Map a 2D array onto a 1D array

Question

I want to represent a 2D array with a 1D array  A function will pass the two indicies  x y  and the value to store  These two indicies would represent a single element of a 1D array  and set it accordingly  I know the 1D array needs to have the size of arrayWidth    arrayHeight  but I don t know how to set each element   For example  how do I distinguish  2 4 3  from  4 2 3   I tried setting the array as the x y  but 2 4 and 4 2 would result in the same spot in the array and I need them to be different

User · Accepted Answer

You need to decide whether the array elements will be stored in row order or column order and then be consistent about it. http://en.wikipedia.org/wiki/Row-major_order

The C language uses row order for Multidimensional arrays

To simulate this with a single dimensional array, you multiply the row index by the width, and add the column index thus:

 int array[width * height];

 int SetElement(int row, int col, int value)
 {
    array[width * row + col] = value;  
 }

User · Answer

It s important to store the data in a way that it can be retrieved in the languages used   C-language stores in row-major order  all of first row comes first  then all of second row      with every index running from 0 to it s dimension-1   So the order of array x 2  3  is x 0  0   x 0  1   x 0  2   x 1  0   x 1  1   x 1  2     So in C language  x i  j  is stored the same place as a 1-dimensional array entry x1dim  i 3  j    If the data is stored that way  it is easy to retrieve in C language   Fortran and MATLAB are different   They store in column-major order  all of first column comes first  then all of second row      and every index runs from 1 to it s dimension   So the index order is the reverse of C and all the indices are 1 greater   If you store the data in the C language order  FORTRAN can find X C language i  j  using X FORTRAN j 1  i 1    For instance  X C language 1  2  is equal to X FORTRAN 3 2    In 1-dimensional arrays  that data value is at X1dim C language 2 Cdim2   3   which is the same position as X1dim FORTRAN 2 Fdim1   3   1    Remember that Cdim2   Fdim1 because the order of indices is reversed   MATLAB is the same as FORTRAN   Ada is the same as C except the indices normally start at 1   Any language will have the indices in one of those C or FORTRAN orders and the indices will start at 0 or 1 and can be adjusted accordingly to get at the stored data   Sorry if this explanation is confusing  but I think it is accurate and important for a programmer to know

User · Answer

You should be able to access the 2d array with a simple pointer in place   The array x  y  will be arranged in the pointer as p 0x   width   0y  0x   width   1y     0x   width   n-1y  1x   width   0y  etc

User · Answer

Example   we want to represent an 2D array of SIZE X and SIZE Y size  That means that we will have MAXY consecutive rows of MAXX size  Hence the set function is  void set array  int x  int y  int val     array  x   SIZE Y   y     val      The get would be   int get array  int x  int y     return array  x   SIZE Y   y

User · Answer

As other have said C maps in row order      include  lt stdio h gt      int main int argc  char   argv       int i  j  k     int arr 5  3      int  arr2    int  arr          for  k 0  k lt 15  k                arr2 k    k            printf  arr  d     2d n   k  arr2 k                     for  i 0  i lt 5  i               for  j 0  j lt  3  j                  printf  arr2  d   d     2d n   i  j  arr i  j                                  Output   arr 0     0 arr 1     1 arr 2     2 arr 3     3 arr 4     4 arr 5     5 arr 6     6 arr 7     7 arr 8     8 arr 9     9 arr 10    10 arr 11    11 arr 12    12 arr 13    13 arr 14    14 arr2 0  0     0 arr2 0  1     1 arr2 0  2     2 arr2 1  0     3 arr2 1  1     4 arr2 1  2     5 arr2 2  0     6 arr2 2  1     7 arr2 2  2     8 arr2 3  0     9 arr2 3  1    10 arr2 3  2    11 arr2 4  0    12 arr2 4  1    13 arr2 4  2    14

User · Answer

using row major example   A i j    a i   j ld      where ld is the leading dimension                           commonly same as array dimension in i      matrix like notation using preprocessor hack  allows to hide indexing  define A i j  A  i     j  ld   double  A        size t ld        A i j               A j i

User · Answer

The typical formula for recalculation of 2D array indices into 1D array index is  index   indexX   arrayWidth   indexY    Alternatively you can use  index   indexY   arrayHeight   indexX     assuming that arrayWidth is measured along X axis  and arrayHeight along Y axis   Of course  one can come up with many different formulae that provide alternative unique mappings  but normally there s no need to    In C C   languages built-in multidimensional arrays are stored in memory so that the last index changes the fastest  meaning that for an array declared as  int xy 10  10     element xy 5  3  is immediately followed by xy 5  4  in memory  You might want to follow that convention as well  choosing one of the above two formulae depending on which index  X or Y  you consider to be the  last  of the two

[c] Map a 2D array onto a 1D array

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