var array2     x000D              1  2  3   x000D              4  5  6   x000D              7  8  9  x000D              x000D           var array3     x000D              1  2  3  4   x000D              5  6  7  8   x000D              9  10  11  12   x000D              13  14  15  16  x000D              x000D   x000D                90 degress Rotation Tests x000D   x000D           var test1   rotate90 array1   x000D           var test2   rotate90 array2   x000D           var test3   rotate90 array3   x000D           console log test1   x000D           console log test2   x000D           console log test3   x000D   x000D               -90 degress Rotation Tests x000D           var test1   counterRotate90 array1   x000D           var test2   counterRotate90 array2   x000D           var test3   counterRotate90 array3   x000D           console log test1   x000D           console log test2   x000D           console log test3   x000D   x000D   x000D

[algorithm] How do you rotate a two dimensional array?

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