Use Binary Search, Recursion (Algorithm 2.1) to search for...

Use Binary Search, Recursion (Algorithm 2.1) to search for the integer 120 in the following list (array) of integers. Show the actions step by step.
$\begin{array}{lllllllll}12 & 34 & 37 & 45 & 57 & 82 & 99 & 120 & 134\end{array}$

Key Concepts

Binary Search

Binary search is an efficient algorithm for finding an item from a sorted list of elements by repeatedly dividing the search interval in half. If the target value is less than the middle element, the search continues on the lower half; otherwise, it continues on the upper half. This method significantly reduces the number of comparisons needed compared to a linear search.

Recursion

Recursion is a programming technique in which a function calls itself in order to solve smaller instances of a problem. In recursive implementations of binary search, the function calls itself with a narrowed search interval until the target element is found or the interval is empty. This approach can simplify the code and make the divide-and-conquer strategy more evident.

Sorted List

A sorted list is a data structure in which elements are arranged in a specific order, typically ascending or descending. Binary search relies on the list being sorted because the algorithm determines which half of the list to continue searching in based on the order of the elements. Without a sorted list, the binary search method would not work correctly.

Divide and Conquer

Divide and conquer is an algorithm design paradigm that breaks a problem into smaller subproblems, solves each of them independently, and then combines their solutions to solve the original problem. Binary search is a classic example of this approach, as it divides the search interval into halves and recursively searches in the relevant half.

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