Nested loops in C++ - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is a nested loop in C++?

A nested loop is a loop inside another loop. The inner loop runs completely every time the outer loop runs once.

beginner

How many times will the inner loop run in this code?

for(int i = 0; i < 3; i++) {
  for(int j = 0; j < 2; j++) {
    // inner loop body
  }
}

The inner loop runs 2 times for each of the 3 outer loop runs, so 3 × 2 = 6 times in total.

beginner

Why do we use nested loops?

We use nested loops to work with multi-dimensional data, like tables or grids, or to repeat tasks inside other repeated tasks.

intermediate

What happens if the inner loop depends on the outer loop variable?

The inner loop can change how many times it runs based on the outer loop variable, allowing more flexible patterns.

beginner

Write a nested loop to print a 3x3 grid of stars (*) in C++.

for(int i = 0; i < 3; i++) {
  for(int j = 0; j < 3; j++) {
    std::cout << "* ";
  }
  std::cout << std::endl;
}

How many times does the inner loop run in this code?

for(int i = 0; i < 4; i++) {
  for(int j = 0; j < 3; j++) {
    // code
  }
}

A 12

B 7

C 4

D 3

The inner loop runs 3 times for each of the 4 outer loop runs, so 4 × 3 = 12 times.

What is the output of this nested loop?

for(int i = 1; i <= 2; i++) {
  for(int j = 1; j <= 2; j++) {
    std::cout << i+j << " ";
  }
  std::cout << std::endl;
}

A 1 1 \n 2 2

B 1 2 \n 2 3

C 2 3 \n 3 4

D 3 4 \n 4 5

For i=1: j=1 (1+1=2), j=2 (1+2=3); for i=2: j=1 (2+1=3), j=2 (2+2=4).

Which statement is true about nested loops?

A Inner loop runs completely for each outer loop iteration.

B Outer loop runs completely for each inner loop iteration.

C Both loops run only once.

D Nested loops cannot be used with for loops.

The inner loop finishes all its iterations every time the outer loop runs once.

What is the time complexity of two nested loops each running n times?

A O(n)

B O(n^2)

C O(1)

D O(log n)

Two nested loops each running n times result in n × n = n² operations.

How can nested loops be useful in real life?

A To avoid repeating tasks.

B To print a single number once.

C To run only one loop.

D To process rows and columns in a table.

Nested loops help handle multi-dimensional data like tables or grids.

Explain what nested loops are and give a simple example in C++.

Think about loops inside loops and how many times the inner loop runs.

Describe a real-world scenario where nested loops would be useful.

Imagine rows and columns or a chessboard.

Practice

1. What does a nested loop in C++ mean?
for (int i = 0; i < 3; i++) {
for (int j = 0; j < 2; j++) {
// code
}
}

easy

A. Two loops running one after another

B. A loop inside another loop

C. A loop that runs only once

D. A loop that never ends

Solution

1. Step 1: Understand the code structure

   The code shows one for loop inside another for loop, which means nested loops.

2. Step 2: Define nested loops

   Nested loops mean one loop runs inside another loop's block of code.

3. Final Answer:

   A loop inside another loop -> Option B

4. Quick Check:

   Nested loop = loop inside loop [OK]

Hint: Look for one loop inside another's braces [OK]

Common Mistakes:

• Thinking loops run one after another, not inside
• Confusing nested loops with single loops
• Assuming nested loops run only once

2. Which of the following is the correct syntax for a nested loop in C++?

easy

A. for(int i=0; i<3; i++) { for(int j=0; j<2; j++) { /* code */ } }

B. for i in range(3): for j in range(2): /* code */

C. while(i<3) { while(j<2) /* code */ }

D. loop(i=0; i<3; i++) { loop(j=0; j<2; j++) { /* code */ } }

Solution

1. Step 1: Identify C++ loop syntax

   C++ uses for(initialization; condition; increment) syntax for loops.

2. Step 2: Check each option

   for i in range(3): for j in range(2): /* code */ uses Python syntax, invalid in C++.
   for(int i=0; i<3; i++) { for(int j=0; j<2; j++) { /* code */ } } uses correct C++ syntax with nested for loops.
   while(i<3) { while(j<2) /* code */ } uses while loops missing initializations and increments.
   loop(i=0; i<3; i++) { loop(j=0; j<2; j++) { /* code */ } } uses invalid loop keyword.

