# Multi-dimensional Arrays

## Rectangular Arrays (Two Dimensional)

You should be familiar with one dimensional arrays. The data in arrays may be any type. While a one dimensional array works for a sequence of data, we need something more for a two dimensional table, where data values vary over both row and column.

If we have a table of integers, for instance with three rows and four columns:

```
2 4 7 55
3 1 8 10
6 0 49 12
```

We could declare an array variable of the right size as

```
int[,] table = new int[3, 4];
```

Multiple indices are separated by commas inside the square brackets.
In declaring an array type, no indices are included so the `[,]`

indicates a two dimensional array. Where the `new`

object is being created,
the values inside the square brackets give each dimension.

In general the notation for a two dimensional array declaration is:

type`[, ]`

variableName

and to create a new array with default values:

new

type`[`

intExpression1`,`

intExpression2`]`

where the expressions evaluate to integers for the dimensions.

To assign the 8 in the table above, consider that it is in the second row in normal counting, but we start array indices at 0, so there are rows 0, 1, and 2, and the 8 has row index 1. Again starting with index 0 for columns, the 8 is at index 2. We can assign a value to that position with

```
table[1, 2] = 8;
```

In fact a two dimensional array just needs two indices that could mean
anything. For instance, it was just the standard convention,
calling the left index the row. They could have been switched everywhere, and
assume the notation `table[column, row]`

:

```
int[,] table = new int[4, 3];
table[2, 1] = 8;
```

but we will *stick with* the original `[row, column]`

model.

Data indexed by more than two integer indices can be stored in a higher dimension array, with more indices between the square braces. We will only consider two dimensional arrays in the examples here.

A shorthand for initializing all the data in the table, analogous to initializing one dimensional arrays is:

```
int[, ] table = { {2, 4, 7, 55},
{3, 1, 8, 10},
{6, 0, 49, 12} };
```

All rows must be the same length when using this notation.

Often two dimensional arrays, like one dimensional arrays, are processed in loops. Multiple dimension arrays are often processed in nested loops. We could print out this table using columns 5 spaces wide with the code:

```
for (int r = 0; r < 3; r++) {
for (int c = 0; c < 4; c++) {
Console.Write("{0, 5}", table[r, c]);
}
Console.WriteLine();
}
```

If we wanted to make a more general function out of that code, we have a problem: the number of rows and columns were literal values that we knew. We need something more general. For one dimensional arrays we had the Length property, but now there are more than one lengths!

The following csharp sequence illustrates the syntax needed:

```
csharp> int[, ] table = { {2, 4, 7, 55},
> {3, 1, 8, 10},
> {6, 0, 49, 12} };
csharp> table.Length;
12
csharp> table.GetLength(0);
3
csharp> table.GetLength(1);
4
csharp> foreach (int n in table) {
> Console.WriteLine(n);
> }
2
4
7
55
3
1
8
10
6
0
49
12
```

Note:

The meaning for the Length property, is now the

*total*number of elements, (3)(4) = 12.The separate method

`GetLength`

is needed to find the number of rows and columns. The entries in the list of array indices in the multi-dimensional array notation are themselves indexed to provide the`GetLength`

method parameter for each dimension. In this case index 0 gives the row length (left index of the array notation), and 1 gives the column length (right index of the array notation).The

`foreach`

statement behavior is consistent with the`Length`

property, giving*all*the elements, row by row. More generally, the rightmost indices vary most rapidly as the`foreach`

statement iterates through all elements.

Just replacing 3 and 4 by `table.GetLength(0)`

and `table.GetLength(1)`

in the
table printing code would make it general.

A more elaborate table might include row and column sums:

```
2 4 7 55 | 68
3 1 8 10 | 22
6 0 49 12 | 67
---------------------
11 5 64 77 | 157
```

For example, the following function from example file print_table/print_table.cs, prints out a table of integers neatly, including row and column sums. It illustrates a number of things. It shows the interplay between one and two dimensional arrays, since the row and column sums are just one dimensional arrays.

