What are the trade-offs of using recursion over iteration?

Using recursion over iteration can lead to simpler code but may also cause higher memory usage and potential stack overflow.

Recursion is a method where the solution to a problem depends on solutions to smaller instances of the same problem. It can make code look cleaner and easier to understand, as it breaks down a complex problem into simpler sub-problems. This is particularly useful in problems that have a natural recursive structure, such as tree and graph traversals, where the problem can naturally be divided into smaller, similar problems. Recursion can also be useful in problems where the number of iterations is not known beforehand, as it can continue to call itself until a base case is reached.

However, recursion has its drawbacks. Each recursive call adds a layer to the system's call stack, which uses up memory. If the recursion is too deep, this can lead to a stack overflow, where the call stack exceeds its limit and the program crashes. This is a particular risk with languages that do not support tail recursion optimisation, where the compiler can reduce the memory usage of certain types of recursive calls.

On the other hand, iteration, which is the repetition of a process within a computer program, can often be more efficient than recursion. Iterative solutions use a loop structure and thus do not have the overhead of repeated function calls and the associated memory usage. This can make them faster and less memory-intensive than their recursive counterparts. However, iterative solutions can sometimes be more complex and harder to understand than recursive ones, particularly for problems that have a natural recursive structure.

In conclusion, the choice between recursion and iteration often depends on the specific problem at hand and the characteristics of the programming language being used. Recursion can lead to simpler, more readable code, but at the cost of higher memory usage and the risk of stack overflow. Iteration can be more efficient, but may result in more complex code.