A compiler may struggle to handle recursive code efficiently in scenarios involving complex recursive structures or deep recursion. In complex recursive structures, where multiple recursive paths are possible, and the recursion involves several intertwined recursive calls, the compiler might not optimise the code effectively. This complexity can lead to increased stack usage and reduced execution efficiency. Deep recursion, where the number of recursive calls is very high, poses a risk of stack overflow. Some compilers might not implement tail recursion optimisation or other memory-saving techniques, leading to inefficient handling of such code. Additionally, in cases of non-tail recursive functions, where additional operations are performed after the recursive call, the compiler cannot convert these calls into iterations, which might lead to inefficient memory usage and slower execution times.

Common errors in writing recursive code include missing base cases, incorrect base cases, and inefficient recursive steps. Missing or incorrect base cases can lead to infinite recursion, as the function never reaches a point where it stops calling itself. This can be avoided by carefully defining clear and correct base conditions before writing the recursive step. Inefficient recursive steps, where the logic does not significantly reduce the problem size or approach the base case with each iteration, can lead to excessive recursive calls and, consequently, stack overflow. This can be mitigated by ensuring that each recursive step logically progresses towards the base case. Another error is mismanaging function parameters or state, leading to incorrect results or unintended behaviour. Students should ensure parameters and any state variables are correctly updated and passed in each recursive call. Regular testing and debugging with various inputs can help identify and rectify these issues.

Detecting and handling potential infinite recursion is a challenging task for compilers. Infinite recursion occurs when the recursive calls never reach a base case, causing the program to run indefinitely and eventually crash due to stack overflow. Compilers use static analysis techniques to detect such scenarios. They analyse the recursive function's control flow, looking for conditions that could lead to infinite loops. However, due to the undecidable nature of the Halting Problem – which states that it is impossible to determine, in every case, whether a given program will finish running or continue to run forever – compilers cannot always detect infinite recursion. When potential infinite recursion is detected, the compiler may issue a warning or an error. Runtime checks can also be implemented, limiting the depth of recursion and preventing the program from crashing by throwing an exception when the depth limit is exceeded.

Yes, recursive functions can be rewritten as iterative functions, and this transformation can significantly impact the compiling process. Turning a recursive function into an iterative one involves using loops and data structures like stacks or queues to mimic the call stack's behaviour in recursion. This transformation is beneficial because iterative versions of recursive algorithms often use less memory and are less prone to stack overflow errors, especially in languages or environments with limited stack space. For the compiler, translating iterative code is generally more straightforward and can be more efficient than handling deep or complex recursion. The iterative code tends to be more predictable in terms of memory usage and execution time. However, the clarity and elegance of recursive solutions, especially for problems inherently recursive in nature, like tree traversals or factorial calculations, might be lost in the transformation to iterative processes.

Compilers utilise several optimisation strategies to prevent stack overflow in recursive code. One common technique is tail recursion optimisation. In tail recursion, the recursive call is the last operation in the function. The compiler optimises this by reusing the current stack frame for the next recursive call instead of creating a new one, effectively converting the recursion into an iteration under the hood. This significantly reduces the stack space used, preventing stack overflow in cases of deep recursion. Another strategy is memoisation, where the results of expensive function calls are cached. If the function is called again with the same parameters, the compiler retrieves the result from the cache instead of recalculating it, reducing the number of recursive calls and, consequently, the stack size. These optimisations are crucial for efficient execution of recursive code, especially in languages and environments where stack space is limited.