Multi-dimensional lists

Multi-dimensional collection of data

Multi-dimensional Lists

In the previous lesson we worked with 1D lists — a single row of values. Now let's go one step further: a multi-dimensional list is a list where each element is itself a list. This gives us a table of rows and columns, which in programming is called a matrix.

Creating a 2D List

This is a 3×3 matrix. matrix is a list of 3 rows, and each row is a list of 3 integers.

Accessing Elements

To access an element you need two indices: matrix[row][col]. Both start at 0:

You can also modify any element the same way:

Dimensions

len(matrix) gives the number of rows. len(matrix[0]) gives the number of columns:

Iterating Over a 2D List

Use nested loops — the outer loop over rows, the inner loop over columns:

Output:

If you only need values and don't care about indices, you can iterate directly:

Or print each row in one shot using *:

Creating a 2D List with Loops

For a fixed small matrix you can write it out manually. But for larger or dynamic sizes, build it with a loop.

The correct way — list comprehension

The wrong way — do NOT do this

This looks correct but creates rows references to the same inner list. Modifying one row modifies all of them:

Always use the list comprehension form to create 2D lists.

Reading a Matrix from Input

The standard CP format: first line is n and m, then n lines each with m integers:

Or more compactly:

Practical Examples

Filling with sequential numbers

Output:

Finding the maximum element and its position

Sum of each row

Transposing a matrix

The transpose of a matrix swaps rows and columns — matrix[i][j] becomes transposed[j][i]:

Diagonal elements

For a square n×n matrix, the main diagonal is where i == j:

The secondary diagonal is where i + j == n - 1:

Beyond 2D

The same idea extends to 3D and higher — a list of matrices is a 3D structure: