Lesson 5.4: Nested Loops

What Are Nested Loops?

A nested loop is a loop inside another loop. The inner loop runs completely for each iteration of the outer loop.

for i in range(3):         # Outer loop: runs 3 times
    for j in range(2):     # Inner loop: runs 2 times PER outer iteration
        print(f"i={i}, j={j}")

The inner loop ran 2 times for each of the 3 outer iterations, giving us 3 × 2 = 6 total prints. This multiplication is key to understanding nested loops.

Tracing Nested Loops

To understand nested loops, trace through them step by step. Write down the values of each variable at each step.

# Trace this code carefully
for row in range(1, 4):
    for col in range(1, 4):
        print(f"{row}x{col}={row*col}", end="  ")
    print()  # New line after each row

Printing Patterns

Nested loops are commonly used to create text-based patterns.

for i in range(1, 6):
    for j in range(i):
        print("* ", end="")
    print()

rows = 4
cols = 6

for i in range(rows):
    for j in range(cols):
        print("* ", end="")
    print()

for i in range(1, 6):
    for j in range(1, i + 1):
        print(j, end=" ")
    print()

Multiplication Table

A classic nested loop example: generating a full multiplication table.

# Multiplication table (1-5)
print("    ", end="")
for i in range(1, 6):
    print(f"{i:4}", end="")
print()
print("    " + "----" * 5)

for i in range(1, 6):
    print(f"{i:2} |", end="")
    for j in range(1, 6):
        print(f"{i*j:4}", end="")
    print()

Working with 2D Data

Nested loops are essential when working with data organized in rows and columns, like a grid or a table.

# Student scores: each inner list is one student's scores
all_scores = [
    [85, 90, 78],   # Student 1
    [92, 88, 95],   # Student 2
    [76, 82, 89],   # Student 3
]

for i in range(len(all_scores)):
    total = 0
    for score in all_scores[i]:
        total += score
    avg = total / len(all_scores[i])
    print(f"Student {i+1} average: {avg:.1f}")

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

target = 5
found = False

for row in range(len(grid)):
    for col in range(len(grid[row])):
        if grid[row][col] == target:
            print(f"Found {target} at row {row}, col {col}")
            found = True

if not found:
    print(f"{target} not found")

Performance Considerations

Nested loops multiply the number of operations. A loop that runs 100 times inside a loop that runs 100 times means 10,000 total iterations. Be aware of this when working with large data.

# Counting total iterations
count = 0

for i in range(10):
    for j in range(10):
        count += 1

print(f"Total iterations: {count}")  # 100