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let pair_mode (l: 'a list) : 'a * 'a = if List.length l <= 1 then failwith "The list is too small and does not contain any pairs!" else let l1 = List.tl (l) in let l2 = List.rev (List.tl (List.rev(l))) in let allTuples = List.combine l2 l1 in mode (allTuples) ;; |
let convert_time ((from_unit, val_) : time_unit value) to_unit : time_unit value = match from_unit, to_unit with | Second, Hour -> (Hour, val_ /. 3600.) | Hour, Second -> (Second, val_ *. 3600.) | Second, Second -> (Second, val_) | Hour, Hour -> (Hour, val_) ;; |
let convert_dist ((from_unit, val_) : dist_unit value) to_unit : dist_unit value = match from_unit, to_unit with | Foot, Foot -> (Foot, val_) | Meter, Meter -> (Meter, val_) | Mile, Mile -> (Mile, val_) | Foot, Meter -> (Meter, val_ *. 0.3048) | Foot, Mile -> (Mile, val_ /. 5280.) | Meter, Foot -> (Foot, val_ /. 0.3048) | Meter, Mile -> (Mile, val_ /. 0.3048 /. 5280.) | Mile, Foot -> (Foot, val_ *. 5280.) | Mile, Meter -> (Meter, val_ *. 5280. *. 0.3048) ;; |
let convert_speed ((from_unit, val_) : speed_unit value) to_unit : speed_unit value = if from_unit = to_unit then ((fst(from_unit), snd(to_unit)) , val_) else let inputDistUnit = fst(from_unit) in let inputTimeUnit = snd(from_unit) in let outputDistUnit = fst(to_unit) in let outputTimeUnit = snd(to_unit) in let outputDistFactor = snd(convert_dist(inputDistUnit, 1.) outputDistUnit) in let outputTimeFactor = snd(convert_time(inputTimeUnit, 1.) outputTimeUnit) in let outputVal = (val_ *. outputDistFactor /. outputTimeFactor) in ((outputDistUnit, outputTimeUnit), outputVal) ;; |
let add_speed (a : speed_unit value) ((b_unit, b_val) : speed_unit value) : speed_unit value = let aUnit = fst(a) in let aNumber = snd(a) in let aInBUnits = convert_speed(aUnit, aNumber) (b_unit) in let aPlusBNumber = snd(aInBUnits) +. b_val in (b_unit, aPlusBNumber) ;; |
let passes_da_vinci t = let rec check l = match l with | [] -> true | Leaf :: tl -> check tl | Branch (width, subtree) :: tl -> if ((check subtree) && (squaredSumSubtrees (width, subtree) <= width)) then check tl else false in check [t] ;; |
let mode (l: 'a list) : 'a = if l == [] then failwith "Invalid input." else let l = List.sort compare (l) in let rec aux l ((cur_el, cur_num) : 'a * int) ((max_el, max_num) : 'a * int) = match l with | [] -> if cur_num > max_num then cur_el else if (cur_num = max_num) && (compare cur_el max_el < 0) then cur_el else max_el | hd :: restOfList -> if compare hd cur_el = 0 then if cur_num + 1 > max_num then aux restOfList (hd, cur_num + 1)(hd, cur_num + 1) else if cur_num + 1 = max_num then if compare cur_el max_el <= 0 then aux restOfList (hd, cur_num + 1)(hd, cur_num + 1) else aux restOfList (hd, cur_num + 1)(max_el, max_num) else aux restOfList(hd, cur_num + 1) (max_el, max_num) else aux restOfList(hd, 1)(max_el, max_num) in aux l (List.hd(l),0) (List.hd(l),0) ;; |
let pair_mode (l: 'a list) : 'a * 'a = if List.length l <= 1 then failwith "The list is too small and does not contain any pairs!" else let l1 = List.tl (l) in let l2 = List.rev (List.tl (List.rev(l))) in let allTuples = List.combine l2 l1 in mode (allTuples) ;; |
let convert_time ((from_unit, val_) : time_unit value) to_unit : time_unit value = match from_unit, to_unit with | Second, Hour -> (Hour, val_ /. 3600.) | Hour, Second -> (Second, val_ *. 3600.) | Second, Second -> (Second, val_) | Hour, Hour -> (Hour, val_) ;; |
let convert_dist ((from_unit, val_) : dist_unit value) to_unit : dist_unit value = match from_unit, to_unit with | Foot, Foot -> (Foot, val_) | Meter, Meter -> (Meter, val_) | Mile, Mile -> (Mile, val_) | Foot, Meter -> (Meter, val_ *. 0.3048) | Foot, Mile -> (Mile, val_ /. 5280.) | Meter, Foot -> (Foot, val_ /. 0.3048) | Meter, Mile -> (Mile, val_ /. 0.3048 /. 5280.) | Mile, Foot -> (Foot, val_ *. 5280.) | Mile, Meter -> (Meter, val_ *. 5280. *. 0.3048) ;; |
let convert_speed ((from_unit, val_) : speed_unit value) to_unit : speed_unit value = if from_unit = to_unit then ((fst(from_unit), snd(to_unit)) , val_) else let inputDistUnit = fst(from_unit) in let inputTimeUnit = snd(from_unit) in let outputDistUnit = fst(to_unit) in let outputTimeUnit = snd(to_unit) in let outputDistFactor = snd(convert_dist(inputDistUnit, 1.) outputDistUnit) in let outputTimeFactor = snd(convert_time(inputTimeUnit, 1.) outputTimeUnit) in let outputVal = (val_ *. outputDistFactor /. outputTimeFactor) in ((outputDistUnit, outputTimeUnit), outputVal) ;; |
let add_speed (a : speed_unit value) ((b_unit, b_val) : speed_unit value) : speed_unit value = let aUnit = fst(a) in let aNumber = snd(a) in let aInBUnits = convert_speed(aUnit, aNumber) (b_unit) in let aPlusBNumber = snd(aInBUnits) +. b_val in (b_unit, aPlusBNumber) ;; |
