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

1. Measure Efficiency: Helps analyze how an algorithm scales with input size.
2. Compare Algorithms: Provides a standard to evaluate and compare different solutions.
3. Worst-Case Analysis: Describes the upper bound of an algorithm’s performance to ensure reliability under all conditions.

Common Big O Notations

1. O(1) – Constant Time
   • The runtime does not depend on the size of the input.
   • Example: Accessing an element in an array by index.
2. O(log n) – Logarithmic Time
   • The runtime grows logarithmically with the input size.
   • Example: Binary search.
3. O(n) – Linear Time
   • The runtime grows directly proportional to the input size.
   • Example: Traversing an array.
4. O(n log n) – Quasilinear Time
   • Often associated with divide-and-conquer algorithms.
   • Example: Merge sort, quicksort (average case).
5. O(n²) – Quadratic Time/O(n³) – Cubic Time 
   • The runtime grows quadratically/cubically with input size.
   • Example: Nested loops, such as in bubble sort.
6. O(2ⁿ) – Exponential Time
   • The runtime doubles with each additional input element.
   • Example: Recursive algorithms for the Fibonacci sequence.
7. 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?

1. Scalability: Determines how well an algorithm performs with large inputs.
2. Optimization: Helps identify bottlenecks and improve performance.
3. Decision Making: Guides the choice of the right algorithm for a given problem.