How will you initialize a three-dimensional array thread 323. How will you refer the first and last element in this array?

Answer 1

The first element will be 0,0,0 and the last will be 2,1,2.

It's always best to think of multi-dimensional arrays in terms of a one-dimensional array. That is, a 3x2x3 array is really a one-dimensional array of 3 elements (the first dimension), where each element is a 2x3 two-dimensional array, and where each of those 2x3 arrays is a one-dimensional array of 2 elements (the second dimension), where each element is a one-dimensional array of 3 elements (the third dimension). Thinking in these terms makes it much easier to visualise arrays with 4 or more dimensions.

Arrays are always allocated contiguously, one element after the other. So the memory layout for your three dimensional array is as follows (where 000 means element 0,0,0):

{{000, 001, 002}, {010, 011, 012}}, {{100, 101, 102}, {110, 111, 112}}, {{200, 201, 202}, {210, 211, 212}}

The curly braces are merely notational, but they help to visualise the layout more clearly, dividing the memory into three groups of two groups of three elements. However, if we stack the three main groups one above the other it will be much easier to see visualise the structure:

{000, 001, 002}, {010, 011, 012} {100, 101, 102}, {110, 111, 112}

{200, 201, 202}, {210, 211, 212}

If you look at each row you can clearly see that the first digit in each element is the same throughout that row. However, each row is really a two-dimensional array (of 2x3 elements), so each row is really a 2x3 table. The top row is therefore table 0, the middle row is table 1 and the bottom row is table 2. Let's look at table 0 more closely:

Table 0:

{000, 001, 002}, {010, 011, 012}

Now let's stack the table's 2 elements so we can see the table more clearly:

Table 0:

{000, 001, 002}

{010, 011, 012}

Now the rows are identified by the second digit, where the top row is row 0 and the bottom row is row 1. Each row has three elements and the third digit identifies the column of that element (0, 1 or 2). Here's the complete structure:

Table 0:

Row 0: {000, 001, 002}

Row 1: {010, 011, 012}

Table 1:

Row 0: {100, 101, 102}

Row 1: {110, 111, 112}

Table 2:

Row 0: {200, 201, 202}

Row 1: {210, 211, 212}

From this we can clearly see that we can refer to any individual element through a table identifier (0, 1 or 2), a row identifier (0 or 1) and a column identifier (0, 1 or 2). Therefore to initialise this structure, we need to cycle through each identifier in turn. Here's how we do that using pseudo-code:

given array A [3,2,3]

for each table in 0 to 2

for each row in 0 to 1

for each column in 0 to 2

initialise A [table, row, column]

next column

next row

next table