For this assignment, you are to define the following Scheme functions. For simplicity, place all of your function definitions in a single file named YOURNAME-hw5.scm, where YOURNAME is your name. Be careful to name your functions exactly as defined in the exercises, and be sure to 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 their BMI. For example, (BMI-Metric 170.0 70.0) should evaluate to approximately 24.22.
Similarly, define a function named BMI-US that takes two inputs, a person's height (in inches) and weight (in pounds), and returns their BMI. For example, (BMI-US 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-US that each take two inputs, the person's height (in cm or inches, respectively) and weight (in kg or lb, respectively). These functions should calculate the person's BMI and return the corresponding CDC classification.
For example, (classify-Metric 170.0 70.0) should evaluate to
normal, while (classify-US 65.0 170.0) should evaluate to
overweight. Note: you should be able to make use of the BMI-Metric and/or BMI-US functions
here.
Define a function named num-pos which takes a list of numbers as input and returns a count of how many of those numbers are positive (i.e., greater than 0). For example, (num-pos '(0 -3.2 6 88 -0.11 3.2)) would return 3.
Define a function named num-between which takes a list of numbers and two numbers (defining a range) as input. The function returns a count of how many of those numbers are in the specified range. For example, (num-between '(0 -3.2 6 88 -0.11 3.2) 0 10) would return 3. 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 number is the lower bound and the second is the upper bound).
Define a function named remove-between which takes a list of numbers and two numbers (defining a range) as input. The function returns a copy of the list with any numbers from that range removed. For example, (remove-between '(0 -3.2 6 88 -0.11 3.2) 0 10) would return (-3.2 88 -0.11) . As with the previous function, you may assume the boundaries of the range are inclusive and the range values are specified in non-decreasing order.
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.
dice-roll that has no inputs and simulates the roll of two six-sided dice. That is, the call (dice-roll) should return an integer from the range 2 through 12, following the appropriate probability distribution (e.g., 7 is the most likely roll, 2 and 12 are the least likely).
Hint: The built-in random function generates a pseudo-random integer from 0 up to its input (exclusive). For example, the call (random 4) would return either 0, 1, 2, or 3.
count-rolls that takes two inputs, both positive integers, representing a number of rolls and the desired total. The function should simulate the specified number of rolls and return the number of times the desired total was obtained. For example, the call (count-rolls 1000 7) should simulate 1000 dice rolls and return the number of times 7 was rolled. Since the number of rolls could be large, your function should utilize tail-recursion. incr that takes two inputs, a list of numbers and a non-negative integer representing an index. The function should return the list with the number at that index incremented. For example, the call (incr '(0 0 0) 1) should return (0 1 0). Since the size of the number lists will likely be fairly small, your solution may utilize full-recursion.count-all-rolls that takes one input, a positive integer, representing a number of rolls. The function should simulate that many rolls and return a list with the counts for each dice total. For example, the call (count-all-rolls 10000) might return (288 526 824 1093 1388 1708 1413 1115 811 563 271), signifying that 288 rolls totaled 2, 526 rolls totaled 3, 824 rolls totaled 4, etc. Since the number of rolls could be large, your function should utilize tail-recursion. Note: you should be able to make use of the incr function here.