Algorithm complexity refers to the measure of resources (time and space) required by an algorithm to solve a problem as a function of the input size. It is independent of programming language or hardware and is crucial for comparing algorithm efficiency.

Two main types of complexity are:

• Time Complexity – The amount of computational time taken to execute an algorithm. It is often expressed using asymptotic notations like Big O (O) for worst-case, Omega (Ω) for best-case, and Theta (Θ) for average-case analysis.

• Space Complexity – The total memory required by the algorithm, including input storage, auxiliary data structures, and recursion stack space.

Common Complexity Classes:

• O(1) – Constant time (e.g., accessing an array element)

• O(log n) – Logarithmic time (e.g., binary search)

• O(n) – Linear time (e.g., linear search)

• O(n²) – Quadratic time (e.g., bubble sort)

• O(2ⁿ) – Exponential time (e.g., subset sum recursion)

• O(n!) – Factorial time (e.g., generating permutations)