Performance of **Binary Search Algorithm**: Therefore, **time complexity** of **binary search algorithm** is O(log_{2}n) which is very efficient. Auxiliary space used by it is O(1) for iterative implementation and O(log_{2}n) for **recursive** implementation due to call stack.

Thereof, what is the time complexity of binary search algorithm?

**Binary search** runs in at worst logarithmic **time**, making O(log n) comparisons, where n is the number of elements in the array, the O is Big O notation, and log is the logarithm. **Binary search** takes constant (O(1)) space, meaning that the space taken by the **algorithm** is the same for any number of elements in the array.

what is recursive binary search algorithm? **Recursive Binary Search Algorithm** in Java – Example Tutorial The **binary search algorithm** is one of the most famous **search algorithms** in computer science. It allows you to **search** a value in logarithmic time i.e. O(logN), which makes it ideal to **search** a number in a huge list.

In this manner, how do you find the time complexity of a recursive algorithm?

It’s often possible to **compute** the **time complexity** of a **recursive function** by formulating and solving a recurrence relation.

**Master theorem**

- T(n) = Θ(n
^{d}) if a < b^{d}, - T(n) = Θ(n
^{d}log n) if a = b^{d}, - T(n) = Θ(n
^{log}_{b}a) if a > b^{d}.

What is binary search complexity?

Worst-case space **complexity**. O(1) In computer science, **binary search**, also known as half-interval **search**, logarithmic **search**, or **binary** chop, is a **search** algorithm that finds the position of a target value within a sorted array. **Binary search** compares the target value to the middle element of the array.