What is Big O notation ?
Big O notation is a mathematical concept used in computer science to describe the time complexity or space complexity of algorithms. It provides a standardized way to compare the efficiency of different algorithms in terms of their worst-case performance.
Purpose of Big O Notation
- Measure Efficiency: Helps analyze how an algorithm scales with input size.
- Compare Algorithms: Provides a standard to evaluate and compare different solutions.
- Worst-Case Analysis: Describes the upper bound of an algorithm’s performance to ensure reliability under all conditions.
Common Big O Notations
- O(1) – Constant Time
- The runtime does not depend on the size of the input.
- Example: Accessing an element in an array by index.
- O(log n) – Logarithmic Time
- The runtime grows logarithmically with the input size.
- Example: Binary search.
- O(n) – Linear Time
- The runtime grows directly proportional to the input size.
- Example: Traversing an array.
- O(n log n) – Quasilinear Time
- Often associated with divide-and-conquer algorithms.
- Example: Merge sort, quicksort (average case).
- O(n²) – Quadratic Time/O(n³) – Cubic Time
- The runtime grows quadratically/cubically with input size.
- Example: Nested loops, such as in bubble sort.
- O(2ⁿ) – Exponential Time
- The runtime doubles with each additional input element.
- Example: Recursive algorithms for the Fibonacci sequence.
- O(n!) – Factorial Time
- Extremely inefficient; used in algorithms that generate permutations.
- Example: Solving the traveling salesman problem using brute force.
Why Is Big O Important?
- Scalability: Determines how well an algorithm performs with large inputs.
- Optimization: Helps identify bottlenecks and improve performance.
- Decision Making: Guides the choice of the right algorithm for a given problem.