Why is Binary Search a divide and conquer algorithm?

Question

I was asked if a Binary Search is a divide and conquer algorithm at an exam. My answer was yes, because you divided the problem into smaller subproblems, until you reached y

Answer 1

Dichotomic in computer science refers to choosing between two antithetical choices, between two distinct alternatives. A dichotomy is any splitting of a whole into exactly two non-overlapping parts, meaning it is a procedure in which a whole is divided into two parts. It is a partition of a whole (or a set) into two parts (subsets) that are: 1. Jointly Exhaustive: everything must belong to one part or the other, and 2. Mutually Exclusive: nothing can belong simultaneously to both parts.

Divide and conquer works by recursively breaking down a problem into two or more sub-problems of the same type, until these become simple enough to be solved directly.

So the binary search halves the number of items to check with each iteration and determines if it has a chance of locating the "key" item in that half or moving on to the other half if it is able to determine keys absence. As the algorithm is dichotomic in nature so the binary search will believe that the "key" has to be in one part until it reaches the exit condition where it returns that the key is missing.