Iteration using range() in Python - Time & Space Complexity

Time Complexity: Iteration using range()

O(n)

Understanding Time Complexity

When we use range() to repeat actions, it is important to know how the time needed grows as the number of repeats increases.

We want to understand how the work changes when the range gets bigger.

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

for i in range(n):
    print(i)

This code prints numbers from 0 up to n-1, repeating the print action n times.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: The print(i) inside the loop.
• How many times: Exactly once for each number from 0 to n-1, so n times.

How Execution Grows With Input

As n grows, the number of print actions grows the same way.

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

Pattern observation: If you double n, the work doubles too. The growth is steady and direct.

Final Time Complexity

Time Complexity: O(n)

This means the time needed grows in a straight line with the size of n.

Common Mistake

[X] Wrong: "The loop runs instantly because it just counts numbers."

[OK] Correct: Even counting and printing each number takes time, so the total time grows with n.

Interview Connect

Understanding how simple loops grow with input size is a key skill. It helps you explain how your code behaves when handling more data.

Self-Check

"What if we changed range(n) to range(0, n, 2)? How would the time complexity change?"

Practice

1. What does range(5) do in a Python for loop?

easy

A. Generates numbers from 0 to 4

B. Generates numbers from 1 to 5

C. Generates numbers from 0 to 5

D. Generates numbers from 1 to 4

Solution

1. Step 1: Understand the range function

   range(5) starts at 0 by default and stops before 5.

2. Step 2: Identify the numbers generated

   The numbers generated are 0, 1, 2, 3, 4.

3. Final Answer:

   Generates numbers from 0 to 4 -> Option A

4. Quick Check:

   range(5) = 0,1,2,3,4 [OK]

Hint: Remember range stops before the end number [OK]

Common Mistakes:

• Thinking range(5) includes 5
• Starting count at 1 by default
• Confusing stop value as inclusive

2. Which of the following is the correct syntax to loop 3 times using range()?

easy

A. for i in range(1, 3):

B. for i in range(3):

C. for i in range(0, 3, 2):

D. for i in range(3, 0):

Solution

1. Step 1: Check each range syntax

   for i in range(1, 3): loops from 1 to 2 (2 times), for i in range(3): loops 0 to 2 (3 times), for i in range(0, 3, 2): loops 0 and 2 (2 times), for i in range(3, 0): runs zero times because start > stop without negative step.

2. Step 2: Identify the correct loop count

   Only for i in range(3): loops exactly 3 times: 0,1,2.

3. Final Answer:

   for i in range(3): -> Option B

4. Quick Check:

   range(3) loops 3 times [OK]

Hint: range(n) loops exactly n times starting at 0 [OK]

Common Mistakes:

• Using range(1, 3) which loops 2 times
• Using invalid range with start > stop
• Confusing step parameter

3. What is the output of this code?

for i in range(2, 7, 2):
    print(i, end=' ')

medium

A. 0 2 4 6

B. 2 3 4 5 6

C. 2 4 6 8

D. 2 4 6

Solution

1. Step 1: Understand the range parameters

   range(2, 7, 2) starts at 2, stops before 7, stepping by 2.

2. Step 2: List the numbers generated

   Numbers are 2, 4, 6.

3. Final Answer:

   2 4 6 -> Option D

4. Quick Check:

   range(2,7,2) = 2,4,6 [OK]

Hint: Start, stop, step control numbers generated [OK]

Common Mistakes:

• Including 7 in output
• Using wrong step size
• Starting from 0 instead of 2

4. Find the error in this code:

for i in range(5, 1):
    print(i)

medium

A. No error, prints 5 to 1

B. SyntaxError due to wrong range syntax

C. Loop does not run because start > stop without step

D. Infinite loop

Solution

1. Step 1: Analyze the range parameters

   range(5, 1) means start at 5, stop before 1, with default step 1.

2. Step 2: Understand loop behavior

   Since start is greater than stop and step is positive, the loop runs zero times.

3. Final Answer:

   Loop does not run because start > stop without step -> Option C

4. Quick Check:

   range(5,1) empty range [OK]

Hint: Positive step needs start < stop to run [OK]

Common Mistakes:

• Expecting loop to run backwards
• Thinking syntax error occurs
• Assuming infinite loop

5. You want to print all odd numbers from 1 to 15 using range(). Which code does this correctly?

hard

A. for i in range(1, 16, 2): print(i)

B. for i in range(0, 15, 2): print(i)

C. for i in range(1, 15): if i % 2 == 1: print(i)

D. for i in range(1, 16): print(i % 2)

Solution

1. Step 1: Identify odd numbers range

   Odd numbers from 1 to 15 are 1,3,5,...,15.

2. Step 2: Check each option

   for i in range(1, 16, 2): print(i) uses range(1,16,2) which generates 1,3,5,...,15 directly. for i in range(0, 15, 2): print(i) starts at 0 (even). for i in range(1, 15): if i % 2 == 1: print(i) misses 15 (range(1,15) goes to 14) and uses extra if check. for i in range(1, 16): print(i % 2) prints 1 or 0, not numbers.

3. Final Answer:

   for i in range(1, 16, 2): print(i) -> Option A

4. Quick Check:

   range(1,16,2) = odd numbers [OK]

Hint: Use step=2 starting at 1 for odd numbers [OK]

Common Mistakes:

• Starting at 0 for odd numbers
• Forgetting to include last number
• Printing modulo instead of number