Big O notation describes how the running time or space requirements of an algorithm grow as the input size n increases. This guide contains Big O practice problems ranging from beginner to advanced, with step-by-step solutions and explanations.
Big O notation?
Big O notation describes how the running time or space requirements of an algorithm grow as the input size n increases. This guide contains Big O practice problems ranging from beginner to advanced, with step-by-step solutions and explanations.
| Complexity | Common example |
|---|---|
| O(1) | Array access |
| O(log n) | Binary search |
| O(n) | Linear search |
| O(n log n) | Merge sort |
| O(n²) | Nested loops |
| O(2ⁿ) | Some recursive algorithms |
O(1)
O(log n)
O(n)
O(n log n)
O(n²)
O(2ⁿ)
n
=
64
:
(1, log₂n, n)
=
(1,
6,
64)
(n log₂n, n²)
=
(384,
4,096)
2n
=
1.84 × 1019
Problem 1: Constant Time O(1)
Question: What is the time complexity?
Solution: O(1)
Explanation: “Inside the function, a constant number of operations is performed: the modulus operation (% 2) and a comparison (== 0). The number of operations does not depend on the size of the input numbum (n).
Problem 2: Linear Time O(n)
Question: What is the time complexity?
Solution: O(n)
Explanation: The function loops through the list of n elements twice. This gives 2n steps. Big O notation drops constant coefficients, so 2n simplifies to O(n).
Problem 3: Logarithmic Time (O(log n))
Question: What is the time complexity?
Solution: \(O(\log n)\)
Explanation: The complexity is \(O(\log n)\) because the variable i doubles in each iteration, scaling logarithmically relative to n.
Explanation: Featuring nested loops where each individual loop runs n times, the total operations scale to \(n^{2}\) while constant-time work occurs inside
