Complexity of an Algorithm

Types of Complexity

Time Complexity: Measures the amount of time an algorithm takes to complete, usually expressed in Big O notation.
Space Complexity: Measures the amount of memory an algorithm uses, also expressed in Big O notation.

Input Size: The size of the input data affects the complexity of an algorithm.
Algorithm Design: The design of the algorithm itself, including the use of loops, recursion, and data structures.
Data Structures: The choice of data structures used in the algorithm can impact complexity.

O(1) - Constant Time: The algorithm takes the same amount of time regardless of the input size.
O(log n) - Logarithmic Time: The algorithm takes time proportional to the logarithm of the input size.
O(n) - Linear Time: The algorithm takes time proportional to the input size.
O(n log n) - Linearithmic Time: The algorithm takes time proportional to the product of the input size and its logarithm.
O(n^2) - Quadratic Time: The algorithm takes time proportional to the square of the input size.
O(2^n) - Exponential Time: The algorithm takes time proportional to 2 raised to the power of the input size.

Predicting Performance: Complexity analysis helps predict how an algorithm will perform on large inputs.
Comparing Performance: Complexity analysis allows comparing the efficiency of different algorithms.
Optimizing Algorithms: Understanding complexity helps identify areas for optimization.