_

champ.fs

let triples n =    
    let mutable triples = []    
    let mutable ones = []    
    let mutable pairs = 
        [   for x = 1 to n+1 do
                for y = x+1 to n+1 do
                    yield x,y]         
    let del k = pairs <- List.filter( (<>) k) pairs
    while not pairs.IsEmpty do
        let (x,y) as xy = pairs.Head
        del xy
        match List.tryFind(fun (a,_) -> a = y) pairs with 
        | None -> 
            ones <- xy :: ones 
        | Some ((a,b) as ab) -> 
            del ab
            match List.tryFind((=) (x,b) ) pairs  with 
            | None ->  
                triples <- [xy; ab] :: triples 
            | Some xb -> 
                del xb
                triples <- [ xy; ab; xb ] :: triples 
    pairs <- ones
    
    while not pairs.IsEmpty do
        let (x,y) as xy = pairs.Head
        del xy
        match List.tryFind(fun (a,b) -> a = x || a = y || b=x || b = y) pairs with 
        | None -> 
            triples <- [xy] :: triples 
        | Some ((a,b) as ab) -> 
            del ab
            triples <- [xy; ab] :: triples 
    triples

fsi_output.txt

---
> List.iteri (printfn "%d : %A") (triples 7) ;;
0 : [(1, 8)]
1 : [(5, 8); (4, 8)]
2 : [(3, 6); (6, 8); (3, 8)]
3 : [(3, 5); (5, 7)]
4 : [(3, 4); (4, 7); (3, 7)]
5 : [(2, 7); (7, 8); (2, 8)]
6 : [(2, 5); (5, 6)]
7 : [(2, 4); (4, 6); (2, 6)]
8 : [(1, 6); (6, 7); (1, 7)]
9 : [(1, 4); (4, 5); (1, 5)]
10 : [(1, 2); (2, 3); (1, 3)]
val it : unit = ()
>