22b. List Exercises 2

Vocabulary

There are four major kinds of functions on lists that we will learn to write. They are: reduce, create, map, and filter.

• reduce: Any function that takes a list of things and produces a single thing. For example: add-them, which adds all of the numbers in a list of numbers. Functions like sea-of-stars that take a list of posns and produce an image also fall in this category.

• create: A function that creates a list from something that is not a list. Example: multiples-of-7, which takes a number N and produces a list of the first N multiples of 7.

• map: A function that performs the same action on every thing in a list of things, giving a list of things as its answer. Example: double-all which doubles every number in a list.

• filter: A function which removes some items from a list of items, leaving a list of items. Example: remove-small which removes every number less than 20 from a list of numbers.

Practice Problems

1. my-range: number(start) number(end) -> list of numbers. Create a list containing all of the numbers from start to end, inclusive. Example: (my-range 5 11) => (list 5 6 7 8 9 10 11).

2. two-power: number(n) -> list of numbers. Create a list of powers of two, starting with 2^n and ending with 2^0. Example: (two-power 5) => (list 32 16 8 4 2 1).

3. double-all: list of numbers -> list of numbers. Double each number in the list. Example (double-all (list 1 30)) => (list 2 60).

4. remove-small: list of numbers -> list of numbers. Create a list that excludes numbers smaller than 20 from the original list.