Lab #7 Solution

Relevant sections of text: HtDP/2e through Section 19.2.




Goals:




abstracting functions




analyzing and improving performance




using the built-in abstraction functions (foldr, map, etc.)




using local and lambda




Instructions. Please submit all answers via Sakai in a single le named lab7.rkt. Do all work in pairs. Include the names of both partners at the top of the le in a comment. You need only submit one lab per pair.




Also submit your current version of Project 1. Call it fish.rkt. You should have completed Milestone 3. The starter le rubric shows exactly which features will be graded.




Basic abstraction problems



Problem 1. Abstract the following two functions into a single function:




;; mini : NELON - Number
;; maxi : NELON - Number
;; to determine the smallest number
;; to determine the largest number
;; on alon
;; on alon
(define (mini alon)
(define (maxi alon)
(cond
(cond
[(empty? (rest alon)) (first alon)]
[(empty? (rest alon)) (first alon)]
[(cons? (rest alon))
[(cons? (rest alon))
(cond
(cond
[(< (first alon)
[( (first alon)
(mini (rest alon)))
(maxi (rest alon)))
(first alon)]
(first alon)]
[else
[else
(mini (rest alon))])]))
(maxi (rest alon))])]))



Both consume non-empty lists of numbers [\NELON"] and produce a single number. The left one produces the smallest number in the list, the right one the largest. Name your abstracted function extreme. Remember to write a general, parametric/polymorphic type signature/contract for your abstract function!!!




De ne mini1 and maxi1 in terms of extreme. Test each of them with the following three lists:




(list 3 7 6 2 9 8)




(list 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1)




1
2




(list 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30)




Why are they slow on the long lists? Note you can use the function time to time a program, e.g.,




(time (mini1 LIST1))




Explain in a comment why the times are as long as they are.




Problem 2. In this problem you will improve the performance of the abstracted function from problem 1. The new and improved version of the abstract function should be named extreme.v2. De ne mini.v2 and maxi.v2 to use extreme.v2.




Here is how to design the improved abstract function. First, introduce a local name for the result of the natural recursion. Then introduce a local, auxiliary function that picks the \correct" one of the two numbers to produce as the result in the cons? clause (basically, this auxiliary function replaces the cond in your rst abstract function).




Test mini1.v2 and maxi1.v2 with the same inputs again, and observe the timing. Report on any timing improvements in a comment with a brief explanation of why the performance improved.




Bank account operations






Problem 3. De ne a type Account, which is a structure with three elds: an account number (a Number), the account holder's name (a String), and the account balance (a Number).




In the following, LoA = [List-of Account].




Design the following functions. Each de nition should use one or more of the list abstraction functions together with a local auxiliary function de nition or a lambda function. Do not use explicit recursion. Do not use an external auxiliary function.




The functions:




get-bigs: given an LoA and a threshold, returns all Accounts in the LoA whose balance is greater than or equal to threshold,




get-names: given an LoA, returns the list of names of the accounts,




total-holdings: given an LoA, returns the sum of their balances,




some-negative?: given an LoA, determines whether the list contains an account with a negative balance,




name-check?: given an LoA, returns #true if and only if all name elds are non-empty,




sort-accounts: given an LoA, returns the LoA sorted by decreasing account balance,




count-multiples: given an LoA and a name, returns the number of accounts in the LoA whose account name matches the given name,




add-interest: given an LoA and an interest rate, returns the list of accounts obtained by adding interest to the balances of each account at the speci ed rate. For each account, if the original balance was b and the rate r, the new balance will be (1 + r)b.




Problem 4. Design function create-accounts, which, given a natural number n and real number m, returns an LoA of length n. The names on the accounts are \N1", \N2", . . . ; the account numbers are 101, 102, . . . . The balance on each account is a random rational number b in [0; m] with at most 2 decimal places, i.e., 100b is an integer. For example, if m is 10, then 0, 1:57, 3, 9:99, and 10 are all possible balances. Your function should be capable of producing any balance satisfying these constraints, and should choose them with approximately equal probability. Your de nition should use build-list and should not use explicit recursion.

3




Hint: consider choosing the number of cents randomly, and then adjusting to get a dollar amount.