Using a stack for recursive routines

• We know that the runtime stack is where we place activation records
  • Return address
  • Parameters
  • Local Variables
  • Copies of registers (save values)
• When we write recursive routines, we are really just using the stack
  • At some point in the computation we must push the current state onto the stack
  • Start a new computation
  • For example:
    • xⁿ
    • If n = 0, return 1
    • Otherwise return x*x^n-1

    • In this case, we are just pushing x onto the stack n-1 times.
    • 
    • We could handle the stack ourselves.
    • 
    • We just loop, while n > 0, and push x onto the stack.
  • In general we will need to loop while the stack is not empty
  • Push the current state onto the stack
  • Or alternatively, push future calls into a queue
  • Work on the next state.
• We could do this to a number of algorithms we have studied sofar
  • Merge sort - just put start and stop positions on the stack
  • quicksort - again, start and stop positions for subarray to sort
  • floodfill - put coordnates to fill
• Some examples
  • exp.C xⁿ
  • ack.C ackerman's function.