Now that we are using arrays,
we can easily look at the same collection of data repeatedly.
It is possible to look at the data one time to just see its maximum
width, and then go through again and print data using a column
width that is just large enough for the longest numbers.
When looking through the data for string lengths, the row and column
structure is not important, so the code illustrates `foreach`

loops
to chug through all the data. We use the earlier trick in
Modular Multiplication Table, creating a custom format string to make columns
the right width.

The code refers once to the earlier `StringOfReps`

in Lab: Loops
for the row of dashes setting off the column sums:

```
static void PrintTableAndSums(int[,] t)
{
int[] rowSum = new int[t.GetLength(0)],
colSum = new int[t.GetLength(1)];
int sum = 0;
for (int r = 0; r < t.GetLength(0); r++) {
for (int c = 0; c < t.GetLength(1); c++) {
rowSum[r] += t[r, c];
colSum[c] += t[r, c];
}
sum += rowSum[r];
}
int width = (""+sum).Length;
foreach (int n in t) {
width = Math.Max(width, (""+n).Length);
}
foreach (int n in colSum) {
width = Math.Max(width, (""+n).Length);
}
foreach (int n in rowSum) {
width = Math.Max(width, (""+n).Length);
}
string format = "{0," + width + "} ";
for (int r = 0; r < t.GetLength(0); r++) {
for (int c = 0; c < t.GetLength(1); c++) {
Console.Write(format, t[r, c]);
}
Console.WriteLine("| " + format, rowSum[r]);
}
string reps = StringOfReps("-",(width+1)*(t.GetLength(1)+1) + 1);
Console.WriteLine(reps);
for (int c = 0; c < t.GetLength(1); c++) {
Console.Write(format, colSum[c]);
}
Console.WriteLine("| " + format, sum);
}
```

### Row and Column Numbering Exercise

Write a function that sets the values in a given rectangular array to 10 * (row index +1) + column index + 1, with the normal row and column indices, starting from 0. For example an array with two rows and five columns would end up with values below. Your method should set the values in the array, not print them out:

```
11 12 13 14 15
21 22 23 24 25
```

If there are no more than 9 rows or columns, this display gives row and column numbers neatly for the normal human counting system, starting from 1.

### Varying Column Width Exercise

Copy the project file print_table/print_table.cs to a file
`print_varying_width_table.cs`

in a projet of yours.
Edit it so that *each* column
is only as wide as it needs to be: the width for the widest entry in
that column.
The earlier data would now print as:

```
2 4 7 55 | 68
3 1 8 10 | 22
6 0 49 12 | 67
----------------
11 5 64 77 | 157
```

Calculate each of these widths *only once*.
Hint: Create an array of widths and an array of format strings.

## Advanced topic: Array of Arrays

Since you can have an array of any type, it is also possible to have an
*array of arrays*.

You could create a table with shape like the initial example in Multi-dimensional Arrays

```
int[][] table2 = new array[3][4];
```

and refer to an element still by row and column index::

```
table2[1][2] = 4;
```

The notational difference so far is just that each index in enclosed in separate square brackets, with no commas.

This takes somewhat more memory and is longer to access than the multidimensional arrays that we have been talking about with the comma-separated notation. For most uses, when you want to refer to a rectangular table of data, like above, this new version has little to offer.

There are a couple of reasons why you might want this format.

First you may have functions that operate on one dimensional arrays,
and individual rows of `table2`

are one dimensional arrays:
`table2[1]`

has type `int[]`

. On the other hand, with the
earlier `table`

with type `int[,]`

, references to part of
the array must always include a comma, so `tabel[1]`

would
not refer to a row, but would be a syntax error.

Also in an array of arrays, since each row is an independent array,
their lengths can *vary*.
Here is code to make a doubly indexed “triangular” collection
(of 0 values).
Each row must be separately created as a new array:

```
int[][] tri = new int[4][]; //create four null int[] elements
for (int i = 0; i < tri.Length; i++) { // Length 4 (rows)
tri[i] = new int[i+1]; // each row has a different length
}
```

With `tri`

constructed as above:

`tri[3, 3]`

would given a compiler error: no changing`[][]`

to`[, ]`

.`tri[3][3]`

would refer to an element.`tri[1][3]`

would given a run-time out-of-bounds error. since`tri[1]`

is an array of length 2.