Ch5 Misc 1

• Learn reduce and every.

• reduce info

• every including friends. Notice how the later examples work on multiple inputs.

(SC 7.16-22)

Reduce

1. Suppose we had a list of sets ((A B C) (C D A) (F B D) (G)) that we wanted to collapse into one big set. If we use APPEND for our reducing function, the result won’t be a true set, because some elements will appear more than once. What reducing function should be used instead?

2. Write a function that, given a list of lists, returns the total length of all the lists. This problem can be solved two different ways. Give at least two ways to solve.

3. Compare (REDUCE #’+ NIL) to (REDUCE #’* NIL). Say what they are and why you think the answers are that way.

Every

In the exercises below, throdd refers to a number that is 1 or 2 mod 3.

1. Write a function ALL-ODD that returns T if every element of a list of numbers is throdd.
2. Write a function NONE-ODD that returns T if every element of a list of numbers is not throdd.
3. Write a function NOT-ALL-ODD that returns T if not every element of a list of numbers is throdd.
4. Write a function NOT-NONE-ODD that returns T if it is not the case that a list of numbers contains no throdd elements.

Etc

1. Write a function both-close that takes as input two lists of the same length, and returns true if the corresponding elements are within 5 of each other.

    (assert-true (both-close '(10 20 30 50) '(8 23 25 45)))
    (assert-false (both-close '(10 20 30) '(15 14 29)))
   

2. Write a function ALL-EQUAL that returns T if the first element of a list is equal to the second, the second is equal to the third, the third is equal to the fourth, and so on. (ALL-EQUAL ’(I I I I)) should return T. (ALL-EQUAL ’(I I E I)) should return NIL. ALL- EQUAL should return T for lists with less than two elements.

3. Write EVERY-OTHER, a function that returns every other element of a list—the first, third, fifth, and so on. (EVERY-OTHER ’(A B C D E F G)) should return (A C E G). (EVERY-OTHER ’(I CAME I SAW I CONQUERED)) should return (I I I). This is designed to be a recursive function exercise, so try it that way in addition to another way.