Two-Dimensional Data

A list holds a line of things. A great deal of real data is not a line: a seating chart, a spreadsheet, a chessboard, an image, a distance table between cities. For those you need a grid, and a grid is a list whose elements are themselves lists.

Building and reaching in

grid = [
    [3, 1, 4],
    [1, 5, 9],
    [2, 6, 5],
]
 
print(grid[1][2])      # 9 — row 1, column 2
grid[0][0] = 7         # top-left becomes 7

Row first, then column. That order is a convention, not a law of nature, and half of all grid bugs are the two indexes swapped. Say it out loud every time: row, then column.

Building an empty grid needs care:

rows = 3
columns = 4
grid = []
for row_number in range(rows):
    row = []
    for column_number in range(columns):
        row.append(0)
    grid.append(row)

The long way is the safe way. The tempting short version, [[0] * columns] * rows, produces three references to the same row — change one and all three change. It is the single most common two-dimensional trap in Python, and it fails silently.

Processing every element

The pattern is a loop inside a loop, and the outer one is the rows:

total = 0
for row in grid:
    for value in row:
        total = total + value

When you need the positions as well as the values, loop over the indexes instead:

for row_number in range(len(grid)):
    for column_number in range(len(grid[row_number])):
        if grid[row_number][column_number] == 0:
            print(f"empty seat at row {row_number}, column {column_number}")

The four traversals worth knowing

You need	The shape
Every element	Loop rows, loop columns
One row	grid[row_number] — it is just a list
One column	Loop the rows, take the same index from each
A neighbour	row ± 1, column ± 1 — and check the edges before you look

That last one is where grids get interesting and where they crash. A cell on the top row has no neighbour above it, so every neighbour check needs a bounds test first:

if row_number > 0 and grid[row_number - 1][column_number] == 1:

Games of life, flood fills, image blurs, and maze solvers are all the same shape: visit each cell, look at its neighbours, decide something.

When should a grid be something else?

When the rows mean different things, use a list of objects rather than a grid of numbers — Objects and Classes exists for exactly that. When most cells are empty, a dictionary keyed by (row, column) costs far less memory than a grid full of zeros, which is a judgement call Choosing a Data Structure walks through.

Curriculum connection

A3.5

create algorithms to process elements in two-dimensional arrays (e.g., multiply each element by a constant, interchange elements, multiply matrices, process pixels in an image);

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A3.1

demonstrate the ability to read from, and write to, an external file (e.g., text file, binary file, database, XML file) from within a computer program;

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