C++ Programming: From Problem Analysis to Program Design
8th Edition
ISBN: 9781337102087
Author: D. S. Malik
Publisher: Cengage Learning
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There are four people who want to cross a rickety bridge; they all begin on the
same side. You have 17 minutes to get them all across to the other side. It is night, and
they have one flashlight. A maximum of two people can cross the bridge at one time. Any
party that crosses, either one or two people, must have the flashlight with them. The
flashlight must be walked back and forth; it cannot be thrown, for example. Person 1
takes 1 minute to cross the bridge, person 2 takes 2 minutes, person 3 takes 5 minutes,
and person 4 takes 10 minutes. A pair must walk together at the rate of the slower
person's pace.
Write the specification of an algorithm that solves the problem.
We have n glasses which can hold a varying amount of liquid. We will say that glass1 is size q1 quarts and glass2 is size q2 quarts, etc. We now give you a size, say x quarts. You must give me a glass of exactly x quarts. You are allowed to fill any glass to exactly its size and to pour any liquid from one glass into another. When you pour, you either have to empty the glass you are pouring from or fill the glass you are pouring into. Can you do it?More concrete example: G1 has size 10 quarts. G2 has size 4 quarts. G3 has size 1 quart. You can get a 5 quart drink by filling G1, pouring 4 quarts from it into G2 and 1 quart of it into G1. After that, G1 has exactly 5 quarts.
In the same problem, we could get 8 quarts by filling G2 twice and emptying it into G1 twice.
Given This:
Write an algorithm to do this and determine its complexity.
Suppose we can buy a chocolate bar from the vending machine for $1 each.Inside every chocolate bar is a coupon. We can redeem six coupons for onechocolate bar from the machine. This means that once you have startedbuying chocolate bars from the machine, you always have some coupons.We would like to know how many chocolate bars can be eaten if we startwith N dollars and always redeem coupons if we have enough for an additional chocolate bar.For example, with 6 dollars we could consume 7 chocolate bars afterpurchasing 6 bars giving us 6 coupons and then redeeming the 6 couponsfor one bar. This would leave us with one extra coupon. For 11 dollars, wecould have consumed 13 chocolate bars and still have one coupon left.For 12 dollars, we could have consumed 14 chocolate bars and have twocoupons left.
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