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

If you have a simple "tail" recursion, then you can use a loop instead (e.g. factorial function). In more complex functions, you have to use a stack structure and a while (!stack.empty()) loop. However, if you have quite complex recursion, such as Towers of Hanoi, Merge Sort, and printing truth table, you will have to use a stack with while loop, as previous, but with a switch statement to determine the current status of call.

Recursive:

void mergeSort(int start, int end)
{
    if (start < end)
    {
         mergeSort(start, (start + end) / 2);
         mergeSort((start + end) / 2 + 1, end);
         Merge(start, end);
    }

}

Iterative:

void mergeSort()
{
  stack st;
  st.push(1);
  int status;

  while (!st.empty())
  {
      status = st.pop();
      switch (status)
      {
        case 1:
             ....
            break;
        case 2:
             break;
      }
  }
}

I highly recommend this excellent pdf which explains the process in detail.