Question

What causes a recursive algorithm to stop calling itself?

Short answer

Answer: A recursive algorithm stops calling itself when it reaches a base case, which is a specific condition or set of conditions defined within the algorithm. This ensures the termination of recursion and allows the solution to be computed without causing an infinite loop.

Step-by-step solution

Introduction to recursive algorithms

Recursive algorithms are a powerful way to solve problems by breaking them down into simpler or smaller instances of the same problem, and solving each instance using the same algorithm. The function calls itself with this smaller instance until a solution is easy enough to obtain directly.

Base cases in recursion

In order to prevent infinite recursion, a recursive algorithm must define a base case(s). A base case is a condition or a set of conditions under which the recursive algorithm stops calling itself and returns a straightforward value without any further recursion. This is essential for solving the problem and to avoid an infinite loop.

Example

Let's take the example of the classic recursive algorithm for calculating the factorial of a number. The factorial of a non-negative integer 'n' is denoted by `n!` and is the product of all positive integers less than or equal to 'n'. For example, `4! = 4 × 3 × 2 × 1 = 24`. Here's the recursive algorithm to calculate the factorial of a number 'n': 1. If `n == 0`, return 1 as `0!` is equal to 1. (This is the base case) 2. Otherwise, return `n × factorial(n-1)`

Stopping recursion with the base case

In the example above, the base case is when `n == 0`. When the recursive function encounters `n == 0`, it stops calling itself and directly returns 1. This causes the recursion to stop and the sequence of function calls to "unwind," allowing the algorithm to compute the factorial of the original number.

Conclusion

To sum up, a recursive algorithm stops calling itself when it reaches a base case, which is a specific condition or set of conditions defined within the algorithm. Reaching the base case ensures the termination of recursion and allows the solution to be computed without causing an infinite loop.