wk4: MergeSort, FuncModelling

Co-authored-by: KaloyanStoykov <KaloyanStoykov@users.noreply.github.com>

wk4/elm.json

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+{
+    "type": "application",
+    "source-directories": [
+        "src"
+    ],
+    "elm-version": "0.19.1",
+    "dependencies": {
+        "direct": {
+            "elm/browser": "1.0.2",
+            "elm/core": "1.0.5",
+            "elm/html": "1.0.0"
+        },
+        "indirect": {
+            "elm/json": "1.1.3",
+            "elm/time": "1.0.0",
+            "elm/url": "1.0.0",
+            "elm/virtual-dom": "1.0.3"
+        }
+    },
+    "test-dependencies": {
+        "direct": {},
+        "indirect": {}
+    }
+}

wk4/src/Modelling1.elm

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+module Modelling1 exposing (..)
+
+{-
+    Modelling Math Functions (part 1)
+    Dimitar Byalkov and Kaloyan Stoykov
+-}
+
+type Function
+  = Poly  Function Int
+  | Mult  Function Function
+  | Div   Function Function
+  | Plus  Function Function
+  | Minus Function Function 
+  | Const Int
+  | X
+
+print: Function -> String
+print f =
+    case f of
+        X ->
+            "x"
+        Const val ->
+            String.fromInt val
+        Poly func val ->
+            "(" ++ print func ++ " ^ " ++ String.fromInt val ++ ")"
+        Mult func1 func2 ->
+            "(" ++ print func1 ++ " * " ++ print func2 ++ ")"
+        Div func1 func2 ->
+            "(" ++ print func1 ++ " / " ++ print func2 ++ ")"
+        Plus func1 func2 ->
+            "(" ++ print func1 ++ " + " ++ print func2 ++ ")"
+        Minus func1 func2 ->
+            "(" ++ print func1 ++ " - " ++ print func2 ++ ")"
+        
+eval: Float -> Function -> Float
+eval num f =
+    case f of
+        X ->
+            num
+        Const val ->
+            toFloat val
+        Poly func val ->
+            eval num func ^ (toFloat val)
+        Mult func1 func2 ->
+            eval num func1 * eval num func2
+        Div func1 func2 ->
+            eval num func1 / eval num func2
+        Plus func1 func2 ->
+            eval num func1 + eval num func2
+        Minus func1 func2 ->
+            eval num func1 - eval num func2 
+
+-- Graph line drawing function
+graphLine: Function -> Int -> Int -> Int -> String
+graphLine func x ymin ymax =
+    let
+        -- value of f(x)
+        funcValue = round (eval (toFloat x) func)
+        -- number of points on the line
+        ySpan = abs ymin + abs ymax
+    in
+        -- Check if the value of f(x) is in the specified range
+        if (funcValue > ymin) && (funcValue < ymax) then
+            stringFill (funcValue - ymin) "*" ++ stringFill (ySpan - (funcValue - ymin)) "-"
+        else if (funcValue > ymin) then
+            stringFill ySpan "*"
+        else
+            stringFill ySpan "-"
+
+-- Recursive function to create a string of specified characters with a given length
+stringFill: Int -> String -> String
+stringFill n sym =
+    if (n <= 0) then
+        ""
+    else
+        sym ++ stringFill (n - 1) sym
+
+-- xmin < xmax; ymin < ymax
+graph: Function -> Int -> Int -> Int -> Int -> String
+graph func xmin xmax ymin ymax =
+    -- Check if range is not possible
+    if xmin > xmax || ymin > ymax then
+      "Error: Range is negative"
+    else if xmin == xmax then
+        graphLine func xmin ymin ymax
+    else
+        graphLine func xmin ymin ymax ++ "\n" ++ graph func (xmin + 1) xmax ymin ymax
+
+testPrint: Bool
+testPrint = print (Plus (Mult (Plus (Const 3) X) (Minus X (Poly X 5))) (Const 2)) == "(((3 + x) * (x - (x ^ 5))) + 2)"
+
+testEval: Bool
+testEval = eval 2 (Plus (Mult (Plus (Const 3) X) (Minus X (Poly X 5))) (Const 2)) == -148
+
+testGraph1: Bool
+testGraph1 = graph (Plus (Minus (Poly (Minus (Div X (Const 5)) (Const 1)) 4) (Poly (Plus (Div X (Const -2)) (Const 2)) 2)) (Const 6)) -10 20 -10 10 == 
+    "********************\n********************\n********************\n*******************-\n**************------\n************--------\n**********----------\n**********----------\n***********---------\n************--------\n*************-------\n**************------\n***************-----\n****************----\n****************----\n****************----\n***************-----\n**************------\n************--------\n**********----------\n********------------\n******--------------\n****----------------\n**------------------\n*-------------------\n**------------------\n***-----------------\n*******-------------\n*************-------\n********************\n********************"
+
+-- for reference 3x2-graph.png
+testGraph2: Bool
+testGraph2 = graph (Mult (Const 3) (Poly X 2)) -5 5 -1 10 == "***********\n***********\n***********\n***********\n****-------\n*----------\n****-------\n***********\n***********\n***********\n***********"
+
+testEmptyParams: Bool
+testEmptyParams = graph (Mult (Const 3) (Poly X 2)) 0 0 0 0 == ""
+
+testSingleLine: Bool
+testSingleLine = graph (Mult (Const 3) (Poly X 2)) 1 1 -1 10 == "****-------"
+
+
+testInvalidArgs: Bool
+testInvalidArgs = graph X 2 1 2 1 == "Error: Range is negative"
+
+testAllGraphs : List Bool
+testAllGraphs = [testGraph1, testGraph2, testEmptyParams, testSingleLine, testInvalidArgs] 

wk4/src/Sorting.elm

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+module Sorting exposing (..)
+
+{-
+    Merge Sort
+    Dimitar Byalkov and Kaloyan Stoykov
+-}
+
+msort: List comparable -> List comparable
+msort myList =
+    case myList of
+        [] ->
+            []
+        [x] ->
+            [x]
+        _ ->
+            let
+                mid = List.length myList // 2
+                left = List.take mid myList
+                right = List.drop mid myList
+            in
+                merge (msort left) (msort right)          
+
+merge: List comparable -> List comparable -> List comparable
+merge listOne listTwo =
+    case (listOne, listTwo) of
+        ([], []) ->
+            []
+        (x, []) ->
+            x
+        ([], y) ->
+            y
+        (x :: xs, y :: ys) ->
+            if x < y then
+                x :: merge xs listTwo
+            else
+                y :: merge listOne ys
+
+-- Tests
+testMergeSortOdd: Bool
+testMergeSortOdd = msort [9,8,4,5,0,8,2,3,4] == [0,2,3,4,4,5,8,8,9]
+
+testMergeSortEven: Bool
+testMergeSortEven = msort [2,3,0,9,4,8,0,4] == [0,0,2,3,4,4,8,9]
+
+testMergeSortEmpty: Bool
+testMergeSortEmpty = msort [] == []
+
+testMergeSort1: Bool
+testMergeSort1 = msort [6] == [6]
+
+testMergeSort2: Bool
+testMergeSort2 = msort [8,2] == [2,8]
+
+testMergeSortPreSorted: Bool
+testMergeSortPreSorted = msort [1,2,3,4,5] == [1,2,3,4,5]
+
+testAllMergeSort: List Bool
+testAllMergeSort = [testMergeSortOdd, testMergeSortEven, testMergeSortEmpty, testMergeSort1, testMergeSort2, testMergeSortPreSorted]