Nested loops

Nested loops and practical examples for them.

Nested Loops

A nested loop is simply a loop placed inside another loop. For every single iteration of the outer loop, the inner loop runs completely from start to finish. This makes nested loops the natural tool for working with grids, tables, pairs of values, and any problem that requires two independent or dependent counters.

Basic Structure

Output:

The outer loop runs 3 times. Each time, the inner loop runs 2 times completely. Total iterations: 3 × 2 = 6.

Multiplication Table

A classic use of nested loops — for each row i, print i * j for every column j:

Output:

print() with no arguments at the end of the outer loop moves to the next line after each row.

Printing Patterns

Nested loops are perfect for printing shapes. The outer loop controls rows, the inner loop controls columns.

Rectangle of stars

Output:

Right triangle

Output:

The inner loop runs i times on row i, creating the triangle shape.

Inverted triangle

Output:

Iterating Over All Pairs

Nested loops let you consider every combination of two values. A common competitive programming task: find all pairs (a, b) where both are in range and satisfy some condition.

For n = 10:

Prime Number Check

To check if a number n is prime, try dividing it by every number from 2 to n-1. If none divide evenly, it is prime:

Now use nested loops to print all primes up to some limit:

For limit = 30:

Time Complexity

Each level of nesting multiplies the number of iterations. If the outer loop runs n times and the inner loop runs n times, the total is n² iterations — we say the time complexity is O(n²). You don't need to master this concept now, but it is good to be aware of it:

With n = 10,000 this would already be 100,000,000 iterations — likely too slow for a competitive programming problem with a 1-second time limit. Always think about how many total iterations your nested loops will perform.

A triple nested loop would be O(n³):

break in Nested Loops

break only exits the innermost loop it is placed in, not all loops at once: