7.4 MULTIDIMENSIONAL ARRAYS

Multidimensional arrays are defined in much the same manner as one-dimensional arrays, except that a separate pair of square brackets is required for each subscript.Thus, a two dimensional array will require two pair of square brackets, a three-dimensional array will require three pair of square brackets, and so on.

In general terms a multidimensional array definition can be written as

storage-class data-type array[expression 1][expression 2].....[expression n] 

where  storage-class refers to the storage class of the array, data-type is its data type, array is the array name, and expression 1, expression 2,......,expression n are positive valued integer expressions that indicate the number of array elements associated with each subscript.Remember that the storage-class is optional ;the default values are automatic for arrays that are defined inside of  a function, and external for arrays defined outside of a function.

Consider the following two dimensional array definition.

int values[3][4] = {1,2,3,4,5,6,7,8,9,10,11,12};

Note that the value can be thought of a table having 3 rows and 4 columns (4 elements per row).Since initial values are assigned by rows (i.e. last subscript increasing most rapidly), the results of this initial assignments are as follows.

values[0][0] = 1  values[0][1] = 2   values[0][2] = 3   values[0][3] = 4
values[1][0] = 5  values[1][1] = 6   values[1][2] = 7   values[1][3] = 8  
values[2][0] = 9  values[2][1] = 10  values[2][2] = 11 values[2][3] = 12 


Remember the first subscript ranges from 0 to 2, and the second subscript ranges from 0 to 3.


Now consider the following three dimensional array definition.

int t[10][20][30] = {
                                  {             /*table 1*/
                                  {1, 2, 3, 4}, /*row 1*/
                                  {5, 6, 7, 8}, /*row 2*/
                                  {9, 10, 11, 12} /*row 3*/
                           },
                           {                  /*table 2*/
                                  {21, 22, 23, 24},  /*row 1*/
                                  {25, 26, 27, 28},  /*row 2*/
                                  {29, 30, 31, 32}  /*row 3*/ 
                            }
}

Think of this array as a collection of 10 tables, each having 20 rows and 30 columns.The groups of initial values will result in the assignment of the following  nonzero values in the first two tables.

t[0][0][0] = 1   t[0][0][1] = 2    t[0][0][2] = 3    t[0][0][3] = 4  
t[0][1][0] = 5   t[0][1][1] = 6    t[0][1][2] = 7    t[0][1][3] = 8  
t[0][2][0] = 9   t[0][2][1] = 10  t[0][2][2] = 11   t[0][2][3] = 12  


t[1][0][0] = 21   t[0][0][1] = 22    t[0][0][2] = 23   t[0][0][3] = 24  
t[1][1][0] = 25   t[0][1][1] = 26    t[0][1][2] = 27   t[0][1][3] = 28  
t[1][2][0] = 29   t[0][2][1] = 30    t[0][2][2] = 31   t[0][2][3] = 32  

All of the remaining array will be assigned zeros.