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## 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!

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

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