added sieve of eratosthenes

Author: sysl91

Diff for: #random-integers-common-factor.ml#

@@ -0,0 +1,26 @@
+(*
+What is the probability of four random integers having a common factor?
+ *)
+
+(* implementation of the Sieve of Eratosthenese
+   we use 0 to denote struck-out numbers.
+   could be made more efficient by choosing to strike out multiples
+   above p^2 rather than p
+*)
+
+let rec strike_nth k n l = match l with
+  | [] -> []
+  | h :: t ->
+     if k = 0 then 0 :: strike_nth (n-1) n t
+     else h :: strike_nth (k-1) n t;;
+
+let primes n =
+  let limit = truncate(sqrt(float n)) in
+  let rec range a b = if a > b then [] else a :: range (a+1) b in
+  let rec sieve_primes l = match l with
+    | [] -> []
+    | 0 :: t -> sieve_primes t
+    | h :: t -> if h > limit then List.filter ((<) 0) l else
+		  h :: sieve_primes (strike_nth (h-1) h t) in
+  sieve_primes (range 2 n);;
+      

Diff for: .#random-integers-common-factor.ml

@@ -0,0 +1 @@
+Sana@MacBook-Pro-6.local.9792

Diff for: .DS_Store

@@ -0,0 +1,15 @@
+(*
+What is the probability of four random integers having a common factor?
+ *)
+
+(* implementation of the Sieve of Eratosthenese
+   we use 0 to denote struck-out numbers.
+   could be made more efficient by choosing to strike out multiples
+   above p^2 rather than p
+*)
+
+let rec strike_nth k n l = match l with
+  | [] -> []
+  | h :: t ->
+     if k = 0 then 0 :: strike_nth (n-1) n t
+     else h :: strike_nth (k-1) n t;;