How to resolve the algorithm Ackermann function step by step in the Action! programming language

Published on 12 May 2024 09:40 PM
#Action!

How to resolve the algorithm Ackermann function step by step in the Action! programming language

Table of Contents

Problem Statement

The Ackermann function is a classic example of a recursive function, notable especially because it is not a primitive recursive function. It grows very quickly in value, as does the size of its call tree.

The Ackermann function is usually defined as follows:

Its arguments are never negative and it always terminates.

Write a function which returns the value of

A ( m , n )

{\displaystyle A(m,n)}

. Arbitrary precision is preferred (since the function grows so quickly), but not required.

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Ackermann function step by step in the Action! programming language

Source code in the action! programming language

DEFINE MAXSIZE="1000"
CARD ARRAY stack(MAXSIZE)
CARD stacksize=[0]

BYTE FUNC IsEmpty()
  IF stacksize=0 THEN
    RETURN (1)
  FI
RETURN (0)

PROC Push(BYTE v)
  IF stacksize=maxsize THEN
    PrintE("Error: stack is full!")
    Break()
  FI
  stack(stacksize)=v
  stacksize==+1
RETURN

BYTE FUNC Pop()
  IF IsEmpty() THEN
    PrintE("Error: stack is empty!")
    Break()
  FI
  stacksize==-1
RETURN (stack(stacksize))

CARD FUNC Ackermann(CARD m,n)
  Push(m)
  WHILE IsEmpty()=0
  DO
    m=Pop()
    IF m=0 THEN
      n==+1
    ELSEIF n=0 THEN
      n=1
      Push(m-1)
    ELSE
      n==-1
      Push(m-1)
      Push(m)
    FI
  OD
RETURN (n)

PROC Main()
  CARD m,n,res

  FOR m=0 TO 3
  DO
    FOR n=0 TO 4
    DO
      res=Ackermann(m,n)
      PrintF("Ack(%U,%U)=%U%E",m,n,res)
    OD
  OD
RETURN

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