3. Final Answer:

   for(int i=0; i<3; i++) { for(int j=0; j<2; j++) { /* code */ } } -> Option A

4. Quick Check:

   C++ nested loops use for(init; cond; inc) [OK]

Hint: Remember C++ loops use for(init; cond; inc) syntax [OK]

Common Mistakes:

• Using Python or other language syntax in C++
• Missing semicolons in for loop header
• Using wrong keywords like 'loop'

3. What is the output of this C++ code?

for(int i = 1; i <= 2; i++) {
  for(int j = 1; j <= 3; j++) {
    std::cout << i*j << " ";
  }
  std::cout << std::endl;
}

medium

A. 3 6 9 \n 6 12 18

B. 1 2 3 4 5 6

C. 1 2 3 \n 2 4 6

D. 1 1 1 \n 2 2 2

Solution

1. Step 1: Trace outer loop values

   Outer loop runs i=1 and i=2.

2. Step 2: Calculate inner loop outputs

   For i=1, j=1 to 3: outputs 1*1=1, 1*2=2, 1*3=3.
   For i=2, j=1 to 3: outputs 2*1=2, 2*2=4, 2*3=6.

3. Final Answer:

   1 2 3 2 4 6 -> Option C

4. Quick Check:

   Multiply i and j in nested loops [OK]

Hint: Multiply outer and inner loop counters for output [OK]

Common Mistakes:

• Ignoring the newline after inner loop
• Adding all numbers instead of printing products
• Confusing loop ranges

4. Find the error in this nested loop code:

for(int i = 0; i < 3; i++) {
  for(int j = 0; j < 3; i++) {
    std::cout << i+j << " ";
  }
  std::cout << std::endl;
}

medium

A. Inner loop increments i instead of j

B. Outer loop condition is wrong

C. Missing semicolon after std::cout

D. No error, code runs fine

Solution

1. Step 1: Check inner loop increment

   Inner loop header uses i++ instead of j++, causing infinite loop or wrong behavior.

2. Step 2: Identify correct increment variable

   Inner loop should increment j to progress through its range.

3. Final Answer:

   Inner loop increments i instead of j -> Option A

4. Quick Check:

   Inner loop must increment its own variable [OK]

Hint: Check loop increments match loop variables [OK]

Common Mistakes:

• Incrementing wrong variable in inner loop
• Assuming code runs without checking increments
• Confusing outer and inner loop variables

5. You want to print a 4x4 multiplication table using nested loops in C++. Which code snippet correctly achieves this?

hard

A. for(int i=1; i<=4; i++) { for(int j=1; j<=4; j++) { std::cout << i-j << " "; } std::cout << std::endl; }

B. for(int i=0; i<4; i++) { for(int j=0; j<4; j++) { std::cout << i+j << " "; } std::cout << std::endl; }

C. for(int i=1; i<=4; i++) { for(int j=1; j<=4; j++) { std::cout << i+j << " "; } std::cout << std::endl; }

D. for(int i=1; i<=4; i++) { for(int j=1; j<=4; j++) { std::cout << i*j << " "; } std::cout << std::endl; }

Solution

1. Step 1: Understand multiplication table logic

   Each cell should print the product of row and column numbers (i*j).

2. Step 2: Check each option's output logic

   for(int i=1; i<=4; i++) { for(int j=1; j<=4; j++) { std::cout << i*j << " "; } std::cout << std::endl; } prints i*j correctly.
   for(int i=0; i<4; i++) { for(int j=0; j<4; j++) { std::cout << i+j << " "; } std::cout << std::endl; } prints sum with zero-based indices.
   for(int i=1; i<=4; i++) { for(int j=1; j<=4; j++) { std::cout << i+j << " "; } std::cout << std::endl; } prints sum with one-based indices.
   for(int i=1; i<=4; i++) { for(int j=1; j<=4; j++) { std::cout << i-j << " "; } std::cout << std::endl; } prints difference.

3. Final Answer:

   for(int i=1; i<=4; i++) { for(int j=1; j<=4; j++) { std::cout << i*j << " "; } std::cout << std::endl; } -> Option D

4. Quick Check:

   Multiplication table = print i*j in nested loops [OK]

Hint: Multiply loop counters for multiplication table [OK]

Common Mistakes:

• Using addition or subtraction instead of multiplication
• Starting loops at 0 instead of 1 for table
• Not printing newline after each row