92 lines
1.9 KiB
Markdown
92 lines
1.9 KiB
Markdown
<center><img src="https://gitea.louisgallet.fr/lgallet/epicours/raw/branch/main/Algo/S%C3%A9minaire/assets/recursivite-meme.png " width=512 height=auto /> </center>
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### 5.1. Simple functions
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To create a recursive function we have to use this structure
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```Ocaml
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(*normal function*)
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# let f = expr -> 1) evaluate expr ; 2) create & link f to the result
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(*recursiv function*)
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# let rec f = expr -> 1) create f ; 2) evaluate expr ; 3) link f to the result
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```
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**Exmple with factorial function**
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```Ocaml
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# let rec fact = function
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| 0 -> 1
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| n -> n * fact(n-1)
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# fact 4;;
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-: int = 24
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```
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> ⚠️ CAML have a call stack limite (it will block with stack overflow if the limit is reach)
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**Basic expression**
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```Ocaml
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let rec f params =
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if stop condition then
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stop expression
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else
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recursive expression
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```
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To write a recurvise function we need two things
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1) There always is a stop case
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2) The parameters of a recursive call are different then its parent call, and go towards the stop condition
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### 5.2. Down
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```Ocaml
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# let rec countdown n =
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if n < 0 then
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()
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else
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begin
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print_int n ;
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print_newline();
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countdown(n-1);
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end;;
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val countdown = int -> unit = ()
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# countdown 3;;
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3
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2
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1
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- : unit = ()
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```
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Flowchart of CAML evaluation
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```mermaid
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flowchart LR
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A[ctd 3] --> B[ctd 2] --> C[ctd 1] --> D[ctd 0] --> E[ctd -1] --> F[ ] --> E --> D --> C --> B --> A
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```
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> ctd is countdown
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## 5.3. Several recursive calls
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A function that have several recursive calls is defind like this
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$$
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Fn = {1 -> \text{if } n\eqslantless{1} \brace{Fn+1+Fn+2} }
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$$
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**Fibonacci functions**
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```Ocaml
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let rec fibonacci n =
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if n = 0 then
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0
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else if n = 1 then
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1
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else
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fibonacci(n-1) + fibonacci(n-2);;
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let rec odd n =
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if n = 0 then
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false
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else
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even (n-1);;
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let rec even n =
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if n = 0 then
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true
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else
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add (n-1);;
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``` |