let passes_da_vinci t = let rec check l = match l with | [] -> true | Leaf :: tl -> check tl | Branch (width, subtree) :: tl -> if ((check subtree) && (squaredSumSubtrees (width, subtree) <= width)) then check tl else false in check [t] ;; |
let mode (l: 'a list) : 'a = if l == [] then failwith "Invalid input." else let l = List.sort compare (l) in let rec aux l ((cur_el, cur_num) : 'a * int) ((max_el, max_num) : 'a * int) = match l with | [] -> if cur_num > max_num then cur_el else if (cur_num = max_num) && (compare cur_el max_el < 0) then cur_el else max_el | hd :: restOfList -> if compare hd cur_el = 0 then if cur_num + 1 > max_num then aux restOfList (hd, cur_num + 1)(hd, cur_num + 1) else if cur_num + 1 = max_num then if compare cur_el max_el <= 0 then aux restOfList (hd, cur_num + 1)(hd, cur_num + 1) else aux restOfList (hd, cur_num + 1)(max_el, max_num) else aux restOfList(hd, cur_num + 1) (max_el, max_num) else aux restOfList(hd, 1)(max_el, max_num) in aux l (List.hd(l),0) (List.hd(l),0) ;; |
let pair_mode (l: 'a list) : 'a * 'a = if List.length l <= 1 then failwith "The list is too small and does not contain any pairs!" else let l1 = List.tl (l) in let l2 = List.rev (List.tl (List.rev(l))) in let allTuples = List.combine l2 l1 in mode (allTuples) ;; |
let convert_time ((from_unit, val_) : time_unit value) to_unit : time_unit value = match from_unit, to_unit with | Second, Hour -> (Hour, val_ /. 3600.) | Hour, Second -> (Second, val_ *. 3600.) | Second, Second -> (Second, val_) | Hour, Hour -> (Hour, val_) ;; |
let convert_dist ((from_unit, val_) : dist_unit value) to_unit : dist_unit value = match from_unit, to_unit with | Foot, Foot -> (Foot, val_) | Meter, Meter -> (Meter, val_) | Mile, Mile -> (Mile, val_) | Foot, Meter -> (Meter, val_ *. 0.3048) | Foot, Mile -> (Mile, val_ /. 5280.) | Meter, Foot -> (Foot, val_ /. 0.3048) | Meter, Mile -> (Mile, val_ /. 0.3048 /. 5280.) | Mile, Foot -> (Foot, val_ *. 5280.) | Mile, Meter -> (Meter, val_ *. 5280. *. 0.3048) ;; |
let convert_speed ((from_unit, val_) : speed_unit value) to_unit : speed_unit value = if from_unit = to_unit then ((fst(from_unit), snd(to_unit)) , val_) else let inputDistUnit = fst(from_unit) in let inputTimeUnit = snd(from_unit) in let outputDistUnit = fst(to_unit) in let outputTimeUnit = snd(to_unit) in let outputDistFactor = snd(convert_dist(inputDistUnit, 1.) outputDistUnit) in let outputTimeFactor = snd(convert_time(inputTimeUnit, 1.) outputTimeUnit) in let outputVal = (val_ *. outputDistFactor /. outputTimeFactor) in ((outputDistUnit, outputTimeUnit), outputVal) ;; |
let add_speed (a : speed_unit value) ((b_unit, b_val) : speed_unit value) : speed_unit value = let aUnit = fst(a) in let aNumber = snd(a) in let aInBUnits = convert_speed(aUnit, aNumber) (b_unit) in let aPlusBNumber = snd(aInBUnits) +. b_val in (b_unit, aPlusBNumber) ;; |
let passes_da_vinci t = let acc = 0. in let rec check l = match l with | [] -> true | Leaf :: tl -> check tl | Branch (width, subtree) :: tl -> if ((check subtree) && (squaredSumSubtrees acc (width, subtree) <= width)) then check tl else false in check [t] ;; |
let mode (l: 'a list) : 'a = if l == [] then failwith "Invalid input." else let l = List.sort compare (l) in let rec aux l ((cur_el, cur_num) : 'a * int) ((max_el, max_num) : 'a * int) = match l with | [] -> if cur_num > max_num then cur_el else if (cur_num = max_num) && (compare cur_el max_el < 0) then cur_el else max_el | hd :: restOfList -> if compare hd cur_el = 0 then if cur_num + 1 > max_num then aux restOfList (hd, cur_num + 1)(hd, cur_num + 1) else if cur_num + 1 = max_num then if compare cur_el max_el <= 0 then aux restOfList (hd, cur_num + 1)(hd, cur_num + 1) else aux restOfList (hd, cur_num + 1)(max_el, max_num) else aux restOfList(hd, cur_num + 1) (max_el, max_num) else aux restOfList(hd, 1)(max_el, max_num) in aux l (List.hd(l),0) (List.hd(l),0) ;; |
let pair_mode (l: 'a list) : 'a * 'a = if List.length l <= 1 then failwith "The list is too small and does not contain any pairs!" else let l1 = List.tl (l) in let l2 = List.rev (List.tl (List.rev(l))) in let allTuples = List.combine l2 l1 in mode (allTuples) ;; |
let convert_time ((from_unit, val_) : time_unit value) to_unit : time_unit value = match from_unit, to_unit with | Second, Hour -> (Hour, val_ /. 3600.) | Hour, Second -> (Second, val_ *. 3600.) | Second, Second -> (Second, val_) | Hour, Hour -> (Hour, val_) ;; |
