Time Complexity Questions with Answers (Big-O Practice)

Interviewers often show a loop and ask for its Big-O. Work out each one before revealing the answer.

1. Q1. What is the time complexity of this code, where size is the input size n?

   low, high = 0, size - 1
   while low <= high:
       mid = (low + high) // 2
       high = mid - 1

   • A. O(2ⁿ)
   • B. O(1)
   • C. O(log n)
   • D. O(n³)
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   Answer: C. O(log n)
   The range is halved every step, like binary search.

2. Q2. What is the time complexity of this code, where size is the input size n?

   for i in range(size):
       for j in range(size):
           for k in range(size):
               pass

   • A. O(n)
   • B. O(n log n)
   • C. O(√n)
   • D. O(n³)
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   Answer: D. O(n³)
   Three nested loops of n each.

3. Q3. What is the time complexity of this code, where n is the input size n?

   low, high = 0, n - 1
   while low <= high:
       mid = (low + high) // 2
       high = mid - 1

   • A. O(n²)
   • B. O(2ⁿ)
   • C. O(n)
   • D. O(log n)
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   Answer: D. O(log n)
   The range is halved every step, like binary search.

4. Q4. What is the time complexity of this code, where n is the input size n?

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

   • A. O(n²)
   • B. O(1)
   • C. O(√n)
   • D. O(n log n)
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   Answer: A. O(n²)
   Two nested loops, each running n times.

5. Q5. What is the time complexity of this code, where size is the input size n?

   x = size * 2 + 7
   print(x)

   • A. O(n²)
   • B. O(n³)
   • C. O(1)
   • D. O(√n)
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   Answer: C. O(1)
   A fixed number of steps regardless of n.

6. Q6. What is the time complexity of this code, where count is the input size n?

   for i in range(count):
       for j in range(10):
           print(i * j)

   • A. O(1)
   • B. O(n)
   • C. O(log n)
   • D. O(n²)
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   Answer: B. O(n)
   The inner loop always runs 10 times (a constant), so it's 10n = O(n).

7. Q7. What is the time complexity of this code, where size is the input size n?

   for i in range(size):
       for j in range(i):
           print(j)

   • A. O(n³)
   • B. O(n²)
   • C. O(1)
   • D. O(n)
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   Answer: B. O(n²)
   0 + 1 + … + (n−1) = n(n−1)/2 steps, which is O(n²).

8. Q8. What is the time complexity of this code, where size is the input size n?

   def fib(size):
       if size < 2:
           return size
       return fib(size - 1) + fib(size - 2)

   • A. O(n³)
   • B. O(√n)
   • C. O(2ⁿ)
   • D. O(1)
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   Answer: C. O(2ⁿ)
   Each call makes two more calls, so the number of calls roughly doubles at every level.

9. Q9. What is the time complexity of this code, where count is the input size n?

   i = 1
   while i < count:
       i = i * 2

   • A. O(n²)
   • B. O(2ⁿ)
   • C. O(log n)
   • D. O(n³)
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   Answer: C. O(log n)
   i doubles each time, so the loop runs about log₂ n times.

10. Q10. What is the time complexity of this code, where size is the input size n?

    for i in range(size):
        for j in range(size):
            print(i, j)

    • A. O(log n)
    • B. O(√n)
    • C. O(n²)
    • D. O(n)
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    Answer: C. O(n²)
    Two nested loops, each running n times.

11. Q11. What is the time complexity of this code, where n is the input size n?

    for i in range(n):
        j = 1
        while j < n:
            j *= 2

    • A. O(n log n)
    • B. O(√n)
    • C. O(2ⁿ)
    • D. O(n³)
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    Answer: A. O(n log n)
    The outer loop runs n times and the inner one log n times.

12. Q12. What is the time complexity of this code, where n is the input size n?

    def fib(n):
        if n < 2:
            return n
        return fib(n - 1) + fib(n - 2)

    • A. O(n³)
    • B. O(2ⁿ)
    • C. O(1)
    • D. O(√n)
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    Answer: B. O(2ⁿ)
    Each call makes two more calls, so the number of calls roughly doubles at every level.