For this assignment, you are to define numerous Scheme functions. For simplicity, place all of your function definitions in a single file named YOURNAME-hw4.ss, where YOURNAME is your last name. Be extremely careful to define your functions exactly as described in the assignment. Points will be deducted for syntax discrepancies, such as a misnamed function or rearranged inputs. Also, be sure to include a comment block at the top of the file containing your name and comment each function as to its behavior.
Define functions for converting between inches and centimeters, and between pounds and kilograms (and vice versa for each). Recall that 1 inch = 2.54 centimeters and 1 pound = 0.45359237 kilograms. For example, (in->cm 10) should evaluate to 25.4, (cm->in 100) should evaluate to approximately 39.37, (kg->lb 10) should evaluate to approximately 22.05, and (lb->kg 100) should evaluate to approximately 45.36.
Body Mass Index (BMI) is often used by doctors and dieticians in assessing the overall health of a patient. The formula is as follows:
BMI = (weight in kilograms) / (height in meters)2
Define a function named BMI-Metric that takes two inputs, a person's height (in centimeters) and weight (in kilograms), and returns his/her BMI. For example, (BMI-Metric 170.0 70.0) should evaluate to approximately 24.22. Similarly, define a function named BMI-American that takes two inputs, a person's height (in inches) and weight (in pounds), and returns his/her BMI. For example, (BMI-American 65.0 170.0) should evaluate to approximately 28.29. Note: you should be able to make use of the BMI-Metric function here.
According to the Center for Disease Control, body mass index correlates to the following weight categories:
BMI < 18.5 underweight 18.5 ≤ BMI < 25.0 normal 25.0 ≤ BMI < 30.0 overweight 30.0 ≤ BMI obese
Define functions classify-Metric and classify-American that each return a pair, where the first value is the calculated BMI and the second is the CDC classification.
For example, (classify-Metric 170.0 70.0) should evaluate to
approximately (24.22 normal), while (classify-American 65.0 170.0) should evaluate to
approximately (28.29 overweight). Note: you should be able to make use of the BMI-Metric and BMI-American functions
here.
When called with no inputs, the built-in random function returns a pseudo-random real number between 0.0 (inclusive) and 1.0 (exclusive). When called with a single integer as input, random returns a pseudo-random integer in the range 0 (inclusive) to that input (exclusive). For example, the call (random 4) might return 0, 1, 2, or 3, with equal likelihood. In addition, Racket defines a library of useful randomness functions which can be loaded using require. For example, the noun function below (with no inputs) uses random-ref to randomly select a random word from a list of nouns.
(require racket/random) ;;; Selects a random noun. (define (noun) (random-ref '(girl boy dog ball computer))
Enter this function in your file and define similar functions named verb and article, which select a random verb and article, respectively. Each should have at least five words of the appropriate type to choose from.
Define functions named sentence, noun-phrase, and verb-phrase, which generate lists of words as defined by the following grammar rules:
sentence <-- noun-phrase + verb-phrase noun-phrase <-- article + noun verb-phrase <-- verb + noun-phrase
For example, the call (noun-phrase) might return '(the ball), the call (verb-phrase) might return '(kicked some ball), and the call (sentence) might return '(some girl kicked a ball). When defining these functions, you should make use of previously defined functions to simplify code and make changes easier.
Modify your noun-phrase function so that the article in the noun phrase is optional. For example, it should be possible for (noun-phrase) to return '(ball) or '(the ball). Similarly, modify your verb-phrase function so that the noun phrase component is optional. In both cases, the optional component should have a 50/50 chance of being included. Note that since the sentence calls both of these functions, the length of generated sentences may vary considerably, from '(girl kicked) to '(some girl kicked a computer).
Define a function named num-pos which takes a list of numbers as input and returns a count of how many of those numbers were positive (i.e., greater than 0). For example, (num-pos '(0 -3.2 88 -0.11 3.2)) would return 2.
Define a function named num-between which takes a list of numbers and two numbers (defining a range) as input. The function returns a a count of how many of those numbers were in the specified range. For example, (num-between '(0 -3.2 88 -0.11 3.2) 0 10) would return 2. Assume the boundaries of the range are inclusive, so 0 is considered to be in the range from 0 to 10. To simplify this task, you may assume that the range values are specified in non-decreasing order (i.e., the first numberin put is the lower bound and the second is the upper bound).
Define a function named roman->num that takes one input, a list of characters representing a roman numeral, and returns the number value represented by that roman numeral. For example, (roman->num '(X V I)) should evaluate to 16. The following is a list of the roman letters and numbers they represent:
You may assume the ancient roman style of writing letters, where 4 is represented IIII and 90 is represented LXXXX. A harder problem, which you may attempt if you like, is to use the modern roman style where 4 is IV and 90 is XC.
Define a function named num->roman that performs the reverse conversion, from a number to a list of characters representing a roman numeral. For example, (roman->num 66) should evaluate to '(L X V I). Again, you may assume the ancient roman style of writing letters.
The function below can be used to simulate the random flip of a coin, returning either 'heads or 'tails with equal likelihood.
;;; Simulates a coin flip. (define (coin-flip) (if (< (random) 0.5) 'heads 'tails))
Define a function named head# that simulates a specified number of coin flips and returns the number of those flips that were heads. For example, the call (head# 1000) would simulate 1,000 flips and return the number of heads, e.g., 508. Since the desired number of flips could be extremely large, your function should only utilize tail-recursion.
Define a function named head% that simulates a specified number of coin flips and returns the percentage of those flips that were heads. For example, the call (head% 1000) would simulate 1,000 flips and return the percentage of heads, e.g., 50.8. In the special case where the number of flips is 0 or negative, we will say that the heads percentage is 0.0. Note: you should be able to make use of the head# function here.