let convert_dist ((from_unit, val_) : dist_unit value) to_unit : dist_unit value = match from_unit, to_unit with | Foot, Foot -> (Foot, val_) | Meter, Meter -> (Meter, val_) | Mile, Mile -> (Mile, val_) | Foot, Meter -> (Meter, val_ *. 0.3048) | Foot, Mile -> (Mile, val_ /. 5280.) | Meter, Foot -> (Foot, val_ /. 0.3048) | Meter, Mile -> (Mile, val_ /. 0.3048 /. 5280.) | Mile, Foot -> (Foot, val_ *. 5280.) | Mile, Meter -> (Meter, val_ *. 5280. *. 0.3048) ;; |
let convert_speed ((from_unit, val_) : speed_unit value) to_unit : speed_unit value = if from_unit = to_unit then ((fst(from_unit), snd(to_unit)) , val_) else let inputDistUnit = fst(from_unit) in let inputTimeUnit = snd(from_unit) in let outputDistUnit = fst(to_unit) in let outputTimeUnit = snd(to_unit) in let outputDistFactor = snd(convert_dist(inputDistUnit, 1.) outputDistUnit) in let outputTimeFactor = snd(convert_time(inputTimeUnit, 1.) outputTimeUnit) in let outputVal = (val_ *. outputDistFactor /. outputTimeFactor) in ((outputDistUnit, outputTimeUnit), outputVal) ;; |
let add_speed (a : speed_unit value) ((b_unit, b_val) : speed_unit value) : speed_unit value = let aUnit = fst(a) in let aNumber = snd(a) in let aInBUnits = convert_speed(aUnit, aNumber) (b_unit) in let aPlusBNumber = snd(aInBUnits) +. b_val in (b_unit, aPlusBNumber) ;; |
let passes_da_vinci t = let acc = 0. in let rec check l = match l with | [] -> true | Leaf :: tl -> check tl | Branch (width, subtree) :: tl -> if ((check subtree) && (squaredSumSubtrees acc (width, subtree) <= width)) then check tl else false in check [t] ;; |
let mode (l: 'a list) : 'a = if l == [] then failwith "Invalid input." else let l = List.sort compare (l) in let rec aux l ((cur_el, cur_num) : 'a * int) ((max_el, max_num) : 'a * int) = match l with | [] -> if cur_num > max_num then cur_el else if (cur_num = max_num) && (compare cur_el max_el < 0) then cur_el else max_el | hd :: restOfList -> if compare hd cur_el = 0 then if cur_num + 1 > max_num then aux restOfList (hd, cur_num + 1)(hd, cur_num + 1) else if cur_num + 1 = max_num then if compare cur_el max_el <= 0 then aux restOfList (hd, cur_num + 1)(hd, cur_num + 1) else aux restOfList (hd, cur_num + 1)(max_el, max_num) else aux restOfList(hd, cur_num + 1) (max_el, max_num) else aux restOfList(hd, 1)(max_el, max_num) in aux l (List.hd(l),0) (List.hd(l),0) ;; |
let pair_mode (l: 'a list) : 'a * 'a = if List.length l <= 1 then failwith "The list is too small and does not contain any pairs!" else let l1 = List.tl (l) in let l2 = List.rev (List.tl (List.rev(l))) in let allTuples = List.combine l2 l1 in mode (allTuples) ;; |
let convert_time ((from_unit, val_) : time_unit value) to_unit : time_unit value = match from_unit, to_unit with | Second, Hour -> (Hour, val_ /. 3600.) | Hour, Second -> (Second, val_ *. 3600.) | Second, Second -> (Second, val_) | Hour, Hour -> (Hour, val_) ;; |
let convert_dist ((from_unit, val_) : dist_unit value) to_unit : dist_unit value = match from_unit, to_unit with | Foot, Foot -> (Foot, val_) | Meter, Meter -> (Meter, val_) | Mile, Mile -> (Mile, val_) | Foot, Meter -> (Meter, val_ *. 0.3048) | Foot, Mile -> (Mile, val_ /. 5280.) | Meter, Foot -> (Foot, val_ /. 0.3048) | Meter, Mile -> (Mile, val_ /. 0.3048 /. 5280.) | Mile, Foot -> (Foot, val_ *. 5280.) | Mile, Meter -> (Meter, val_ *. 5280. *. 0.3048) ;; |
let convert_speed ((from_unit, val_) : speed_unit value) to_unit : speed_unit value = if from_unit = to_unit then ((fst(from_unit), snd(to_unit)) , val_) else let inputDistUnit = fst(from_unit) in let inputTimeUnit = snd(from_unit) in let outputDistUnit = fst(to_unit) in let outputTimeUnit = snd(to_unit) in let outputDistFactor = snd(convert_dist(inputDistUnit, 1.) outputDistUnit) in let outputTimeFactor = snd(convert_time(inputTimeUnit, 1.) outputTimeUnit) in let outputVal = (val_ *. outputDistFactor /. outputTimeFactor) in ((outputDistUnit, outputTimeUnit), outputVal) ;; |
let add_speed (a : speed_unit value) ((b_unit, b_val) : speed_unit value) : speed_unit value = let aUnit = fst(a) in let aNumber = snd(a) in let aInBUnits = convert_speed(aUnit, aNumber) (b_unit) in let aPlusBNumber = snd(aInBUnits) +. b_val in (b_unit, aPlusBNumber) ;; |
let passes_da_vinci t = let acc = 0. in let rec check l = match l with | [] -> true | Leaf :: tl -> check tl | Branch (width, subtree) :: tl -> if ((check subtree) && ((squaredSumSubtrees acc subtree) <= width)) then check tl else false in check [t] ;; |
