Nested Loops — Loops Inside Loops

Real-world analogy

What is it?

Nested loops are loops placed inside other loops. The inner loop completes all its iterations for every single iteration of the outer loop. They are essential for working with 2D structures like grids, tables, and patterns, and appear frequently in competitive programming.

Real-world relevance

Nested loops appear in CP problems involving grids, matrices, pattern printing, brute-force pair checking, and 2D array processing. Many beginner CP contests include pattern-printing problems that require nested loops. Understanding them is also the first step toward grasping time complexity.

Key points

• What Are Nested Loops? — A nested loop is a loop inside another loop. The outer loop runs, and for each iteration of the outer loop, the inner loop runs completely from start to finish. If the outer loop runs R times and the inner loop runs C times, the inner body executes R × C times total.
• Rows and Columns — The most common way to think about nested loops: the outer loop controls rows (going down) and the inner loop controls columns (going across). After the inner loop finishes one row, you print a newline and the outer loop moves to the next row.
• Rectangle Star Pattern — To print a 4×5 rectangle of stars: outer loop i from 1 to 4 (rows), inner loop j from 1 to 5 (columns), print '*' in the inner loop, print endl after the inner loop. You get 4 rows of 5 stars each.
• Right Triangle Pattern — For a right triangle, the inner loop depends on the outer loop variable. Row 1 prints 1 star, row 2 prints 2 stars, row i prints i stars. Use for(int j = 1; j <= i; j++) as the inner loop. This connection between outer and inner loop is key.
• Inverted Triangle Pattern — Flip the triangle upside down by making the inner loop count from i to n: for(int j = i; j <= n; j++). Row 1 prints n stars, row 2 prints n-1 stars, and so on. Alternatively, the inner loop can run from 1 to n-i+1.
• Multiplication Table — A multiplication table is a perfect nested loop example. Outer loop i from 1 to n (rows), inner loop j from 1 to n (columns), print i*j. Each cell shows the product of its row and column number.
• Time Complexity Warning — If both loops go up to N, the inner body runs N × N = N² times. For N = 1000, that is 1 million operations (fast). For N = 100,000, that is 10 billion operations (too slow!). Always think about how many times the inner body runs in CP.
• Using Different Variables — Always use different variable names for nested loops — typically i for outer and j for inner. Using the same variable name causes the inner loop to overwrite the outer loop variable, creating confusing bugs.

Code example

#include <bits/stdc++.h>
using namespace std;

int main() {
    int n;
    cin >> n;

    // Rectangle of stars (n rows, n columns)
    cout << "Rectangle:" << endl;
    for (int i = 1; i <= n; i++) {
        for (int j = 1; j <= n; j++) {
            cout << "* ";
        }
        cout << endl;
    }

    // Right triangle
    cout << "Right Triangle:" << endl;
    for (int i = 1; i <= n; i++) {
        for (int j = 1; j <= i; j++) {
            cout << "* ";
        }
        cout << endl;
    }

    // Multiplication table
    cout << "Multiplication Table:" << endl;
    for (int i = 1; i <= n; i++) {
        for (int j = 1; j <= n; j++) {
            cout << i * j << "\t";
        }
        cout << endl;
    }

    return 0;
}

Line-by-line walkthrough

1. 1. We read n to control the size of our patterns.
2. 2. Rectangle: outer loop i goes from 1 to n, controlling which row we are on.
3. 3. Inner loop j goes from 1 to n, printing one star per column.
4. 4. After the inner loop finishes a row, cout << endl moves to the next line.
5. 5. Right triangle: the inner loop goes from 1 to i (not n), so row 1 gets 1 star, row 2 gets 2, etc.
6. 6. This is the key idea — the inner loop limit depends on the outer loop variable i.
7. 7. Multiplication table: inner loop prints i * j, which gives the product of the row and column.
8. 8. The \t prints a tab character to align the columns neatly.
9. 9. For n = 4, the rectangle has 4 × 4 = 16 stars, the triangle has 1+2+3+4 = 10 stars.
10. 10. The total iterations grow as n², so large n values will take noticeably longer.

Spot the bug

#include <bits/stdc++.h>
using namespace std;

int main() {
    int n = 4;
    // Print right triangle
    for (int i = 1; i <= n; i++) {
        for (int i = 1; i <= i; i++) {
            cout << "* ";
        }
        cout << endl;
    }
    return 0;
}

Explain like I'm 5

Fun fact

Hands-on challenge

More resources

• Nested Loops & Star Patterns in C++ (YouTube)
• Nested Loops — Learn C++ (LearnCpp.com)
• Pattern Problems (HackerRank)