Ackermann's Function

• A(m,n) =
  • n+1 when m = 0
  • A(m-1, 1) when n = 0
  • A(m-1, A(m, n-1)) otherwise.
• A trace

  A(1,1) = A(0, A(1,0)) 
                           A(1,0) = A(0,1)
                           A(0,1) = 2
           A(0,2) = 3
  
  A(2,2) = A(1,A(2,1))
               A(2,1) = A(1,A(2,0))
                            A(2,0) = A(1,1)
                                   = 3 from above
                      = A(1,3) = A(0, A(1,2))
                                      A(1,2) = A(0, A(1,1))
                                                    A(1,1) = 3 from above
                                             = A(0,3)  = 4
                                 A(0,4) = 5
           A(1,5) = A(0,A(1,4))
                        A(1,4) = A(0, A(1,3))
                                      A(1,3) = 5 from above.
                                 A(0,5) = 6
                    A(0,6) = 7
      

• I wrote it here
• I also modified fib.cpp
  • I added the ability to count the number of calls to the recursive function.
  • I added a memoized recursive function.
  • I added an iterative version.