let mode (l: 'a list) : 'a = if l == [] then failwith "Invalid input." else let l = List.sort compare (l) in let rec aux l ((cur_el, cur_num) : 'a * int) ((max_el, max_num) : 'a * int) = match l with | [] -> if cur_num > max_num then cur_el else if (cur_num = max_num) && (compare cur_el max_el < 0) then cur_el else max_el | hd :: restOfList -> if compare hd cur_el = 0 then if cur_num + 1 > max_num then aux restOfList (hd, cur_num + 1)(hd, cur_num + 1) else if cur_num + 1 = max_num then if compare cur_el max_el <= 0 then aux restOfList (hd, cur_num + 1)(hd, cur_num + 1) else aux restOfList (hd, cur_num + 1)(max_el, max_num) else aux restOfList(hd, cur_num + 1) (max_el, max_num) else aux restOfList(hd, 1)(max_el, max_num) in aux l (List.hd(l),0) (List.hd(l),0) ;; |
let pair_mode (l: 'a list) : 'a * 'a = if List.length l <= 1 then failwith "The list is too small and does not contain any pairs!" else let l1 = List.tl (l) in let l2 = List.rev (List.tl (List.rev(l))) in let allTuples = List.combine l2 l1 in mode (allTuples) ;; |
let convert_time ((from_unit, val_) : time_unit value) to_unit : time_unit value = match from_unit, to_unit with | Second, Hour -> (Hour, val_ /. 3600.) | Hour, Second -> (Second, val_ *. 3600.) | Second, Second -> (Second, val_) | Hour, Hour -> (Hour, val_) ;; |
let convert_dist ((from_unit, val_) : dist_unit value) to_unit : dist_unit value = match from_unit, to_unit with | Foot, Foot -> (Foot, val_) | Meter, Meter -> (Meter, val_) | Mile, Mile -> (Mile, val_) | Foot, Meter -> (Meter, val_ *. 0.3048) | Foot, Mile -> (Mile, val_ /. 5280.) | Meter, Foot -> (Foot, val_ /. 0.3048) | Meter, Mile -> (Mile, val_ /. 0.3048 /. 5280.) | Mile, Foot -> (Foot, val_ *. 5280.) | Mile, Meter -> (Meter, val_ *. 5280. *. 0.3048) ;; |
let convert_speed ((from_unit, val_) : speed_unit value) to_unit : speed_unit value = if from_unit = to_unit then ((fst(from_unit), snd(to_unit)) , val_) else let inputDistUnit = fst(from_unit) in let inputTimeUnit = snd(from_unit) in let outputDistUnit = fst(to_unit) in let outputTimeUnit = snd(to_unit) in let outputDistFactor = snd(convert_dist(inputDistUnit, 1.) outputDistUnit) in let outputTimeFactor = snd(convert_time(inputTimeUnit, 1.) outputTimeUnit) in let outputVal = (val_ *. outputDistFactor /. outputTimeFactor) in ((outputDistUnit, outputTimeUnit), outputVal) ;; |
let add_speed (a : speed_unit value) ((b_unit, b_val) : speed_unit value) : speed_unit value = let aUnit = fst(a) in let aNumber = snd(a) in let aInBUnits = convert_speed(aUnit, aNumber) (b_unit) in let aPlusBNumber = snd(aInBUnits) +. b_val in (b_unit, aPlusBNumber) ;; |
let passes_da_vinci t = let acc = 0. in let rec check l = match l with | [] -> true | Leaf :: tl -> check tl | Branch (width, subtree) :: tl -> if ((check subtree) && ((squaredSumSubtrees acc subtree) <= (width *. width))) then check tl else false in check [t] ;; |
let mode (l: 'a list) : 'a = let rec aux l ((cur_el, cur_num) : 'a * int) ((max_el, max_num) : 'a * int) = match l with | [] -> if cur_num > max_num then cur_el else max_el | x::xs -> if cur_el = x then aux xs (cur_el,(cur_num + 1)) (max_el, max_num) else if cur_num > max_num then aux xs (x, 1) (cur_el, cur_num) else aux xs (x,1) (max_el, max_num) in match List.sort compare l with | [] -> failwith "No mode" | x::xs -> aux xs (x,1) (x,1) ;; |
let pair_mode (l: 'a list) : 'a * 'a = let rec get_tupples l last_el tup_l = match l with | [] -> mode tup_l | x::xs -> get_tupples xs x ((last_el, x)::tup_l) in match l with | [] -> failwith "No mode" | x::xs -> if xs = [] then failwith "No mode" else get_tupples xs x [] ;; |
let convert_time ((from_unit, val_) : time_unit value) to_unit : time_unit value = match from_unit, to_unit with | Second, Hour -> (Hour, val_ /. 3600.) | Hour, Second -> (Second, val_ *. 3600.) | _, _ -> (from_unit, val_) ;; |
let convert_dist ((from_unit, val_) : dist_unit value) to_unit : dist_unit value = match from_unit, to_unit with | Meter, Foot -> (Foot, val_ /. 0.3048) | Meter, Mile -> (Mile, val_ /. 0.3048 /. 5280.) | Mile, Meter -> (Meter, val_ *. 5280. *. 0.3048) | Mile, Foot -> (Foot, val_ *. 5280.) | Foot, Mile -> (Mile, val_ /. 5280.) | Foot, Meter -> (Meter, val_ *. 0.3048) | _, _ -> (from_unit, val_) ;; |
let convert_speed ((from_unit, val_) : speed_unit value) to_unit : speed_unit value = let (a,b), v, (c,d) = from_unit, val_, to_unit in ((c,d), ((snd (convert_dist (a, v) c)) /. (snd (convert_time (b, 1.0) d)))) ;; |
let add_speed (a : speed_unit value) ((b_unit, b_val) : speed_unit value) : speed_unit value = let ((a,b), v1), (c,d), v2 = a, b_unit, b_val in ((c,d), v2 +. snd (convert_speed ((a,b), v1) (c,d))) ;; |
let passes_da_vinci t = match t with | Leaf -> true | Branch(x,y) -> if x*.x >= (square_lst_tree y 0.) then func y else false;; |
