Nested Loops and Grid Traversal

15 min · Beginner

When dealing with two-dimensional data such as tables, matrices, or screen coordinates, we nest one loop inside another.

Inner and outer loops

Nested loop is a loop placed inside the body of another loop. For every round of the outer loop, the inner loop runs all of its rounds from the start.

For every single cycle of the outer loop, the inner loop completes all of its iterations.

Python

for i in range(1, 3):    for j in range(1, 4):        print(f"({i}, {j})", end=" ")    print()

Example 1 · Counting shifts in a roster

Python

rounds = 0for day in range(1, 4):    for shift in range(1, 3):        rounds += 1print(f"Total shifts: {rounds}")

Output

Total shifts: 6

What this code does

There are 3 days, and each day has 2 shifts.
The inner body runs 3 * 2 = 6 times, so rounds ends at 6.

The inner loop runs 3 times for i=1 and 3 times for i=2, producing a 2 * 3 coordinate grid.

Generating multiplication tables

Nested loops calculate tabular products by multiplying row and column indices.

Python

for row in range(1, 4):    for col in range(1, 4):        print(f"{row * col:2}", end=" ")    print()

Example 2 · Times table grid

Python

for row in range(1, 4):    for col in range(1, 6):        print(f"{row * col:3}", end="")    print()

Output

  1  2  3  4  5
  2  4  6  8 10
  3  6  9 12 15

What this code does

{row * col:3} pads each number to a width of 3, so the columns line up.
end="" keeps the numbers of one row on the same line.
The empty print() after the inner loop starts a new line for the next row.

The :2 format specifier aligns numbers in neat columns.

Pattern printing

Pattern is a shape drawn with characters. The outer loop picks the row, and the inner loop or a string repeat decides what that row contains.

Generate triangles and pyramids by making the inner loop range depend on the outer loop index.

Python

for r in range(1, 4):    print("*" * r)

Example 3 · Centred pyramid

Python

rows = 4for r in range(1, rows + 1):    print(" " * (rows - r) + "*" * (2 * r - 1))

Output

   *
  ***
 *****
*******

What this code does

Row r has rows - r spaces and then 2 * r - 1 stars.
The star count grows by 2 each row, which gives the pyramid its shape.
" " * n repeats a space n times, so no inner loop is needed.

Example 4 · Number triangle

Python

size = 3for r in range(1, size + 1):    for c in range(1, r + 1):        print(c, end=" ")    print()

Output

1 
1 2 
1 2 3

What this code does

Prints a number triangle where row r prints numbers from 1 to r.
Row 1 prints 1; row 2 prints 1 2; row 3 prints 1 2 3.

In Python, string multiplication "*" * r often elegantly replaces manual inner loops for simple character patterns.

Next step

Check your understanding

10 quick questions

Nested Loops and Grid Traversal

15 min · Beginner

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When dealing with two-dimensional data such as tables, matrices, or screen coordinates, we nest one loop inside another.

Inner and outer loops

Nested loop is a loop placed inside the body of another loop. For every round of the outer loop, the inner loop runs all of its rounds from the start.

For every single cycle of the outer loop, the inner loop completes all of its iterations.

Python

for i in range(1, 3):    for j in range(1, 4):        print(f"({i}, {j})", end=" ")    print()

Example 1 · Counting shifts in a roster

Python

rounds = 0for day in range(1, 4):    for shift in range(1, 3):        rounds += 1print(f"Total shifts: {rounds}")

Output

Total shifts: 6

What this code does

There are 3 days, and each day has 2 shifts.
The inner body runs 3 * 2 = 6 times, so rounds ends at 6.

The inner loop runs 3 times for i=1 and 3 times for i=2, producing a 2 * 3 coordinate grid.

Generating multiplication tables

Nested loops calculate tabular products by multiplying row and column indices.

Python

for row in range(1, 4):    for col in range(1, 4):        print(f"{row * col:2}", end=" ")    print()

Example 2 · Times table grid

Python

for row in range(1, 4):    for col in range(1, 6):        print(f"{row * col:3}", end="")    print()

Output

  1  2  3  4  5
  2  4  6  8 10
  3  6  9 12 15

What this code does

{row * col:3} pads each number to a width of 3, so the columns line up.
end="" keeps the numbers of one row on the same line.
The empty print() after the inner loop starts a new line for the next row.

The :2 format specifier aligns numbers in neat columns.

Pattern printing

Pattern is a shape drawn with characters. The outer loop picks the row, and the inner loop or a string repeat decides what that row contains.

Generate triangles and pyramids by making the inner loop range depend on the outer loop index.

Python

for r in range(1, 4):    print("*" * r)

Example 3 · Centred pyramid

Python

rows = 4for r in range(1, rows + 1):    print(" " * (rows - r) + "*" * (2 * r - 1))

Output

   *
  ***
 *****
*******

What this code does

Row r has rows - r spaces and then 2 * r - 1 stars.
The star count grows by 2 each row, which gives the pyramid its shape.
" " * n repeats a space n times, so no inner loop is needed.

Example 4 · Number triangle

Python

size = 3for r in range(1, size + 1):    for c in range(1, r + 1):        print(c, end=" ")    print()

Output

1 
1 2 
1 2 3

What this code does

Prints a number triangle where row r prints numbers from 1 to r.
Row 1 prints 1; row 2 prints 1 2; row 3 prints 1 2 3.

In Python, string multiplication "*" * r often elegantly replaces manual inner loops for simple character patterns.

Next step

Check your understanding

10 quick questions