Counter-based while loop in Python - Time & Space Complexity

Time Complexity: Counter-based while loop

O(n)

Understanding Time Complexity

We want to understand how the time it takes to run a counter-based while loop changes as the number it counts to gets bigger.

How does the number of steps grow when the loop runs more times?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

count = 0
limit = 100
while count < limit:
    print(count)
    count += 1

This code counts from 0 up to one less than the limit, printing each number.

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 0 up to (limit - 1).

How Execution Grows With Input

Each time the limit gets bigger, the loop runs more times in a straight line.

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

Pattern observation: The number of steps grows directly with the input size.

Final Time Complexity

Time Complexity: O(n)

This means the time to finish grows in a straight line as the limit gets bigger.

Common Mistake

[X] Wrong: "The loop runs a fixed number of times no matter the limit."

[OK] Correct: The loop actually runs once for each number up to the limit, so bigger limits mean more steps.

Interview Connect

Understanding how loops grow with input size helps you explain your code clearly and shows you know how programs behave as data grows.

Self-Check

"What if we changed the loop to count down from the limit to zero? How would the time complexity change?"

Practice

1.

What is the main purpose of a counter in a while loop?

easy

A. To keep track of how many times the loop has run

B. To store the final result of the loop

C. To stop the program immediately

D. To print messages inside the loop

Solution

1. Step 1: Understand the role of a counter

   A counter is a variable that counts how many times the loop runs.

2. Step 2: Identify the purpose in a while loop

   The counter helps the loop know when to stop by checking its value in the condition.

3. Final Answer:

   To keep track of how many times the loop has run -> Option A

4. Quick Check:

   Counter tracks loop runs = D [OK]

Hint: Counter counts loop repeats to control stopping [OK]

Common Mistakes:

• Thinking counter stores final result
• Confusing counter with printing inside loop
• Believing counter stops program immediately

2.

Which of the following is the correct syntax to start a counter at 0 before a while loop?

?

easy

A. counter := 0

B. while counter = 0:

C. counter == 0

D. counter = 0

Solution

1. Step 1: Identify correct variable assignment

   To start a counter, assign 0 using a single equal sign: counter = 0.

2. Step 2: Check other options for syntax errors

   while counter = 0: uses assignment in while condition (invalid), C uses comparison, D uses walrus operator incorrectly here.

3. Final Answer:

   counter = 0 -> Option D

4. Quick Check:

   Assign counter with = 0 before loop = A [OK]

Hint: Use single = to assign counter before loop [OK]

Common Mistakes:

• Using == instead of = for assignment
• Trying to assign inside while condition
• Confusing walrus operator usage

3.

What will be the output of this code?

counter = 1
while counter <= 3:
    print(counter)
    counter += 1

medium

A. 1 2 3

B. 1 2 3 4

C. 0 1 2 3

D. 3 2 1

Solution

1. Step 1: Trace the loop iterations

   Counter starts at 1, prints 1, then increments to 2, prints 2, increments to 3, prints 3, then increments to 4.

2. Step 2: Check loop condition

   Loop stops when counter is 4 because 4 <= 3 is false. So printed numbers are 1, 2, 3.

3. Final Answer:

   1 2 3 -> Option A

4. Quick Check:

   Prints 1 to 3 with counter increment = C [OK]

Hint: Loop runs while counter ≤ 3, prints 1,2,3 [OK]

Common Mistakes:

• Including 4 in output
• Starting count from 0 instead of 1
• Printing numbers in reverse

4.

Find the error in this code and choose the fix:

counter = 0
while counter < 5
    print(counter)
    counter += 1

medium

A. Change < to <= in the while condition

B. Initialize counter to 1 instead of 0

C. Add a colon ':' after the while condition

D. Remove the increment line inside the loop

Solution

1. Step 1: Identify syntax error in while loop

   The while statement is missing a colon ':' at the end of the condition line.

2. Step 2: Check other options

   Changing < to <= is not an error fix, initializing counter differently or removing increment causes logic errors.

3. Final Answer:

   Add a colon ':' after the while condition -> Option C

4. Quick Check:

   Missing colon causes syntax error = B [OK]

Hint: Always put ':' after while condition [OK]

Common Mistakes:

• Forgetting colon after while condition
• Changing loop logic instead of fixing syntax
• Removing counter increment causing infinite loop

5.

Write a counter-based while loop that prints only even numbers from 2 to 10 inclusive.

counter = 2
while counter <= 10:
    print(counter)
    ?

What should replace ? to correctly increment the counter?

hard

A. counter += 1

B. counter += 2

C. counter = counter * 2

D. counter -= 2

Solution

1. Step 1: Understand the goal

   We want to print even numbers from 2 to 10, so counter should increase by 2 each time.

2. Step 2: Choose correct increment

   Using counter += 2 moves counter from 2 to 4, 6, 8, 10 correctly.

3. Final Answer:

   counter += 2 -> Option B

4. Quick Check:

   Increment by 2 to print evens = A [OK]

Hint: Increase counter by 2 to get even numbers [OK]

Common Mistakes:

• Incrementing by 1 prints odd numbers too
• Multiplying counter causes wrong jumps
• Decrementing counter causes infinite loop