let mode (l: 'a list) : 'a = let rec aux l ((cur_el, cur_num) : 'a * int) ((max_el, max_num) : 'a * int) = match l with | [] -> if cur_num > max_num then cur_el else max_el | x::xs -> if cur_el = x then aux xs (cur_el,(cur_num + 1)) (max_el, max_num) else if cur_num > max_num then aux xs (x, 1) (cur_el, cur_num) else aux xs (x,1) (max_el, max_num) in match List.sort compare l with | [] -> failwith "No mode" | x::xs -> aux xs (x,1) (x,1) ;; |
let pair_mode (l: 'a list) : 'a * 'a = let rec get_tupples l last_el tup_l = match l with | [] -> mode tup_l | x::xs -> get_tupples xs x ((last_el, x)::tup_l) in match l with | [] -> failwith "No mode" | x::xs -> if xs = [] then failwith "No mode" else get_tupples xs x [] ;; |
let convert_time ((from_unit, val_) : time_unit value) to_unit : time_unit value = match from_unit, to_unit with | Second, Hour -> (Hour, val_ /. 3600.) | Hour, Second -> (Second, val_ *. 3600.) | _, _ -> (from_unit, val_) ;; |
let convert_dist ((from_unit, val_) : dist_unit value) to_unit : dist_unit value = match from_unit, to_unit with | Meter, Foot -> (Foot, val_ /. 0.3048) | Meter, Mile -> (Mile, val_ /. 0.3048 /. 5280.) | Mile, Meter -> (Meter, val_ *. 5280. *. 0.3048) | Mile, Foot -> (Foot, val_ *. 5280.) | Foot, Mile -> (Mile, val_ /. 5280.) | Foot, Meter -> (Meter, val_ *. 0.3048) | _, _ -> (from_unit, val_) ;; |
let convert_speed ((from_unit, val_) : speed_unit value) to_unit : speed_unit value = let (a,b), v, (c,d) = from_unit, val_, to_unit in ((c,d), ((snd (convert_dist (a, v) c)) /. (snd (convert_time (b, 1.0) d)))) ;; |
let add_speed (a : speed_unit value) ((b_unit, b_val) : speed_unit value) : speed_unit value = let ((a,b), v1), (c,d), v2 = a, b_unit, b_val in ((c,d), v2 +. snd (convert_speed ((a,b), v1) (c,d))) ;; |
let passes_da_vinci t = match t with | Leaf -> true | Branch(x,y) -> if x*.x >= (square_lst_tree y 0.) then func y else false;; |
let mode (l: 'a list) : 'a = let rec aux l ((cur_el, cur_num) : 'a * int) ((max_el, max_num) : 'a * int) = match l with | [] -> if cur_num > max_num then cur_el else max_el | hd :: tl -> if hd = cur_el then aux tl (cur_el, cur_num + 1) (max_el, max_num) else if cur_num > max_num then aux tl (hd, 1) (cur_el, cur_num) else aux tl (hd, 1) (max_el, max_num) in let s = List.sort compare l in if (List.length s) = 0 then failwith "This list is invalid." else aux s (List.hd s, 0) (List.hd s, 0) ;; let remove_hd (l: 'a list) : 'a list = match l with | [] -> [] | x :: xs -> xs ;; |
let pair_mode (l: 'a list) : 'a * 'a = if (List.length l) < 2 then failwith "This list is invalid." else let l1 = remove_hd l in let l2 = List.rev (remove_hd (List.rev l)) in mode (List.combine l2 l1) ;; |
let convert_time ((from_unit, val_) : time_unit value) to_unit : time_unit value = match from_unit with | Second -> if to_unit = Hour then (Hour, val_ /. 3600.) else (Second, val_) | Hour -> if to_unit = Second then (Second, val_ *. 3600.) else (Hour, val_) ;; |
let convert_dist ((from_unit, val_) : dist_unit value) to_unit : dist_unit value = match from_unit with | Foot -> if to_unit = Meter then (Meter, val_ *. 0.3048) else if to_unit = Mile then (Mile, val_ /. 5280.) else (Foot, val_) | Meter -> if to_unit = Foot then (Foot, val_ /. 0.3048) else if to_unit = Mile then (Mile, val_ *. 0.000621371) else (Meter, val_) | Mile -> if to_unit = Foot then (Foot, val_ *. 5280.) else if to_unit = Meter then (Meter, val_ *. 1609.344) else (Mile, val_) ;; |
let convert_speed ((from_unit, val_) : speed_unit value) to_unit : speed_unit value = let final_dist = fst (to_unit) in let final_time = snd (to_unit) in let init_dist = fst (fst (from_unit, val_)) in let init_time = snd (fst (from_unit, val_)) in let final_value = (snd (convert_dist (init_dist, val_) final_dist)) /. (snd (convert_time (init_time, 1.) final_time)) in (to_unit, final_value) ;; |
let add_speed (a : speed_unit value) ((b_unit, b_val) : speed_unit value) : speed_unit value = let new_a = convert_speed a b_unit in (fst (b_unit, b_val), snd (new_a) +. snd (b_unit, b_val)) ;; |
let passes_da_vinci t = let rec sum_ l acc = match l with | [] -> acc | Leaf :: tl -> sum_ tl acc | Branch (width, subtree) :: tl -> sum_ tl ((sq width) +. acc) in let rec check l = match l with | [] -> true | Leaf :: tl -> check tl | Branch (width, subtree) :: tl -> if ((check subtree) && ((sum_ subtree 0. <= (sq width)))) then false else check tl in check [t] ;; |
let mode (l: 'a list) : 'a = let rec aux l ((cur_el, cur_num) : 'a * int) ((max_el, max_num) : 'a * int) = match l with | [] -> if cur_num > max_num then cur_el else max_el | hd :: tl -> if hd = cur_el then aux tl (cur_el, cur_num + 1) (max_el, max_num) else if cur_num > max_num then aux tl (hd, 1) (cur_el, cur_num) else aux tl (hd, 1) (max_el, max_num) in let s = List.sort compare l in if (List.length s) = 0 then failwith "This list is invalid." else aux s (List.hd s, 0) (List.hd s, 0) ;; let remove_hd (l: 'a list) : 'a list = match l with | [] -> [] | x :: xs -> xs ;; |
