1.2 · Nested Loops & 2D Lists

Goal: handle nested iteration and two-dimensional data. Recall: nested loops are explicitly 2C, not compulsory.

Why nested loops

When a single loop isn't enough — you need a loop inside another loop.

for i in range(3):
    for j in range(3):
        print(i, j)

Outputs all 9 combinations.

2D lists in Python

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

print(grid[0][2])    # 3
print(grid[2][0])    # 7

for row in grid:
    for val in row:
        print(val, end=" ")
    print()

Creating a 2D list safely

ROWS, COLS = 5, 4
matrix = [[0] * COLS for _ in range(ROWS)]

⚠️ Don't do matrix = [[0] * COLS] * ROWS — every row would share the same list reference!

Common operations

# Sum all elements
total = 0
for row in grid:
    for v in row:
        total += v

# Find max
biggest = grid[0][0]
for row in grid:
    for v in row:
        if v > biggest:
            biggest = v

# Transpose
T = [[grid[r][c] for r in range(len(grid))] for c in range(len(grid[0]))]

Worked example · Tic-tac-toe winner check

def check_winner(board):
    lines = []
    lines.extend(board)                            # rows
    lines.extend(list(zip(*board)))                # columns (zip transposes)
    lines.append([board[i][i] for i in range(3)]) # main diagonal
    lines.append([board[i][2-i] for i in range(3)]) # anti-diagonal

    for line in lines:
        if line[0] != " " and line.count(line[0]) == 3:
            return line[0]
    return None

Common student mistakes

• Sharing inner lists when initialising a 2D list.
• Mixing up grid[row][col] vs grid[col][row].
• Off-by-one in nested ranges.

Exam-style question

Q (5 marks): Write a Python function print_table(n) that prints the multiplication table for 1 to n, formatted as a square grid.

Sample answer:

def print_table(n):
    for i in range(1, n + 1):
        for j in range(1, n + 1):
            print(f"{i*j:>4}", end="")
        print()

print_table(5)

Output:

   1   2   3   4   5
   2   4   6   8  10
   3   6   9  12  15
   4   8  12  16  20
   5  10  15  20  25

Key takeaways

• Use nested loops for combinations.
• Use list comprehensions for 2D init.

➡️ Next: 1.3 Sub-programs & Parameters