Due: &list-recursion-due; Summary: You will apply the basic and helper recursion patterns to a short series of problems. Purposes: To practice writing a variety of procedures that perform recursion over lists. Expected Time: Two to three hours. Collaboration: We encourage you to work in groups of size three. You may, however, work alone or work in a group of size two or size four. You may discuss this assignment with anyone, provided you credit such discussions when you submit the assignment. Submitting: Email your answer to &grader-email;. The title of your email should have the form &list-recursion-subject; and should contain your answers to all parts of the assignment. Scheme code should be in the body of the message. Warning: So that this assignment is a learning experience for everyone, we may spend class time publicly critiquing your work.

You may wish to review the summary of recursion patterns.

a. Write a procedure, (closest-to-zero values), that, given a list of real numbers (including both positive and negative numbers), returns the value closest to zero in the list. Your solution should use basic recursion. Hint: Think about how, given two numbers, you determine which is closer to zero. b. Write a second version of closest-to-zero that uses helper recursion. That is, you should have an additional helper procedure that takes closest-so-far and remaining as parameters. c. Explain which version of closest-to-zero you prefer and why.

Write and document a procedure (safe-sum values) that, given a list of values as a parameter, computes the sum of the numeric values in the list. That is, safe-sum should ignore all non-numeric values. > (safe-sum (list 1 2 3)) 6 > (safe-sum (list 3 'a 'b 5)) 8 > (safe-sum (list 'a 'b)) 0

We've seen how to average two colors using rgb-blend from the assignment on Exploring Colors and a list of colors in the lab on Recursion Basics. But what if we want to do something different: Given a list of colors, we want averages, but only of neighboring elements in the list. Write a procedure, (rgb-averages colors), that, given a list of colors, computes a new list of colors, by averaging subsequent pairs of colors. For example, if the input list is the standard seven rainbow colors (red, orange, yellow, green, blue, indigo, and violet), the output list will consist of a red-orange average, an orange-yellow average, a yellow-green average, a green-blue average, a blue-indigo average, and an indigo-violet average. The length of the resulting list will be one less than the length of the input list.

Students who provide correct procedures for each question will earn a &hw-grade-check;. Students who provide oddly formatted or inelegant solutions to the problems may be publicly critiqued for their odd formatting and inelegance, and will also receive a &hw-grade-minus;. Students who provide particularly elegant formatting or strategies will earn a &hw-grade-plus;.