For loops in MATLAB - Time & Space Complexity

Time Complexity: For loops

O(n)

Understanding Time Complexity

When we use for loops in MATLAB, the program repeats some actions many times. Understanding how this repetition affects the time it takes to run helps us write better code.

We want to know: how does the running time grow when the loop runs more times?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

for i = 1:n
    disp(i);
end
    

This code prints numbers from 1 to n, repeating the display action n times.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: The disp(i) command inside the for loop.
• How many times: It runs exactly n times, once for each number from 1 to n.

How Execution Grows With Input

As n gets bigger, the number of times the loop runs grows the same way.

Input Size (n)	Approx. Operations
10	10
100	100
1000	1000

Pattern observation: If you double n, the number of operations also doubles. The growth is steady and direct.

Final Time Complexity

Time Complexity: O(n)

This means the time to run the code grows in a straight line with the size of n.

Common Mistake

[X] Wrong: "The loop runs faster because it just prints numbers."

[OK] Correct: Even simple actions inside the loop add up. The total time depends on how many times the loop runs, not just what it does each time.

Interview Connect

Knowing how loops affect running time helps you explain your code clearly and shows you understand how programs work as they grow.

Self-Check

"What if we added a second nested for loop inside the first? How would the time complexity change?"

Practice

1. What does a for loop do in MATLAB?

easy

A. Stops the program immediately

B. Runs commands only once

C. Creates a new variable

D. Repeats a set of commands a fixed number of times

Solution

1. Step 1: Understand the purpose of a for loop

   A for loop is designed to repeat commands multiple times based on a range or list.

2. Step 2: Compare options with the definition

   Only Repeats a set of commands a fixed number of times correctly describes repeating commands a fixed number of times.

3. Final Answer:

   Repeats a set of commands a fixed number of times -> Option D

4. Quick Check:

   For loop = repeat commands [OK]

Hint: For loops repeat commands multiple times [OK]

Common Mistakes:

• Thinking for loops run only once
• Confusing for loops with if statements
• Believing for loops stop the program

2. Which of the following is the correct syntax for a for loop in MATLAB?

easy

A. for i = 1:5
disp(i)
end

B. for (i = 1; i <= 5; i++)
disp(i)
end

C. loop i from 1 to 5
disp(i)
end

D. for i in range(1,5):
disp(i)

Solution

1. Step 1: Identify MATLAB for loop syntax

   MATLAB uses 'for variable = start:end' and ends with 'end'.

2. Step 2: Check each option

   for i = 1:5 disp(i) end matches MATLAB syntax. Options B, C, and D use other languages' syntax.

3. Final Answer:

   for i = 1:5\n disp(i)\nend -> Option A

4. Quick Check:

   MATLAB for loop = for i = 1:5 ... end [OK]

Hint: MATLAB for loops use 'for var = start:end' and end with 'end' [OK]

Common Mistakes:

• Using parentheses like C or JavaScript
• Using Python or other language syntax
• Forgetting the 'end' keyword

3. What is the output of this MATLAB code?

sum = 0;
for i = 1:3
  sum = sum + i;
end
disp(sum)

medium

A. 6

B. 3

C. 0

D. Error

Solution

1. Step 1: Trace the loop iterations

   The loop runs i = 1, 2, 3. sum starts at 0.

2. Step 2: Calculate sum after each iteration

   sum = 0+1=1, then 1+2=3, then 3+3=6.

3. Final Answer:

   6 -> Option A

4. Quick Check:

   1+2+3 = 6 [OK]

Hint: Add numbers 1 to 3 inside loop [OK]

Common Mistakes:

• Forgetting to initialize sum
• Adding outside the loop
• Confusing loop range

4. Identify the error in this MATLAB for loop:

for i = 1:4
  disp(i)
  i = i + 1;
end

medium

A. Missing 'end' keyword

B. Modifying loop variable inside the loop

C. Incorrect loop range syntax

D. disp function is invalid

Solution

1. Step 1: Review loop variable usage

   The loop variable 'i' is controlled by MATLAB and should not be changed inside the loop.

2. Step 2: Identify the problem

   Changing 'i' inside the loop causes unexpected behavior or errors.

3. Final Answer:

   Modifying loop variable inside the loop -> Option B

4. Quick Check:

   Do not change loop variable inside for loop [OK]

Hint: Never change the loop variable inside the loop [OK]

Common Mistakes:

• Changing loop variable inside loop body
• Forgetting 'end' keyword (not the case here)
• Misunderstanding disp function

5. How can you use a for loop in MATLAB to create a vector v containing squares of numbers from 1 to 5?

hard

A. v = [];
for i = 1:5
v = v + i^2;
end

B. for i = 1:5
v(i) = i*2;
end

C. v = zeros(1,5);
for i = 1:5
v(i) = i^2;
end

D. v = 1:5;
for i = 1:5
v(i) = i + 2;
end

Solution

1. Step 1: Initialize vector to store results

   Pre-allocate vector v with zeros to hold 5 elements.

2. Step 2: Use for loop to assign squares

   For each i from 1 to 5, assign v(i) = i squared.

3. Final Answer:

   v = zeros(1,5);\nfor i = 1:5\n v(i) = i^2;\nend -> Option C

4. Quick Check:

   Pre-allocate vector and assign squares in loop [OK]

Hint: Pre-allocate vector, assign squares inside loop [OK]

Common Mistakes:

• Not pre-allocating vector before loop
• Adding instead of assigning inside loop
• Using wrong operation for squares