While loops in MATLAB - Time & Space Complexity

Time Complexity: While loops

O(N)

Understanding Time Complexity

We want to understand how the time a while loop takes changes as the input grows.

How many times does the loop run when input size changes?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

n = 1;
while n <= N
    disp(n);
    n = n + 1;
end

This code prints numbers from 1 up to N using a while loop.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: The while loop runs repeatedly.
• How many times: It runs once for each number from 1 to N, so N times.

How Execution Grows With Input

As N gets bigger, the loop runs more times, growing steadily.

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

Pattern observation: The number of operations grows directly with N.

Final Time Complexity

Time Complexity: O(N)

This means the time grows in a straight line as the input size increases.

Common Mistake

[X] Wrong: "The while loop runs forever or a fixed number of times regardless of N."

[OK] Correct: The loop runs exactly N times because it counts from 1 to N, so it depends directly on input size.

Interview Connect

Understanding how loops grow with input helps you explain your code clearly and shows you can think about efficiency.

Self-Check

"What if we changed the loop to increase n by 2 each time? How would the time complexity change?"

Practice

1. What does a while loop do in MATLAB?

easy

A. Repeats a block of code as long as a condition is true

B. Executes code only once

C. Runs code a fixed number of times

D. Stops the program immediately

Solution

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

   A while loop runs repeatedly while its condition remains true.

2. Step 2: Compare options with definition

   Only Repeats a block of code as long as a condition is true correctly describes this behavior.

3. Final Answer:

   Repeats a block of code as long as a condition is true -> Option A

4. Quick Check:

   While loop = repeat while true [OK]

Hint: While loops run while condition is true, not fixed times [OK]

Common Mistakes:

• Thinking while loops run a fixed number of times
• Confusing while with if statement
• Believing while loops run only once

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

easy

A. while condition
statements
end

B. while (condition) {
statements
}

C. while condition:
statements
end

D. while condition do
statements
end

Solution

1. Step 1: Recall MATLAB while loop syntax

   MATLAB uses 'while condition' followed by statements and ends with 'end'.

2. Step 2: Check each option

   while condition statements end matches MATLAB syntax; others use syntax from other languages.

3. Final Answer:

   while condition\n statements\nend -> Option A

4. Quick Check:

   MATLAB uses 'end' to close loops [OK]

Hint: MATLAB while loops end with 'end', no braces [OK]

Common Mistakes:

• Using braces {} instead of 'end'
• Adding colons after condition
• Using 'do' keyword

3. What will be the output of this MATLAB code?

i = 1;
while i <= 3
  disp(i)
  i = i + 1;
end

medium

A. 1 2 3 4

B. 1 2 3

C. 1 2

D. Error: infinite loop

Solution

1. Step 1: Analyze loop condition and increments

   The loop runs while i is less than or equal to 3, starting at 1 and increasing by 1 each time.

2. Step 2: Trace output values

   Values displayed are 1, then 2, then 3. When i becomes 4, condition fails and loop stops.

3. Final Answer:

   1 2 3 -> Option B

4. Quick Check:

   Loop prints 1 to 3 [OK]

Hint: Increment loop variable to avoid infinite loop [OK]

Common Mistakes:

• Forgetting to increment i causing infinite loop
• Expecting output to include 4
• Confusing loop condition with < instead of <=

4. Identify the error in this MATLAB code snippet:

count = 5;
while count > 0
  disp(count)
end

medium

A. disp function cannot be used inside while

B. Incorrect while syntax

C. Missing increment or decrement inside the loop

D. Variable 'count' not initialized

Solution

1. Step 1: Check loop condition and body

   The loop condition is 'count > 0', but inside the loop count is never changed.

2. Step 2: Understand effect of missing update

   Without changing count, the condition stays true forever, causing an infinite loop.

3. Final Answer:

   Missing increment or decrement inside the loop -> Option C

4. Quick Check:

   Update loop variable to avoid infinite loop [OK]

Hint: Always update loop variable inside while loop [OK]

Common Mistakes:

• Forgetting to change loop variable
• Assuming disp causes error
• Thinking syntax is wrong

5. Write a MATLAB while loop that sums numbers from 1 to 10 and stores the result in total. Which code correctly does this?

hard

A. total = 0;
i = 1;
while i <= 10
total = total + i;
i = i - 1;
end

B. total = 0;
i = 1;
while i < 10
total = total + i;
end

C. total = 0;
for i = 1:10
total = total + i;
end

D. total = 0;
i = 1;
while i <= 10
total = total + i;
i = i + 1;
end

Solution

1. Step 1: Understand the goal and loop condition

   We want to add numbers 1 through 10 using a while loop that stops when i > 10.

2. Step 2: Check each option for correctness

   total = 0; i = 1; while i <= 10 total = total + i; i = i + 1; end initializes total and i, adds i to total, increments i, and stops at 10 correctly. total = 0; i = 1; while i < 10 total = total + i; end misses increment causing infinite loop. total = 0; for i = 1:10 total = total + i; end uses for loop, not while. total = 0; i = 1; while i <= 10 total = total + i; i = i - 1; end decrements i causing infinite loop.

3. Final Answer:

   total = 0;\ni = 1;\nwhile i <= 10\n total = total + i;\n i = i + 1;\nend -> Option D

4. Quick Check:

   Increment i to sum 1 to 10 [OK]

Hint: Increment loop variable to reach end condition [OK]

Common Mistakes:

• Forgetting to increment i
• Using for loop instead of while
• Decrementing i causing infinite loop