Nested Lists and Matrices

15 min · Beginner

A list containing other lists is a nested list, ideal for representing matrices, game boards, and tables. Beware of Python's reference multiplication behavior.

2D lists and coordinate access

Nested list is a list whose items are lists. It models a table: the outer list holds the rows, each row is an inner list, and matrix[row][col] reads one cell.

Access items using row and column indices: matrix[row][col].

Python

1grid = [2    [1, 2, 3],3    [4, 5, 6],4    [7, 8, 9]5]6print(grid[1][2])

Example 1 · Adding up every cell

Python

1matrix = [2    [10, 20],3    [30, 40]4]5total_sum = 06for row in matrix:7    for val in row:8        total_sum += val9
10print(f"Matrix sum: {total_sum}")

Output

Matrix sum: 100

What this code does

The outer loop takes one row at a time. The inner loop takes each value in that row.
All 4 cells are added: 10 + 20 + 30 + 40 = 100.

grid[1] accesses the second row [4, 5, 6], and [2] accesses the third column element 6.

The [[0]N]N trap

Writing [[0] * 3] * 3 creates three references to the exact same row list in memory.

Python

bad_grid = [[0] * 3] * 3bad_grid[0][0] = 9print(bad_grid)

Two ways to build a 3 by 3 grid. With [[0] * 3] * 3, the slots grid[0], grid[1] and grid[2] all point to one row, so changing one cell changes every row. With a list comprehension, each slot has its own row.

Example 2 · Shared rows

Python

seats = [["free"] * 3] * 2seats[0][1] = "booked"print(seats)

Output

[['free', 'booked', 'free'], ['free', 'booked', 'free']]

What this code does

* 2 repeats a reference to the same row, it does not build a second row.
So the change made through seats[0] also shows in seats[1].

Modifying bad_grid[0][0] changes the first element in all three rows ([[9, 0, 0], [9, 0, 0], [9, 0, 0]]) because all three rows point to the same memory object!

Creating grids properly with comprehensions

Always use a list comprehension to create distinct, independent row lists.

Python

good_grid = [[0] * 3 for _ in range(3)]good_grid[0][0] = 9print(good_grid)

Example 3 · Row totals with a comprehension

Python

sales = [[120, 80, 100], [90, 60, 110]]row_totals = [sum(row) for row in sales]first_column = [row[0] for row in sales]print(row_totals)print(first_column)

Output

[300, 260]
[120, 90]

What this code does

Looping over sales gives one row at a time, so sum(row) adds that row.
row[0] picks the first cell of every row, which is the first column.

Each iteration of the comprehension instantiates a fresh row list in memory, modifying only good_grid[0][0].

Copying a nested list

Shallow copy is a new outer list whose items are the same inner lists as before. Changing a cell through the copy also changes the original. copy.deepcopy() copies the inner lists too.

A copy of a nested list can still share its rows. Use copy.deepcopy() when the copy must be fully independent.

Python

1import copy2
3grid = [[1, 2], [3, 4]]4shallow = grid.copy()5deep = copy.deepcopy(grid)6grid[0][0] = 997print(shallow)8print(deep)

Example 4 · A table copy that stays independent

Python

table = [[1, 2], [3, 4]]safe = [row[:] for row in table]table[0][0] = 50print(table)print(safe)

Output

[[50, 2], [3, 4]]
[[1, 2], [3, 4]]

What this code does

row[:] copies each row, so safe has its own rows.
The change to table does not reach safe.

shallow has its own outer list but shares the rows, so it shows 99. deep copied the rows too, so it keeps the old value.

Next step

Check your understanding

9 quick questions

Nested Lists and Matrices

15 min · Beginner

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A list containing other lists is a nested list, ideal for representing matrices, game boards, and tables. Beware of Python's reference multiplication behavior.

2D lists and coordinate access

Nested list is a list whose items are lists. It models a table: the outer list holds the rows, each row is an inner list, and matrix[row][col] reads one cell.

Access items using row and column indices: matrix[row][col].

Python

1grid = [2    [1, 2, 3],3    [4, 5, 6],4    [7, 8, 9]5]6print(grid[1][2])

Example 1 · Adding up every cell

Python

1matrix = [2    [10, 20],3    [30, 40]4]5total_sum = 06for row in matrix:7    for val in row:8        total_sum += val9
10print(f"Matrix sum: {total_sum}")

Output

Matrix sum: 100

What this code does

The outer loop takes one row at a time. The inner loop takes each value in that row.
All 4 cells are added: 10 + 20 + 30 + 40 = 100.

grid[1] accesses the second row [4, 5, 6], and [2] accesses the third column element 6.

The [[0]N]N trap

Writing [[0] * 3] * 3 creates three references to the exact same row list in memory.

Python

bad_grid = [[0] * 3] * 3bad_grid[0][0] = 9print(bad_grid)

Example 2 · Shared rows

Python

seats = [["free"] * 3] * 2seats[0][1] = "booked"print(seats)

Output

[['free', 'booked', 'free'], ['free', 'booked', 'free']]

What this code does

* 2 repeats a reference to the same row, it does not build a second row.
So the change made through seats[0] also shows in seats[1].

Modifying bad_grid[0][0] changes the first element in all three rows ([[9, 0, 0], [9, 0, 0], [9, 0, 0]]) because all three rows point to the same memory object!

Creating grids properly with comprehensions

Always use a list comprehension to create distinct, independent row lists.

Python

good_grid = [[0] * 3 for _ in range(3)]good_grid[0][0] = 9print(good_grid)

Example 3 · Row totals with a comprehension

Python

sales = [[120, 80, 100], [90, 60, 110]]row_totals = [sum(row) for row in sales]first_column = [row[0] for row in sales]print(row_totals)print(first_column)

Output

[300, 260]
[120, 90]

What this code does

Looping over sales gives one row at a time, so sum(row) adds that row.
row[0] picks the first cell of every row, which is the first column.

Each iteration of the comprehension instantiates a fresh row list in memory, modifying only good_grid[0][0].

Copying a nested list

Shallow copy is a new outer list whose items are the same inner lists as before. Changing a cell through the copy also changes the original. copy.deepcopy() copies the inner lists too.

A copy of a nested list can still share its rows. Use copy.deepcopy() when the copy must be fully independent.

Python

1import copy2
3grid = [[1, 2], [3, 4]]4shallow = grid.copy()5deep = copy.deepcopy(grid)6grid[0][0] = 997print(shallow)8print(deep)

Example 4 · A table copy that stays independent

Python

table = [[1, 2], [3, 4]]safe = [row[:] for row in table]table[0][0] = 50print(table)print(safe)

Output

[[50, 2], [3, 4]]
[[1, 2], [3, 4]]

What this code does

row[:] copies each row, so safe has its own rows.
The change to table does not reach safe.

shallow has its own outer list but shares the rows, so it shows 99. deep copied the rows too, so it keeps the old value.

Next step

Check your understanding

9 quick questions

2D lists and coordinate access

What this code does

The [[0]*N]*N trap

What this code does

Creating grids properly with comprehensions

What this code does

Copying a nested list

What this code does

2D lists and coordinate access

What this code does

The [[0]*N]*N trap

What this code does

Creating grids properly with comprehensions

What this code does

Copying a nested list

What this code does

The [[0]N]N trap

The [[0]N]N trap