Assignment 1, CSC430, Winter 2018
1 Guidelines
For this and all remaining assignments, every function you develop must come with the following things:
A commented purpose statement line that expresses the result of the function in terms of its inputs, written in English. Be as precise as you can within the space of a line or two,
type declarations for argument and return types, and
test cases. A function without test cases is incomplete. Write the test cases first, please.
For this assignment, you must develop your solutions using the typed/racket language. Your test cases must use the (check-equal? ...) form.
Your solution should take the form of a single file. Solve each problem separately, ands make sure that each solution appears in a separate part of the file, with comments separating each problem’s solution.
Hand in your solution using the handin server. For help with the handin server, please see the course web page.
1.1 Mutation
There’s no need for mutation in any of the first three assignments in this class. Don’t mutate bindings, and don’t mutate structure fields. Yikes!
1.2 A note on Numbers
For this assignment (as well as all the others), there’s no need for complex numbers. Accordingly, you should use the type Real rather than the type Number. This will save you some hassle in using the check-= form that checks for numeric near-equality.
2 Assignment
2.1 Some Textbook Problems
Solve the following two problems from the textbook How To Design Programs, available online at www.htdp.org:
2.2 Writing Implements
Here is a data definition for writing implements:
; represents a writing implement (define-type Writer (U Pen Pencil)) ; ink volume in ml, how-full a number in the range 0.0 to 1.0 (struct Pen ([ink-volume : Real] [how-full : Real]) #:transparent) ; length in cm (struct Pencil ([length : Real]) #:transparent)
Develop the function how-far-to-write, which accepts a writing implement and returns the distance (in meters) that the implement will write before it’s done. Assume that pens can write 150 meters for each ml of ink left in the tank, and that pencils write 56 meters for each remaining cm of length.
2.3 Low-degree Polynomials
Develop a data definition for a polynomial (with type name Polynomial) that includes variants for linear (Ax + B) and quadratic (Ax^2 + Bx + C) polynomials of one variable. Call the variants Linear and Quadratic; each should accept the coefficients in the order given here (i.e., A comes first). For the purposes of this and the next problem, you should assume that the first coefficient (A) of a quadratic polynomial is never zero. The first coefficient of a linear polynomial, however, may be zero.
Next, define the function interp that accepts a polynomial and a value for the variable and produces the result of plugging in the value for the variable.
2.4 Derivative
Using the data definition you developed in the last problem, develop the function derivative that accepts a polynomial and returns another polynomial that represents its derivative. Ensure that your derivative function does not return a quadratic polynomial whose first coefficient is zero.
2.5 Binary Tree
Develop a data definition for a binary tree called BTree with symbols at the leaves but no values at the interior nodes. Its variants should be named Leaf and Node. Include a define-type and at least three examples of the data.
2.6 Mirror
Using the data definition you developed in the last problem, develop the mirror function that accepts a binary tree and produces a new binary tree that is the left-right mirror image of the first one. That is, if the input tree has the symbol 'horse at the far left of the tree, the new one should have the symbol 'horse at the far right of the tree.
2.7 Min-Depth
Using the BTree data definition, develop the min-depth function that accepts a binary tree and produces the length of the shortest path to a leaf. A single leaf has a min-depth of zero.
2.8 Substitution
Using the same data definition, develop the subst function that accepts a BTree and a symbol and a replacement BTree and returns a new tree where every instance of the symbol is replaced by the replacement tree. (Make sure to use this ordering for the arguments, or my tests will all fail....)