Add some math functions

Math/Ceil.ml

@@ -0,0 +1,5 @@
+(* Ceil function *)
+
+let ceil x = 
+	if 2 - int_of_float x <= 0 then int_of_float(x)
+	else int_of_float(x) + 1;;

Math/Euclidean gcd.ml

@@ -0,0 +1,18 @@
+(* Euclidean GCD*)
+
+let euclidean_gcd a b =
+	let t = ref a in
+	let a = ref a in
+	let b = ref b in
+	while !b <> 0 do
+		t := !a;
+		a := !b;
+		b := !t mod !b;
+	done;
+	!a ;;
+
+
+(* Euclidean GCD Recursive *)
+
+let rec euclidean_gcd_recursive a b = 
+	if b == 0 then a else euclidean_gcd_recursive b (a mod b);;

Math/Fibonacci Sequence Recursion.ml

@@ -0,0 +1,9 @@
+(*Recursive Fibonacci function*)
+
+let rec fib n = match n with
+	| 1 -> 1
+	| 2 -> 1
+	| _ -> fib (n - 1) + fib(n - 2);;
+
+
+

Math/Find max recursion.ml

@@ -0,0 +1,6 @@
+(* Find max recursion *)
+
+let rec find_max l = match l with
+	|[x] -> x
+	|t::q -> if t > (find_max q) then t else find_max q
+	|[] -> failwith "Liste vide!";;

Math/Find min recursion.ml

@@ -0,0 +1,6 @@
+(* Find min recursion *)
+
+let rec find_min l = match l with
+	|[x] -> x
+	|t::q -> if t < (find_min q) then t else find_min q
+	|[] -> failwith "Liste vide!";;

Math/Sum of digits.ml

@@ -0,0 +1,5 @@
+(* Sum of digits *)
+
+let rec sum_of_digits_recursion n =
+	let abs x = if x > 0 then x else -x in (* We need the absolute value of the number for the result to be positive) *)
+	if abs(n) < 10 then abs(n) else abs(n) mod 10 + sum_of_digits_recursion (n / 10);;

Math/abs.ml

@@ -0,0 +1,3 @@
+(* Absolute value *)
+
+let abs x = if x > 0 then x else -x;;

Math/power-using-recursion.ml

@@ -0,0 +1,5 @@
+(* Power using recursion *)
+(* power : float -> int -> float *)
+
+let rec power base exponent = 
+	if exponent <> 0 then  base *. power base (exponent - 1) else 1.;;

project_euler/problem_001/sol1.ml

@@ -0,0 +1,9 @@
+(* Project Euler - Problem 1 *)
+
+let rec sum n = match n with
+	| 1 -> 0
+	| _ -> if n mod 3 = 0 || n mod 5 = 0 then n + sum (n - 1) else sum (n - 1)
+	;;
+
+sum (1000 - 1);; 
+

project_euler/problem_002/sol11.ml

@@ -0,0 +1,11 @@
+(* Euler project - Problem 2 *)
+
+let rec sum current previous max accu = 
+	if current > max 
+		then accu 
+		else
+			if current mod 2 = 0 
+				then sum (current + previous) current max (accu + current)
+				else sum (current + previous) current max accu;;
+
+sum 2 1 4000000 0;;	

project_euler/problem_003/sol1.ml

@@ -0,0 +1,16 @@
+(* Euler Project - Problem 3 *)
+
+let rec bigger_div n d =
+	if n mod d = 0 then n/d
+	else bigger_div n (d + 1);;
+
+let is_composed n = bigger_div n 2 <> 1;;
+
+let solution n = 
+	let test = ref (bigger_div n 2) in
+	while is_composed !test do
+		test := bigger_div !test 2
+		done;
+	!test;;
+
+solution 600851475143 ;;	

project_euler/problem_004/sol1.ml

@@ -0,0 +1,22 @@
+(* Euler Project - Problem 4 *)
+
+let is_palindromic n = 
+	let str_n = string_of_int n in
+	let len_n = 1 + int_of_float(log10(float_of_int n)) in
+	let rec palindrom_test = function
+		| i when i = len_n / 2 -> true
+		| i -> str_n.[i] = str_n.[len_n - i - 1] && palindrom_test (i + 1)
+	in palindrom_test 0;;
+
+let solution = 
+	let largest = ref 0 in
+	for a = 100 to 999 do
+		for b = 100 to 999 do
+			if is_palindromic (a * b) then
+				if (a * b) > !largest then largest := (a * b)
+		done
+	done;
+	!largest
+	;;
+
+solution;;

project_euler/problem_005/sol1.ml

@@ -0,0 +1,15 @@
+(* Euler Project - Problem 5 *)
+
+let solution =
+	let solved = ref false in
+	let i = ref (20*19) in
+	while !solved = false do
+		solved := true;
+		for d = 2 to 20 do
+			if !i mod d <> 0 then solved := false
+		done;
+		if !solved = false then i := !i + (20*19)
+	done;
+	!i;;
+
+solution;;