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Re: Ackermann dependency graph

by ikegami (Pope)
on Feb 03, 2011 at 22:54 UTC ( #886092=note: print w/replies, xml ) Need Help??


in reply to [OT]: threading recursive subroutines.

I built a dependency graph for Ackermann. Don't know if it helps.

╔═════╦═════╦═════╦═════╗
║ m=  ║  1  ║  2  ║  3  ║
╠═════╬═════╬═════╬═════╣
║ n=0 ║  2  ║     ║     ║
╚═════╬══v══╣     ║     ║
      ║  3  >  3  ║     ║
      ╠══v══╬══v══╣     ║
      ║  4  ║     ║     ║
      ╠══v══╣     ║     ║
      ║  5  >  5  >  5  ║
      ╠══v══╬══v══╬══v══╣
      ║  6  ║     ║     ║
      ╠══v══╣     ║     ║
      ║  7  >  7  ║     ║
      ╠══v══╬══v══╣     ║
      ║  8  ║     ║     ║
      ╠══v══╣     ║     ║
      ║  9  >  9  ║     ║
      ╠══v══╬══v══╣     ║
      ║ 10  ║     ║     ║
      ╠══v══╣     ║     ║
      ║ 11  > 11  ║     ║
      ╠══v══╬══v══╣     ║
      ║ 12  ║     ║     ║
      ╠══v══╣     ║     ║
      ║ 13  > 13  > 13  ║
      ╠══v══╬══v══╬══v══╣
      ║ 14  ║     ║     ║
      ╠══v══╣     ║     ║
      ║ 15  > 15  ║     ║
      ╠══v══╬══v══╣     ║
      ║ 16  ║     ║     ║
      ╠══v══╣     ║     ║
      ║ 17  > 17  ║     ║
      ╠══v══╬══v══╣     ║
      ║ 18  ║     ║     ║
      ╠══v══╣     ║     ║
      ║ 19  > 19  ║     ║
      ╠══v══╬══v══╣     ║
      ║ 20  ║     ║     ║
      ╠══v══╣     ║     ║
      ║ 21  > 21  ║     ║
      ╠══v══╬══v══╣     ║
      ║ 22  ║     ║     ║
      ╠══v══╣     ║     ║
      ║ 23  > 23  ║     ║
      ╠══v══╬══v══╣     ║
      ║ 24  ║     ║     ║
      ╠══v══╣     ║     ║
      ║ 25  > 25  ║     ║
      ╠══v══╬══v══╣     ║
      ║ 26  ║     ║     ║
      ╠══v══╣     ║     ║
      ║ 27  > 27  ║     ║
      ╠══v══╬══v══╣     ║
      ║ 28  ║     ║     ║
      ╠══v══╣     ║     ║
      ║ 29  > 29  > 29  ║
      ╚═════╩═════╩═════╝

Each box along the vertical axis is one "n" higher, so A(3,2)=A(2,13)=A(1,27)=29.

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