Merge pull request #1 from RoRu/hw02

Complete second homework

list_func/Program.fs

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+// Solution for functions of List via List.fold
+// by Yumatov Vladimir
+// SPBSU 171 gr.
+
+// Expected execution time: 2 h
+// Real time: 3.5 h
+
+// Task 9
+// List.iter : ('a -> unit) -> 'a list -> unit
+
+// Task 10 
+let Reverse ls = List.fold (fun res elm -> elm::res) [] ls
+
+
+// Task 11 
+let Filter f ls = List.foldBack (fun elm res -> 
+ if f(elm) then elm::res else res) ls []
+
+
+// Task 12 
+let Map f ls = List.foldBack (fun elm res -> f(elm)::res) ls []
+
+
+// Task 13 Horner's method
+let Horner a cfs = List.fold (fun res elm -> elm + res * a) 0 cfs
+
+
+[<EntryPoint>]
+let main argv = 
+ printfn "Task 9 - List.iter : ('a -> unit) -> 'a list -> unit\n"
+
+ let ls = [1; 2; 3; 4; 5; 6] 
+
+ let n = Reverse ls
+ printfn "Task 10 - Reversed list %A is %A\n" ls n
+
+ let fil z = 
+ z % 2 = 0
+ let n = Filter fil ls
+ printfn "Task 11 - Filter: Even elements of %A are %A\n" ls n
+
+ let Dbl z = 
+ z * 2
+ let n = Map Dbl ls
+ printfn "Task 12 - Map: Doubled elements of %A are %A\n" ls n
+
+
+ let cfs = [4; 5; 9; 1] // 4x^3 + 5x^2 + 9x + 1
+ let x0 = 5
+ let n = Horner x0 cfs
+ printfn "Task 13 - Horner's result with coefficients %A in x=%d is %d\n" cfs x0 n
+ 0 

poly_binsearch_tree/binsearch_tree.fs

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+// Task 14
+// Solution for polymorphic binary search tree
+// by Vladimir Yumatov
+// SPBSU 171 gr.
+
+// Expected execution time: 2.5 h
+// Real time: ~3.5 h
+
+
+// Type for Binary search tree
+type BsTree<'A> = 
+ | Empty 
+ | Item of 'A * BsTree<'A> * BsTree<'A> 
+
+// Add element x to tree t
+let rec BstAdd x t =
+ match x, t with
+ | x, Empty -> Item(x, Empty, Empty)
+ | x, Item(y, lft, rgt) ->
+ match (compare x y) with
+ | c when c > 0 -> Item(y, lft, BstAdd x rgt)
+ | c when c < 0 -> Item(y, BstAdd x lft, rgt)
+ | _ -> t
+
+// Delete element x from tree t
+let rec BstDel x t = 
+ match x, t with
+ | _, Empty -> Empty
+ | _, Item(y, lft, rgt) ->
+ match (compare x y) with
+ | c when c > 0 -> Item(y, lft, BstDel x rgt)
+ | c when c < 0 -> Item(y, BstDel x lft, rgt)
+ | _ -> 
+ match lft, rgt with
+ | Empty, _ -> rgt
+ | _, Empty -> lft
+ | _, Item(y', Empty, rgt') -> Item(y', lft, rgt')
+ | _, Item(y', lft', rgt') ->
+ let rec ReplaceSearch t = 
+ match t with
+ | Empty -> y' 
+ | Item(n, Empty, _) -> n
+ | Item(_, l, _) -> ReplaceSearch l
+
+ let rep = ReplaceSearch lft'
+ Item(rep, lft, BstDel rep (Item(y', lft', rgt')))
+
+// Print tree t
+let rec BstPrint opt t = 
+ match t with
+ | Empty -> ()
+ | Item(x, lft, rgt) ->
+ match opt with
+ | "LCR" -> 
+ BstPrint opt lft
+ printf "%A " x
+ BstPrint opt rgt
+ | "LRC" ->
+ BstPrint opt lft
+ BstPrint opt rgt
+ printf "%A " x
+ | "CLR" -> 
+ printf "%A " x
+ BstPrint opt lft
+ BstPrint opt rgt
+ | _ -> printf "%s " "Unknown command\n"
+
+
+
+// Task 15 Map for tree
+let rec TreeMap f tr = 
+ match tr with
+ | Empty -> Empty
+ | Item(x, lft, rgt) -> Item(f x, TreeMap f lft, TreeMap f rgt)
+
+
+// Task 16 Fold for tree
+let rec TreeFold f res tr = 
+ match tr with
+ | Empty -> res
+ | Item(x, lft, rgt) -> TreeFold f (TreeFold f (f res x) lft) rgt
+ //f (f (TreeFold f res lft) (TreeFold f res rgt)) x
+
+
+// Task 17 Sum of elements in integer tree
+let TreeSum tr = TreeFold (fun a b -> a + b) 0 tr 
+
+
+// Task 18 Find min value in tree
+let TreeMin tr = 
+ let rec LessElm a b = // Returns the least element out of a, b
+ match a with
+ | None -> Some b
+ | Some a -> Some (min a b)
+ TreeFold LessElm None tr
+
+
+// Task 19 Copy tree
+let TreeCopy tr = TreeFold (fun res t -> BstAdd t res) Empty tr
+
+
+[<EntryPoint>]
+let main argv =
+ let mutable ts = Empty
+ BstPrint "LCR" ts
+ printf "\n"
+
+ ts <- BstAdd "x" ts
+ ts <- BstAdd "z" ts
+ ts <- BstAdd "y" ts
+ ts <- BstAdd "d" ts
+ ts <- BstAdd "l" ts
+
+ printfn "Task 14 - Tree with stings:"
+ BstPrint "LCR" ts
+ printf "\n"
+
+ ts <- BstDel "x" ts
+ ts <- BstDel "l" ts
+
+ printfn "\nSame tsee with two deleted elements:"
+ BstPrint "LCR" ts
+ printf "\n"
+
+ let mutable tr = Empty
+
+ tr <- BstAdd 4 tr
+ tr <- BstAdd 2 tr
+ tr <- BstAdd 1 tr
+ tr <- BstAdd 3 tr
+ tr <- BstAdd 9 tr
+ tr <- BstAdd 10 tr
+
+ printfn "\nTest tree:"
+ BstPrint "LCR" tr
+
+
+ let n = TreeMap (fun z -> z * 2) tr
+ printfn "\n\nTask 15 (Map) - Doubled elements of tree:"
+ BstPrint "LCR" n;
+
+ let n = TreeFold (fun a b -> if (b % 2 = 0) then a + b else a) 0 tr
+ printfn "\n\nTask 16 (Fold) - Sum of even elements:\n2+4+10 = %d" n
+
+ let n = TreeSum tr
+ printfn "\nTask 17 - Sum of elements:\n4+2+1+3+9+10 = %d\n" n
+
+ let n = TreeMin tr
+ printfn "Task 18 - The least element is %A\n" n
+
+ let n = TreeCopy tr
+ printfn "Task 19 - Copying of tree:"
+ BstPrint "LCR" n
+ printfn "\n"
+ 0