let pair_mode (l: 'a list) : 'a * 'a = if (List.length l) < 2 then failwith "This list is invalid." else let l1 = remove_hd l in let l2 = List.rev (remove_hd (List.rev l)) in mode (List.combine l2 l1) ;; |
let convert_time ((from_unit, val_) : time_unit value) to_unit : time_unit value = match from_unit with | Second -> if to_unit = Hour then (Hour, val_ /. 3600.) else (Second, val_) | Hour -> if to_unit = Second then (Second, val_ *. 3600.) else (Hour, val_) ;; |
let convert_dist ((from_unit, val_) : dist_unit value) to_unit : dist_unit value = match from_unit with | Foot -> if to_unit = Meter then (Meter, val_ *. 0.3048) else if to_unit = Mile then (Mile, val_ /. 5280.) else (Foot, val_) | Meter -> if to_unit = Foot then (Foot, val_ /. 0.3048) else if to_unit = Mile then (Mile, val_ *. 0.000621371) else (Meter, val_) | Mile -> if to_unit = Foot then (Foot, val_ *. 5280.) else if to_unit = Meter then (Meter, val_ *. 1609.344) else (Mile, val_) ;; |
let convert_speed ((from_unit, val_) : speed_unit value) to_unit : speed_unit value = let final_dist = fst (to_unit) in let final_time = snd (to_unit) in let init_dist = fst (fst (from_unit, val_)) in let init_time = snd (fst (from_unit, val_)) in let final_value = (snd (convert_dist (init_dist, val_) final_dist)) /. (snd (convert_time (init_time, 1.) final_time)) in (to_unit, final_value) ;; |
let add_speed (a : speed_unit value) ((b_unit, b_val) : speed_unit value) : speed_unit value = let new_a = convert_speed a b_unit in (fst (b_unit, b_val), snd (new_a) +. snd (b_unit, b_val)) ;; |
let passes_da_vinci t = let rec sum_ l acc = match l with | [] -> acc | Leaf :: tl -> sum_ tl acc | Branch (width, subtree) :: tl -> sum_ tl ((sq width) +. acc) in let rec check l = match l with | [] -> true | Leaf :: tl -> check tl | Branch (width, subtree) :: tl -> if ((check subtree) && ((sum_ subtree 0. <= (sq width)))) then false else check tl in check [t] ;; |
let mode (l: 'a list) : 'a = let rec aux l ((cur_el, cur_num) : 'a * int) ((max_el, max_num) : 'a * int) = match l with | [] -> begin match cur_num > max_num with | true -> cur_el | false -> max_el end | first::tl -> let new_cur_num, new_max_el, new_max_num = match first = cur_el with | true -> (cur_num + 1, max_el, max_num) | false when cur_num > max_num -> (1, cur_el, cur_num) | _ -> (1, max_el, max_num) in aux tl (first, new_cur_num) (new_max_el, new_max_num) in let negative_num = -1 in match List.sort compare l with | head::tl -> aux tl (head, 1) (head, negative_num) | [] -> failwith "empty list" ;; |
let pair_mode (l: 'a list) : 'a * 'a = List.fold_right (fun item (pairs, after) -> match after with | None -> pairs, Some item | Some value -> let pairs = (item, value) :: pairs in pairs, (Some item)) l ([], None) |> fst |> mode ;; |
let convert_time ((from_unit, val_) : time_unit value) to_unit : time_unit value = let value = 3600. in if from_unit = Hour && to_unit = Second then to_unit, val_ *. value else if from_unit = Second && to_unit = Hour then to_unit, val_ /. value else to_unit, val_ ;; |
let convert_dist ((from_unit, val_) : dist_unit value) to_unit : dist_unit value = let mile_to_foot v = v *. 5280. in let foot_to_mile v = v /. 5280. in let meter_to_mile v = v /. 1609.344 in let mile_to_meter v = v *. 1609.344 in let meter_to_foot v = val_ /. 0.3048 in let foot_to_meter v = val_ *. 0.3048 in match from_unit, to_unit with | Mile, Foot -> to_unit, mile_to_foot val_ | Foot, Mile -> to_unit, foot_to_mile val_ | Mile, Meter -> to_unit, mile_to_meter val_ | Meter, Mile -> to_unit, meter_to_mile val_ | Meter, Foot -> to_unit, meter_to_foot val_ | Foot, Meter -> to_unit, foot_to_meter val_ | _ -> to_unit, val_ ;; |
let convert_speed ((from_unit, val_) : speed_unit value) to_unit : speed_unit value = let dist, time = from_unit in let dist', time' = to_unit in let converted_dist = convert_dist (dist, val_) dist' in let converted_time = convert_time (time, 1.) time' in (fst converted_dist, fst converted_time), (snd converted_dist /. snd converted_time) ;; |
let dist_traveled time ((speed_unit, speed_val) : speed_unit value) : dist_unit value = let dist = snd (convert_time time (snd speed_unit)) *. speed_val in (fst speed_unit), dist ;; let rec passes_da_vinci t = match t with | Leaf -> true | Branch (num, children) -> let children_values = List.fold_left (fun acc i -> match i with | Leaf -> 0. | Branch (value, _) -> acc +. value *. value ) 0. children in List.for_all passes_da_vinci children && children_values <= (num *. num) ;; |
