- Signing up for lab sessions

Just show up at any one of the labs below.

**Lab Session****Monday****Tuesday**3:30-5:00 PM M1 (Sewall 101) 7:00-8:30 PM M2 (Sewall 207) T1 (Dell Butcher 214)

- Pizza Mania

Pizza Mania is having a special on the same kind of pizza (i.e. same thickness and same ingredients). The special comes in two shapes: rectangular (4" by 6") for $4.99 and round (5" in diameter) for $3.99. Which one is the better deal? Write a program to solve this problem. Why do we want to write a program to solve something as simple as this one anyway?

**Solution #1:** We can solve this problem by writing the following Scheme
function using the program design methodology taught in Comp 210.

; Data Definition:

; the price of a pizza is a number

; the width and the length of a rectangular pizza are numbers

; the diameter of round pizza is a number.

; Contract:

; is-better: number number number number number -> boolean

; Purpose:

; (is-better p1 x y p2 d) returns true

; if the rectangular pizza with price p1, width x, and length y

; is a better deal than the round pizza with price p2 and diameter d,

; else returns false.

; Examples:

; (is-better 4.99 4 6 3.99 5) = true.

; (is-better 4.99 4 6 3.99 4) = false.

; Header:

; (define (is-better p1 x y p2 d) ...)

(define (is-better p1 x y p2 d)

; compare the price/area ratios of the rectangular and round pizzas

)

What is good about the above solution?

What is bad about the above solution?

What if the special is about two round pizzas of different diameters instead?

What is the *real* problem to be solved here? Does the above solution
solve the *real* problem or a specific example of the problem?

!!!More discussion here!!!!

**Solution #2**: Here is a more flexible solution in Scheme.

;Data Definition:

; A Pizza is either

; (make-RectPizza p w l) where

; p is the price of the rectangular pizza with width w and length l,

; or

; (make-RoundPizza p d) where

; p is the price of the round pizza with diameter d.

; Contract:

; is-better1: Pizza Pizza -> boolean

; Purpose:

; (is-better1 piz1 piz2) returns true

; if the pizza piz1 is a better deal than the pizza piz2

; else returns false.

; Examples:

; (is-better1 (make-RectPizza 4.99 4 6) (make-RoundPizza 3.99 5)) = true.

; (is-better1 (make-RectPizza 4.99 4 6) (make-RoundPizza 3.99 4)) = false.

; Header:

; (define (is-better1 piz1 piz2)

; (cond

; [(RectPizza? piz1)...]

; [(RoundPizza? piz1) ...]))

(define (is-better1 piz1 piz2)

; compare the price/area ratios of pizzas piz1 and piz2

)

What is good about the above solution?

What is bad about the above solution?

What if the special is about a rectangular pizza and a triangular pizza instead?

What is the *real* problem to be solved here? Does the above solution
solve the *real* problem or a specific example of the problem?

!!!More discussion here!!!!

**Solution #3**: An even more flexible solution to the problem is to write
a function to compute the price/area ratio of a pizza and use it to find the
better deal.

; Contract:

; price/area: Pizza -> number

; Purpose:

; (price/area piz) returns the price/area ratio of the pizza piz

; Examples:

; (price/area (make-RectPizza 4.99 4 6)) = ???.

; (price/area (make-RoundPizza 3.99 4)) = ???.

; Header:

; (define (price/area piz)

; (cond

; [(RectPizza? piz)...]

; [(RoundPizza? piz) ...]))

(define (price/area piz)

; computes the price/area ratio of the pizza piz.

)

; Contract:

; is-better2: Pizza Pizza -> boolean

; Purpose:

; (is-better2 piz1 piz2) returns true

; if the pizza piz1 is a better deal than the pizza piz2

; else returns false.

; Examples:

; (is-better2 (make-RectPizza 4.99 4 6) (make-RoundPizza 3.99 5)) = true.

; (is-better2 (make-RectPizza 4.99 4 6) (make-RoundPizza 3.99 4)) = false.

; Header:

; (define (is-better2 piz1 piz2)

; (... (price/area piz1) ...

; ... (price/area piz2) ...)

(define (is-better2 piz1 piz2)

(< (price/area piz1) (price/area piz2)))

What is good about the above solution?

What is bad about the above solution?

What if the special is about a rectangular pizza and a triangular pizza instead?

What is the *real* problem to be solved here? Does the above solution
solve the *real* problem or a specific example of the problem?

!!!More discussion here!!!!

To be continued... Same time, same channel...

Copyright 2005, Dung X. Nguyen - All rights reserved.