BrainFuck part 11 - Iterative and recursive ways

A first recursive way

Now, let's try to implement a recursion. The recursive call will be

factorial(N): return factorial(N-1) x N

Let's start

• Memory: 0 N 0 0 0 0
• Cursor: second cell
• Input: any

Process

• while N is not null
  • copy N-1 on the right
  • go to the copy
• loop
• write 1 (result for N=0)
• go to previous N value
• while there is a N value
  • multiply N by result
• loop

Note: this looks like

• Generate in memory values N, N-1, N-2, ..., 3, 2, 1, 0
• unwind by multiplying values to current result

Code

[                         while current N is not null
  [->+>+<<]>>[-<<+>>]<-   copy N and subtract 1
]                         and loop on this new value
+                         generate result
<[                        while current N is not null
  -[>[->+>+<<]>[-<+>]<<-] multiply result by N minus 1
  >>>[-<<+>>]<<[-<+>]     and add result one more to get result x N
<<]                       loop on next N

Minified version

[[->+>+<<]>>[-<<+>>]<-]+<[-[>[->+>+<<]>[-<+>]<<-]>>>[-<<+>>]<<[-<+>]<<]

Final state

• Memory: 0 N!
• Cursor: first cell
• Input: unchanged
• Output: unchanged

Test program

This programs prints x, code 120 = 5!

>+++++[[->+>+<<]>>[-<<+>>]<-]+<[-[>[->+>+<<]>[-<+>]<<-]>>>[-<<+>>]<<[-<+>]<<]>.