let mode (l: 'a list) : 'a = let rec aux l ((cur_el, cur_num) : 'a * int) ((max_el, max_num) : 'a * int) = match l with | [] -> begin match cur_num > max_num with | true -> cur_el | false -> max_el end | first::tl -> let new_cur_num, new_max_el, new_max_num = match first = cur_el with | true -> (cur_num + 1, max_el, max_num) | false when cur_num > max_num -> (1, cur_el, cur_num) | _ -> (1, max_el, max_num) in aux tl (first, new_cur_num) (new_max_el, new_max_num) in let negative_num = -1 in match List.sort compare l with | head::tl -> aux tl (head, 1) (head, negative_num) | [] -> failwith "empty list" ;; |
let pair_mode (l: 'a list) : 'a * 'a = List.fold_right (fun item (pairs, after) -> match after with | None -> pairs, Some item | Some value -> let pairs = (item, value) :: pairs in pairs, (Some item)) l ([], None) |> fst |> mode ;; |
let convert_time ((from_unit, val_) : time_unit value) to_unit : time_unit value = let value = 3600. in if from_unit = Hour && to_unit = Second then to_unit, val_ *. value else if from_unit = Second && to_unit = Hour then to_unit, val_ /. value else to_unit, val_ ;; |
let convert_dist ((from_unit, val_) : dist_unit value) to_unit : dist_unit value = let mile_to_foot v = v *. 5280. in let foot_to_mile v = v /. 5280. in let meter_to_mile v = v /. 1609.344 in let mile_to_meter v = v *. 1609.344 in let meter_to_foot v = val_ /. 0.3048 in let foot_to_meter v = val_ *. 0.3048 in match from_unit, to_unit with | Mile, Foot -> to_unit, mile_to_foot val_ | Foot, Mile -> to_unit, foot_to_mile val_ | Mile, Meter -> to_unit, mile_to_meter val_ | Meter, Mile -> to_unit, meter_to_mile val_ | Meter, Foot -> to_unit, meter_to_foot val_ | Foot, Meter -> to_unit, foot_to_meter val_ | _ -> to_unit, val_ ;; |
let convert_speed ((from_unit, val_) : speed_unit value) to_unit : speed_unit value = let dist, time = from_unit in let dist', time' = to_unit in let converted_dist = convert_dist (dist, val_) dist' in let converted_time = convert_time (time, 1.) time' in (fst converted_dist, fst converted_time), (snd converted_dist /. snd converted_time) ;; |
let dist_traveled time ((speed_unit, speed_val) : speed_unit value) : dist_unit value = let dist = snd (convert_time time (snd speed_unit)) *. speed_val in (fst speed_unit), dist ;; let rec passes_da_vinci t = let rec tree_list_sum = function | [] -> 0. | cur :: left_branches -> (tree_list_sum left_branches) +. (if cur = Leaf then 0. else node_sum cur) and node_sum (Branch (cur_value, tree_lists)) = tree_list_sum tree_lists +. cur_value *. cur_value in match t with | Leaf -> true | Branch (num, b) -> List.for_all passes_da_vinci b && (tree_list_sum b) <= (num *. num) ;; |
let mode (l: 'a list) : 'a = let l= List.sort compare l in let head l:'a = match l with |[] -> failwith "Undefined input" |el::li -> el in let rec aux (l: 'a list) ((cur_el, cur_num) : 'a * int) ((max_el, max_num) : 'a * int) = match l with |[] -> if cur_num >max_num then cur_el else max_el |el::li -> if el=cur_el then aux li (cur_el, cur_num+1) (max_el, max_num) else if cur_num > max_num then aux li (el, 1) (cur_el, cur_num) else aux li (el, 1) (max_el, max_num) in aux l ( head l, 0) (head l, 0) ;; |
let pair_mode (l: 'a list) : 'a * 'a = if [] = l then failwith "Undefined input" else if (List.length l)<2 then failwith "Undefined input" else let rec shift (l: 'a list) (z: 'a list) (i:int)= if 0< i then shift l (List.append [List.nth l i] z) (i-1) else mode (List.combine l (List.append z [List.nth l 0])) in shift l [] ((List.length l)-1) ;; |
let convert_time ((from_unit, val_) : time_unit value) to_unit : time_unit value = match (from_unit,val_) with |(Second, _ ) -> (match to_unit with |Hour -> (Hour, val_/.3600.0) |Second -> (Second, val_)) |(Hour, _ )->(match to_unit with |Hour -> (Hour, val_) |Second -> (Second, val_*.3600.0)) ;; |
let convert_dist ((from_unit, val_) : dist_unit value) to_unit : dist_unit value = match (from_unit,val_) with |(Foot, _ ) -> (match to_unit with |Foot -> (Foot, val_) |Meter -> (Meter, val_*.0.3048) |Mile -> (Mile, val_/.5280.0) ) |(Meter, _ )->(match to_unit with |Foot -> (Foot, val_/.0.3048) |Meter -> (Meter, val_) |Mile -> (Mile, val_*.0.000621371)) |(Mile, _) ->(match to_unit with |Foot -> (Foot, val_*.5280.0) |Meter -> (Meter, val_*.(1609.344)) |Mile -> (Mile, val_)) ;; |
let convert_speed ((from_unit, val_) : speed_unit value) to_unit : speed_unit value = let ((f, a), k )= (from_unit, val_)in let (c, b)= to_unit in let (t_unit, val_T)=(convert_time (a,1.0) b) in let (d_unit, val_d)=(convert_dist (f,val_) c) in (to_unit, val_d /. (val_T) ) ;; |
