Nested loops & 2-D lists

A loop inside a loop

• You can put one loop inside another loop.
• For every pass of the outer loop, the inner loop runs fully.
• So an outer of 2 and an inner of 3 runs the body 2 × 3 = 6 times.

for row in range(2):
    for col in range(3):
        print(row, col)

A list of lists

• A 2-D list is a list whose items are themselves lists.
• It models a grid or table: rows of columns.
• Reach one cell with two indexes: grid[row][col].

grid = [[1, 2], [3, 4]]
print(grid[0][1])
print(grid[1][0])

Loop over a grid

• Use a nested loop to visit every cell.
• The outer loop walks the rows; the inner loop walks the columns.
• for row in grid: gives one row (a list) at a time.

grid = [[1, 2], [3, 4]]
for row in grid:
    for value in row:
        print(value)

In Cambridge pseudocode

• We model the exam's fixed-size 2-D array with a Python list of lists. Cambridge arrays declare bounds and an element type; Python rows can have different lengths. Read the declared bounds rather than assuming 1 in every program.

DECLARE Grid : ARRAY[1:2, 1:2] OF INTEGER
DECLARE R : INTEGER
DECLARE C : INTEGER
FOR R ← 1 TO 2
    FOR C ← 1 TO 2
        Grid[R, C] ← (R - 1) * 2 + C
        OUTPUT Grid[R, C]
    NEXT C
NEXT R

The pseudocode assigns each cell before reading it. It prints 1, 2, 3, 4, matching the Python grid above. A declaration alone is not a promise that every cell already contains zero.

Common mistakes

• The inner loop finishes all its turns for each single turn of the outer loop.
• Index a grid row first, then column: grid[row][col].
• Repeating a mutable row repeats its reference: row = [0, 0]; grid = [row, row] shares one row. Changing grid[0][0] also changes grid[1][0]. Create a fresh row on each outer-loop pass.
• Iterate over the values of each Python row to handle different row lengths and empty rows. A total or count starts at zero and stays zero for an empty grid. Return the result when the algorithm is wrapped in a function.

Now you try

• Use a nested loop in each task.
• Press Check answer to test your code.