Can every recursion be changed to iteration?

Question

Is every recursive function convertible to iteration? What characteristic should a recursive function have in order for it to be implemented using iteration?

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Answer 1

It is generally possible to convert any recursive algorithm into loop. The method is simple: we can imitate how the compiler generate code for function call: entering function, returning from function, and continue execution.

To turn a recursive function into an iterative loop, you can:

• Define a record, which stores the arguments to the function and the local variables. This is equivalent to stack frame.
• Define a stack, to which records a pushed. This is analogy to the program stack.
• When a function is called, create a record of the current value of the arguments and local variables and push to stack.
• When you return from the function, pop out from stack and overwrite the current value with that from the record.

The whole process above is done in a while loop, which will exit when the stack is empty,