let add_speed (a : speed_unit value) ((b_unit, b_val) : speed_unit value) : speed_unit value = let (un, dist)= convert_speed (a) b_unit in let (un2, dist2)= (b_unit, b_val) in (un2,(dist2)+.(dist)) ;; |
let passes_da_vinci t = let rec checker l= match l with | [] -> true | Leaf::tl-> checker tl | Branch (witdth,subtree)::tl -> if not (checker (subtree) && witdth*.witdth >= (sum_sq subtree 0.0)) then false else checker tl in checker [t] ;; |
let mode (l: 'a list) : 'a = let l= List.sort compare l in let head l:'a = match l with |[] -> failwith "Undefined input" |el::li -> el in let rec aux (l: 'a list) ((cur_el, cur_num) : 'a * int) ((max_el, max_num) : 'a * int) = match l with |[] -> if cur_num >max_num then cur_el else max_el |el::li -> if el=cur_el then aux li (cur_el, cur_num+1) (max_el, max_num) else if cur_num > max_num then aux li (el, 1) (cur_el, cur_num) else aux li (el, 1) (max_el, max_num) in aux l ( head l, 0) (head l, 0) ;; |
let pair_mode (l: 'a list) : 'a * 'a = if [] = l then failwith "Undefined input" else if (List.length l)<2 then failwith "Undefined input" else let rec shift (l: 'a list) (z: 'a list) (i:int)= if 0< i then shift l (List.append [List.nth l i] z) (i-1) else mode (List.combine l (List.append z [List.nth l 0])) in shift l [] ((List.length l)-1) ;; |
let convert_time ((from_unit, val_) : time_unit value) to_unit : time_unit value = match (from_unit,val_) with |(Second, _ ) -> (match to_unit with |Hour -> (Hour, val_/.3600.0) |Second -> (Second, val_)) |(Hour, _ )->(match to_unit with |Hour -> (Hour, val_) |Second -> (Second, val_*.3600.0)) ;; |
let convert_dist ((from_unit, val_) : dist_unit value) to_unit : dist_unit value = match (from_unit,val_) with |(Foot, _ ) -> (match to_unit with |Foot -> (Foot, val_) |Meter -> (Meter, val_*.0.3048) |Mile -> (Mile, val_/.5280.0) ) |(Meter, _ )->(match to_unit with |Foot -> (Foot, val_/.0.3048) |Meter -> (Meter, val_) |Mile -> (Mile, val_/.(5280.0*.0.3048))) |(Mile, _) ->(match to_unit with |Foot -> (Foot, val_*.5280.0) |Meter -> (Meter, val_*.(5280.0*.0.3048)) |Mile -> (Mile, val_)) ;; |
let convert_speed ((from_unit, val_) : speed_unit value) to_unit : speed_unit value = let ((f, a), k )= (from_unit, val_)in let (c, b)= to_unit in let (t_unit, val_T)=(convert_time (a,1.0) b) in let (d_unit, val_d)=(convert_dist (f,val_) c) in (to_unit, val_d /. (val_T) ) ;; |
let add_speed (a : speed_unit value) ((b_unit, b_val) : speed_unit value) : speed_unit value = let (un, dist)= convert_speed (a) b_unit in let (un2, dist2)= (b_unit, b_val) in (un2,(dist2)+.(dist)) ;; |
let passes_da_vinci t = let rec checker l= match l with | [] -> true | Leaf::tl-> checker tl | Branch (witdth,subtree)::tl -> if not (checker (subtree) && witdth*.witdth >= (sum_sq subtree 0.0)) then false else checker tl in checker [t] ;; |
let mode (l: 'a list) : 'a = let rec aux l ((cur_el, cur_num) : 'a * int) ((max_el, max_num) : 'a * int) = match l with | [] -> if cur_num > max_num then cur_el else max_el | x :: xs -> if cur_el = x then aux xs (x, 1 + cur_num) (max_el, max_num) else if cur_num > max_num then aux xs (x, 1) (cur_el, cur_num) else aux xs (x, 1) (max_el, max_num) in match List.sort compare l with | [] -> failwith "List too small." | x :: xs -> aux xs (x, 1) (x, 1) ;; |
let pair_mode (l: 'a list) : 'a * 'a = if List.length l < 2 then failwith "List too small." else match l with | [] -> failwith "List too small." | _::l2 -> match List.rev l with | _::ls -> mode (List.combine (List.rev ls) l2) | [] -> failwith "List too small." ;; |
let convert_time ((from_unit, val_) : time_unit value) to_unit : time_unit value = match (from_unit, to_unit) with | (Second, Hour) -> (Hour, val_ /. 3600.) | (Hour, Second) -> (Second, val_ *. 3600.) | (_, _) -> (from_unit, val_) ;; |
let convert_dist ((from_unit, val_) : dist_unit value) to_unit : dist_unit value = match (from_unit, to_unit) with | (Foot, Meter) -> (Meter, val_ *. 0.3048) | (Meter, Foot) -> (Foot, val_ /. 0.3048) | (Mile, Foot) -> (Foot, val_ *. 5280.) | (Foot, Mile) -> (Mile, val_ /. 5280.) | (Mile, Meter) -> (Meter, val_ *. 5280. *. 0.3048) | (Meter, Mile) -> (Mile, val_ /. 0.3048 /. 5280.) | (_, _) -> (from_unit, val_) ;; |
let convert_speed ((from_unit, val_) : speed_unit value) to_unit : speed_unit value = let ((dist_1, time_1), (dist_2, time_2)) = (from_unit, to_unit) in let ((d_unit, d), (t_unit, t)) = ((convert_dist (dist_1, val_) dist_2), (convert_time (time_1, 1.) time_2)) in ((d_unit, t_unit), d /. t) ;; |
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