Commit e76a300d by MARCHE Claude

### In progress: euler003

parent 2b6fffc3
 ... @@ -14,37 +14,64 @@ use import number.Divisibility ... @@ -14,37 +14,64 @@ use import number.Divisibility use import number.Prime use import number.Prime (** returns the smallest divisor of [n] greater or equal to [d] *) (** returns the smallest divisor of [n] greater or equal to [d] *) let rec prim_fact (d n:int) : int let rec smallest_divisor (d n:int) : int requires { 2 <= n } requires { 1 <= d <= n } requires { 1 <= d <= n } ensures { d <= result <= n } ensures { d <= result <= n } ensures { divides result n } ensures { divides result n } ensures { forall i:int. d <= i < result -> not divides result i } ensures { forall i:int. d <= i < result -> not divides result i } variant { n - d } variant { n - d } = if d * d > n then n else = if d * d > n then n else if mod n d = 0 then d else if d >= 2 && mod n d = 0 then d else prim_fact (d+1) n smallest_divisor (d+1) n let test2 () = smallest_divisor 2 13195 (* 5 *) let test5 () = smallest_divisor 5 13195 (* 5 *) let test6 () = smallest_divisor 6 13195 (* 7 *) let test8 () = smallest_divisor 8 13195 (* 13 *) let test14 () = smallest_divisor 14 13195 (* 29 *) let test30 () = smallest_divisor 30 13195 (* 35 *) exception Exit use import ref.Ref use import ref.Ref use import list.List val factors : ref (list int) let largest_prime_factor (n:int) : int let largest_prime_factor (n:int) : int requires { 2 <= n } requires { 2 <= n } ensures { prime result } ensures { prime result } ensures { divides result n } ensures { divides result n } ensures { forall i:int. result < i <= n -> not (prime i /\ divides i n) } ensures { forall i:int. result < i <= n -> not (prime i /\ divides i n) } = let factor = ref 1 in = let d = smallest_divisor 1 n in try let factor = ref d in while True do let target = ref (div n d) in invariant { 1 <= !factor < n } factors := Cons d Nil; invariant { divides !factor n } while !target >= 2 do let d = prim_fact (!factor+1) n in invariant { !target = 1 \/ 2 <= !factor <= !target } if d = n then raise Exit; (* invariant { 2 <= !factor <= n } *) factor := d (* invariant { divides !target n } *) done; invariant { divides !factor n } absurd invariant { prime !factor } with Exit -> !factor variant { !target } end let d = smallest_divisor !factor !target in factor := d; factors := Cons d !factors; target := div !target d done; !factor let test () = largest_prime_factor 13195 (* should be 29 *) let solve () = largest_prime_factor 600851475143 (* should be 6857 *) end end ... ...
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