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You and Alice and Bob are driving to Tijuana for spring break in Bob's car. You are saving your money for the trip and so you want to minimize the cost of gas on the way. In order to minimize your gas costs you have compiled the following information. Bob's car can reliably travel m miles on a tank of gas (but no further). Alice has compiled gas-station data from the web and has plotted every gas station along your route along with the price of gas at that gas station. Specifically Alice has created a list of n gas station prices P[1,..., n], from closest to furthest, and a list of n distances D[1,..., n] between two adjacent gas stations (the first distance is the distance from Bob's house to the first gas station). Gas station number n is the closest gas station to your hotel in Tijuana. For convenience Alice has converted the cost of gas into price per mile traveled in Bob's car and also computed the distance d(i, j) = Ek=i+1 D[k] the distance from gas station i to gas station j for 0 ≤i

You and Alice and Bob are driving to Tijuana for spring break in Bob's car. You are saving your money for the trip and so you want to minimize the cost of gas on the way. In order to minimize your gas costs you have compiled the following information. Bob's car can reliably travel m miles on a tank of gas (but no further). Alice has compiled gas-station data from the web and has plotted every gas station along your route along with the price of gas at that gas station. Specifically Alice has created a list of n gas station prices P[1,..., n], from closest to furthest, and a list of n distances D[1,..., n] between two adjacent gas stations (the first distance is the distance from Bob's house to the first gas station). Gas station number n is the closest gas station to your hotel in Tijuana. For convenience Alice has converted the cost of gas into price per mile traveled in Bob's car and also computed the distance d(i, j) = Ek=i+1 D[k] the distance from gas station i to gas station j for 0 ≤i

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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b) State a self-reduction for this problem. c) State a dynamic programming algorithm based off of your self-reduction that computes the minimum gas cost and use it to compute minimum cost for the following lists of gas stations, distances and gas tank capacity. Prices (cents per mile) [14, 12, 13, 12, 10, 11, 12, 11, 14, 16, 12, 13, 12, 14, 12, 15, 16, 15, 14, 10] Distances (miles) [10, 20, 20, 70,30,30, 20, 100, 50, 175, 75, 100, 30, 20, 20, 200, 160, 20, 90, 10] Bob's car can travel 350 miles on a tank of gas. d) What is the worst case run time of your dynamic programming algorithm?
Transcribed Image Text:b) State a self-reduction for this problem. c) State a dynamic programming algorithm based off of your self-reduction that computes the minimum gas cost and use it to compute minimum cost for the following lists of gas stations, distances and gas tank capacity. Prices (cents per mile) [14, 12, 13, 12, 10, 11, 12, 11, 14, 16, 12, 13, 12, 14, 12, 15, 16, 15, 14, 10] Distances (miles) [10, 20, 20, 70,30,30, 20, 100, 50, 175, 75, 100, 30, 20, 20, 200, 160, 20, 90, 10] Bob's car can travel 350 miles on a tank of gas. d) What is the worst case run time of your dynamic programming algorithm?
You and Alice and Bob are driving to Tijuana for spring break in Bob's car. You are saving your money for the trip and so you want to minimize the cost of gas on the way. In order to minimize your gas costs you have compiled the following information. Bob's car can reliably travel m miles on a tank of gas (but no further). Alice has compiled gas-station data from the web and has plotted every gas station along your route along with the price of gas at that gas station. Specifically Alice has created a list of n gas station prices P[1,..., n], from closest to furthest, and a list of n distances D[1,..., n] between two adjacent gas stations (the first distance is the distance from Bob's house to the first gas station). Gas station number n is the closest gas station to your hotel in Tijuana. For convenience Alice has converted the cost of gas into price per mile traveled in Bob's car and also computed the distance d(i, j) = Ek=i+1 D[k] the distance from gas station i to gas station j for 0≤i<j≤n (gas station 0 is Bob's house). Bob ensures you will begin your journey with a full tank of gas. You have decided to minimize the number of stops by always filling the tank full whenever you stop. Also when you get to Tijuana you will fill the tank up full. You need to determine which gas stations to stop at to minimize the cost of gas on your trip. a) State this problem as formally as possible.
Transcribed Image Text:You and Alice and Bob are driving to Tijuana for spring break in Bob's car. You are saving your money for the trip and so you want to minimize the cost of gas on the way. In order to minimize your gas costs you have compiled the following information. Bob's car can reliably travel m miles on a tank of gas (but no further). Alice has compiled gas-station data from the web and has plotted every gas station along your route along with the price of gas at that gas station. Specifically Alice has created a list of n gas station prices P[1,..., n], from closest to furthest, and a list of n distances D[1,..., n] between two adjacent gas stations (the first distance is the distance from Bob's house to the first gas station). Gas station number n is the closest gas station to your hotel in Tijuana. For convenience Alice has converted the cost of gas into price per mile traveled in Bob's car and also computed the distance d(i, j) = Ek=i+1 D[k] the distance from gas station i to gas station j for 0≤i<j≤n (gas station 0 is Bob's house). Bob ensures you will begin your journey with a full tank of gas. You have decided to minimize the number of stops by always filling the tank full whenever you stop. Also when you get to Tijuana you will fill the tank up full. You need to determine which gas stations to stop at to minimize the cost of gas on your trip. a) State this problem as formally as possible.
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