# Algorithm all possible combinations

**URL:** <https://discuss.ocaml.org/t/algorithm-all-possible-combinations/8050>\
**Category:** Learning\
**Created:** [June 25, 2021, 9:31am UTC](https://discuss.ocaml.org/t/algorithm-all-possible-combinations/8050 "2021-06-25T09:31:04Z")\
**Posts on this page:** 2\
**Page:** 1

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**Author:** ![DonCorleone](https://sea2.discourse-cdn.com/flex020/user_avatar/discuss.ocaml.org/doncorleone/32/2985_2.png) [@DonCorleone](https://discuss.ocaml.org/u/DonCorleone)\
**Post date:** [June 25, 2021, 9:31am UTC](https://discuss.ocaml.org/t/algorithm-all-possible-combinations/8050/1 "2021-06-25T09:31:04Z")

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Hello, I wrote the function “main” which is passed as an argument to two positive integers “a” “b” and returns “k list list” which is a list of all possible lists where the length of “k list” is “a” and the sum of its elements is "b ", (Win - 3, Draw - 1, Loose - 0).  
example:  
main 3 4;;

- : k list list =  
[[Loose; Draw; Win]; [Loose; Win; Draw]; [Win; Draw; Loose];  
[Draw; Win; Loose]; [Draw; Loose; Win]; [Win; Loose; Draw]]  
I’m afraid the “create” function might not work because of the Random.int function.  
Can you offer me a more optimal solution or help me to fix that problem.  
here is my code:  
type k = Win | Draw | Loose  
let rec sum n = match n with [] → 0 | h::t → h + sum t;;  
let rec create n = let k = Random.int 4 in if k != 2&&n \> 0 then k::create (n-1) else if k = 2&&n \> 0 then create n else [];;  
let rec convert l = match l with [] → [] | h::t → if h = 3 then Win::convert t else if h = 1 then Draw::convert t else Loose::convert t;;  
let rec pow a = function | 0 → 1 | 1 → a | n → let b = pow a (n / 2) in b \* b \* (if n mod 2 = 0 then 1 else a);;  
let rec calculate a b acc = match acc with 0 → [] | acc → let k = create a in if sum (k) = b then (convert (k))::calculate a b (acc - 1) else calculate a b (acc - 1);;  
let f acc x = if List.mem x acc = false then x::acc else acc@[];;  
let rec similar l = List.fold\_left f [] l;;  
let main a b = similar (calculate a b 580000);;

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**Author:** ![octachron](https://avatars.discourse-cdn.com/v4/letter/o/49beb7/32.png) [@octachron](https://discuss.ocaml.org/u/octachron)\
**Post date:** [June 25, 2021, 9:54am UTC](https://discuss.ocaml.org/t/algorithm-all-possible-combinations/8050/2 "2021-06-25T09:54:36Z")

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You should format your code with

````auto
```ocaml
(*your code here*)
`​``

````

But yes, using rejection sampling to enumerate all possible combinations is never efficient. You should enumerate then directly with a recursive function `combination len sum`.