Which algorithmic approach recursively splits a problem into multiple smaller subproblems of the same type until solvable directly?

• A. Divide and Conquer
• B. Brute Force
• C. Dynamic Programming
• D. Greedy

Answer: (A)

Dividing a big problem into smaller instances of the same problem, solving those pieces, and then combining the results is the essence of this approach. It recurses by creating several smaller subproblems that resemble the original task, solving each one, and finally merging their solutions to form the final answer. The base cases are the simplest problems that can be solved directly, and that’s where the recursion stops. This pattern is exactly what divide and conquer is all about, with familiar examples like merge sort and quicksort showing how the big task is broken down, solved, and then stitched back together.

Brute force is about exploring possibilities, usually in a straightforward or exhaustive way, without the systematic recursive split into smaller, identical problems. Dynamic programming also breaks problems into subproblems, but its hallmark is solving overlapping subproblems and storing results to avoid recomputation, rather than simply splitting into independent subproblems to be solved and merged. Greedy takes a different tack, making locally optimal choices without continually decomposing the problem into a tree of smaller, identical subproblems to solve and combine.