Question

2. Suppose you and your friend live on the same street D miles away from each other. Between your house and your friend's house there are n motorized scooters positioned at distances Ti, 32,... , x,n miles from your house towards your friend's house. Each scooter has a battery that may or may not be fully charged. Let's say that the scooters can take you distances di, d2,... , dn miles down the road Any time you encounter another scooter, you may take the new scooter and leave your old scooter behind There is an additional scooter at your house that you start with and it can go distance do miles. You wish to go to your friend's house minimizing the number of times you change scooters. Your House Your Friend's House 田 田 Describe a greedy strategy that finds the smallest set of scooters that you can take to get to your friend's house. (5 points) Prove that it is optimal. (9 points) Describe how to implement it efficiently. (3 points) Calculate the runtime. (3 points)

Answer 1

is your home ts your friend's home The distance between A aud 8 is D miles On the way to your frend's home C) foon yeur hom) our home (A) the scooters are positioned at every an miles The scooters can travel for dn miles istance bet oeen 2 2 sccoters from ewhere you startel し= d from dks distance that a scootercan travel Here, initialy the scooter is at your home fa (A b B) do Escoter Batter chagedl) for (A dk) if ( new scooter arrived check cohether tere is another scooter after ths scooter and before dk distance Canother scooter is there) Go to there and o coith thal scooter else Take scooter on

Definetely the solution ol be opimal. Because it wwil check whether there is anofter scooter befode the maximum distance that a scooter can travel This wwill help us to minimum scoters usage gneach the destination help us to minimum us to minimum scooters usage For the efficent inplementation of Hs problem it is befter to choose "Job Sequencing" because it coill help us ttrovel more distance corth (ess number of scooters To reach B from A, cse need travel the shole distauce aud ve mead to take ned Scooters in betveen A aud B. So the nuntime will be (