CS 8, Fall 2009

Short Assignment 1: Simple Haskell Functions

This short assignment asks you to write several Haskell functions. For each one write the type signature of the function and the function definition.

Instructions

You should print out your solutions to this assignment, and either turn them in at lecture, or leave them in the TA's mailbox at Sudikoff by class time on Mon. Sep. 28, 2009.

Please also e-mail an electronic version of your code to cs8hw@cs.dartmouth.edu, with the subject "CS 8 Short Assignment 1". Please attach your code as one or more enclosures to the message, and do not include it directly in the body of the e-mail message.

You must work alone on this short assignment.

Squares
Write a function computeSquares that takes a list of Doubles and returns a list of the squares of the numbers in the list. Thus computeSquares [1.0, 2.0, -3.0] => [1.0, 4.0, 9.0] Do this using a higher-order function, not recursion.
Distance
Write a function distance that finds the distance between two n-dimensional points, where the points are represented as lists of their coordinates. The coordinates are represented as Doubles. Thus to find the distance between the points (1, 0, 0) and (0, 1, 0) you should call distance [1.0, 0.0, 0.0] [0.0, 1.0, 0.0] While good style would usually be to define helper functions (e.g. listSum), I want you to do this as a "one-liner" using a subset of the four higher-order functions that we have seen. You also may use the sqrt function.
Making change
Do exercise 5.9 on p. 73. Your function should always use as many coins of a given size as possible before moving on to the next coin size in the list. Thus makeChange 80 [25, 10, 5, 1] => [3, 0, 1, 0]. Solve this problem using recursion.
Evens and Odds
Write the functions takeEvens and takeOdds. Given a list of Integers, takeEvens should return the items in the 0th, 2nd, 4th, etc. positions and takeOdds should return the items in the 1st, 3rd, 5th, etc. positions. Thus
```
takeEvens [1, 2, 3, 4] => [1, 3]
takeEvens [1] => [1]
takeEvens []  => []
takeOdds [1, 2, 3, 4] => [2, 4]
takeOdds [1] => []
takeOdds []  => []
```
Solve this problem using recursion.

Department of Computer Science, Dartmouth College, Hanover, New Hampshire, USA

Last modified: 12-August-2009