What is the impact of recursion on memory usage?

Recursion significantly increases memory usage as each recursive call adds a new layer to the system's stack.

Recursion is a powerful tool in computer science, allowing us to solve complex problems by breaking them down into simpler, more manageable sub-problems. However, this power comes at a cost, specifically in terms of memory usage. Each time a recursive function is called, a new layer is added to the system's stack. This layer contains information about the current state of the function, including any variables and their values. As the recursion deepens, more and more of these layers are added, each consuming a portion of the system's memory.

The memory usage of a recursive function is directly proportional to the depth of the recursion. The deeper the recursion, the more memory is used. This is because each recursive call requires its own stack frame to store variables and other information. If the recursion is too deep, it can lead to a stack overflow, where the system runs out of memory to allocate new stack frames. This can cause the program to crash or behave unpredictably.

In contrast, iterative solutions, which use loops instead of recursion, generally use less memory. This is because they do not require the creation of new stack frames for each iteration. Instead, they reuse the same memory space for each iteration, updating the values of variables as needed. This makes them more memory-efficient, although they may be more difficult to implement for certain problems.

In conclusion, while recursion can be a powerful tool for solving complex problems, it is important to be aware of its impact on memory usage. It is crucial to consider the trade-off between the simplicity and elegance of a recursive solution and the potential for increased memory usage and the risk of stack overflow.