(* Hope Crosier CPSC 3400 HW 4 All of the code you turn in must have been written by you without immediate reference to another solution to the problem you are solving. That means that you can look at other programs to see how someone solved a similar problem, but you shouldn't have any code written by someone else visible when you write yours (and you shouldn't have looked at a solution just a few seconds before you type!). You should compose the code you write based on your understanding of how the features of the language you are using can be used to implement the algorithm you have chosen to solve the problem you are addressing. Doing it this way is "real programming" - in contrast to just trying to get something to work by cutting and pasting stuff you don't actually understand. It is the only way to achieve the learning objectives of the course. I attest to the statement above *) ///PART ONE ///Given a length, width and height, computes the volume as a float let cubeVolume (x,y,z) = float x * y * z ///goes through a list of tuples and creates a list of their volumes let rec volumelist list = if list = [] then [] else let hd :: tl = list // compute volume of head values and append to list cubeVolume(hd) :: volumelist tl ///goes through a list of volumes and finds the max volume let maxVolume list = let rec loop max = function | [] -> max // if hd volume is greater than max, send hd as new max // otherise continue with previous max | hd :: tl -> loop (if hd > max then hd else max) tl loop 0.0 list ///calls the functions above on a list to correctly get the max cube volume let maxCubeVolume list = maxVolume (volumelist (list)) /// PART TWO /// Takes in a key x and a head value (y,z) to see if x and y are equal let checkChar (x: string) ((y,z): string*int) = if x = y then true else false /// Takes in a head value (a,b) and returns only b let getChar ((a,b): string*int) = b /// Takes in a key value x and a list of (string*int) values and gets int values /// of list items that match the given key let rec getListMatches x list = if list = [] then [] else let hd :: tl = list // see if current hd values match key if (checkChar x hd) then // get the integer value from current hd and append to list getChar hd :: getListMatches x tl // otherwise ignore currnet hd and continue to rest of list else getListMatches x tl /// Function to call getListMatches and sort the resulting list let findMatches x list = let matchlist = getListMatches x list // sort the integers that match the key from previous function call let result = List.sort matchlist result /// PART THREE /// Tree definition for problem 3 type BST = | Empty | TreeNode of int * BST * BST /// takes a value and and a tree to insert a new node with passed in value to let rec insert value tree = match tree with // if tree is empty, add node with no following nodes | Empty -> TreeNode(value, Empty, Empty) // if tree has existsing node and new node value is less than previous node // then insert it on the left side of the existing node | TreeNode(oldVal, node1, node2) when value < oldVal -> TreeNode(oldVal, insert value node1, node2) // will recursively go until right spot is found // if tree has existing node and new node value is greater than previous node // then insert it on the right side of the existing node | TreeNode(oldVal, node1, node2) when value > oldVal -> TreeNode(oldVal, node1, insert value node2) // will recursively go until right spot is found // when value = oldVal, no insertion will take place since it already exists in the tree | _ -> tree /// Recursively searches a tree to see if the provided value exists within a node let rec contains value = function // Base case when value has not been found or when tree is empty | Empty -> false // Goes through and searches tree depending on what value of current node is | TreeNode(compareVal, node1, node2) -> if value = compareVal then true elif value < compareVal then contains value node1 // search left else contains value node2 // search right /// given a function that returns true or false, counts the number of nodes that satisfy that function let rec count func = function | Empty -> 0 | TreeNode(value, node1, node2) -> // recursively sum all the counts from each side of tree (count func node1) + (count func node2) + (if (func value) then 1 else 0) /// counts the number of nodes in a tree whose value is even let evenCount tree = let result = count (fun value -> value % 2 = 0) tree result