Understanding Recursion in JavaScript

What is the maximum recursion depth in JavaScript and how can we demonstrate the correctness of recursive algorithms?

Maximum Recursion Depth in JavaScript

Recursion depth is the maximum number of nested calls in a recursive function, including the initial call. In JavaScript, the maximum recursion depth limit imposed by the JavaScript engine is typically around 10000. While some engines may permit more recursive calls, exceeding 100000 is likely to surpass the limit on most engines.

Demonstrating Recursive Algorithms' Correctness

One way to demonstrate the correctness of recursive algorithms is through mathematical induction. This method involves two steps: establishing a base case and performing an inductive step.

The base case serves as the starting point for the induction, typically when a certain parameter reaches a specific condition. For example, in a recursive function where k equals 0 or k is odd while n is even, this would represent a base case.

Next, the inductive step involves proving that if the algorithm works for a particular case, it will also work for the next case. By following this formal or mathematical reasoning, we can show the correctness of a recursive algorithm for all potential inputs.