Question

What causes a recursive algorithm to stop calling itself?

Short answer

Answer: A recursive algorithm stops calling itself when it reaches the base case, which is a condition or set of conditions designed to directly solve the simplest form of the problem without further recursion. This ensures that the algorithm eventually terminates and does not continue calling itself infinitely.

Step-by-step solution

Definition of a Recursive Algorithm

A recursive algorithm is a method of solving problems by breaking them down into smaller sub-problems, which are solved using recursion – a process where a function calls itself as a subroutine. The main goal of using recursion is to simplify complex problems by addressing smaller instances of the same problem.

Base Case

In a recursive algorithm, there is always a base case. This is a condition or set of conditions that allows the recursion to cease, preventing the function from calling itself endlessly. The base case is created by identifying the simplest sub-problem that can be directly solved without further recursion.

Recursive Step

A recursive algorithm also includes a recursive step where the larger problem is broken down into smaller sub-problems. With each recursive call, the current problem's size moves closer to the base case. If designed correctly, it ensures that the recursion will eventually reach the base case and stop calling itself. So, in conclusion:

Cause of Recursive Algorithm Stopping

A recursive algorithm stops calling itself when it reaches the base case. The base case is a condition or set of conditions that is created to identify and directly solve the simplest form of the problem, without further recursion. This ensures that the algorithm does not continue calling itself infinitely and eventually terminates.