7 Consider Professor Bille going for a walk with his personal dog. The professor follows a...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
7 Consider Professor Bille going for a walk with his personal dog. The professor follows a path of points p1,...,Pa and the dog follows a path of points q,ı,...4m: We assume that the walk is partitioned into a number of small steps, where the professor and the dog in each step either both move from p; tp P+1 and from q, to q41, respectively, or only one of them moves and the other one stays. The goal is to find the smallest possible length L of the leash, such that the professor and the dog can move from p, and q1, resp., to p, and q,. They cannot move backwards, and we only consider the distance between points. The distance L is also known as the discrete Fréchet distance. We let L(i, j) denote the smallest possible length of the leash, such that the professor and the dog can move from p, and q, to p, and q,, resp. For two points p and q, let d(p,q) denote the distance between the them. In the example below the dotted lines denote where Professor Bille (black nodes) and the dog (white nodes) are at time 1 to 8. The minimum leash length is L = d(p1,44). P1 P2 P3 P4 Ps 96 95 94 7.1 Give a recursive formula for L(i, j). 7.2 Give pseudo code for an algorithm that computes the length of the shortest possible leash. Analyze space and time usage of your solution. 7.3 Extend your algorithm to print out paths for the professor and the dog. The algorithm must return where the professor and the dog is at each time step. Analyze the time and space usage of your solution. 7 Consider Professor Bille going for a walk with his personal dog. The professor follows a path of points p1,...,Pa and the dog follows a path of points q,ı,...4m: We assume that the walk is partitioned into a number of small steps, where the professor and the dog in each step either both move from p; tp P+1 and from q, to q41, respectively, or only one of them moves and the other one stays. The goal is to find the smallest possible length L of the leash, such that the professor and the dog can move from p, and q1, resp., to p, and q,. They cannot move backwards, and we only consider the distance between points. The distance L is also known as the discrete Fréchet distance. We let L(i, j) denote the smallest possible length of the leash, such that the professor and the dog can move from p, and q, to p, and q,, resp. For two points p and q, let d(p,q) denote the distance between the them. In the example below the dotted lines denote where Professor Bille (black nodes) and the dog (white nodes) are at time 1 to 8. The minimum leash length is L = d(p1,44). P1 P2 P3 P4 Ps 96 95 94 7.1 Give a recursive formula for L(i, j). 7.2 Give pseudo code for an algorithm that computes the length of the shortest possible leash. Analyze space and time usage of your solution. 7.3 Extend your algorithm to print out paths for the professor and the dog. The algorithm must return where the professor and the dog is at each time step. Analyze the time and space usage of your solution.
Expert Answer:
Answer rating: 100% (QA)
Well start with three basic scenarios If Professor Billie and the dog are both at first steps the sh... View the full answer
Related Book For
Elementary Statistics
ISBN: 978-0538733502
11th edition
Authors: Robert R. Johnson, Patricia J. Kuby
Posted Date:
Students also viewed these algorithms questions
-
In Formula 6-1 we assume that the population is infinite, that we are sampling with replacement, or that the population is very large. If we have a relatively small population such that n > 0.05N,...
-
If we assume that each driver is equally as likely to have talked on the cell phone while driving as not, what is the chance that a randomly selected individual will have talked on the cell phone...
-
Let P and Q be points on nonintersecting skew lines with directions n1 and n2, and let n = n1 Ã n2 Figure 8. Show that the distance d between these lines is given by And use this result to...
-
8 for 0 < < 6 for 6
-
1. When Chris started Fruit Guys in 1998, his leadership qualities included vision, value and a mission. Why was that not enough to prevent the problems his firm encountered in 2001? 2. In the early...
-
These transactions are for Sekwele Tractors, a business that sells tractors to farmers in the Eastern Cape, for the period June to August 20x9: 1 On 1 June, Sekwele Tractors bought 12 tractors and...
-
Determine the direction of the magnetic force exerted at the center of the wire or on the particles in Figure 28. 20. Data from Figure 28. 20 Figure 28.20 (a) (b) N S S N +8 te
-
This problem requires you to research the disclosure requirements for fixed assets using the FASB Codification at www.fasb.org. Access to the FASB Codification requires that your educational...
-
4. 5. In which of following conditions a real gas would behave ideally? (a) Low pressure and low temperature ha (b) At value of temperature equal to its Boyle's temperature (c) Between its critical...
-
Assume the periodic message signal m(t), shown below, is applied to a phase modulator with a phase sensitivity of kp-2n rad/Volt. Assume a carrier frequency of fe=1 Hz. a) Sketch the phase of the...
-
6. Rewrite the following code to force the synthesis tools to share hardware resources. Draw the logic circuit synthesized from the codes before and after applying the resource sharing. signal cntrl...
-
The High End Company is a retail department store chain. The companys fiscal year ends on the Saturday closest to January 31 of each year. The company is publicly held and submits quarterly financial...
-
Which of the following are acceptable input formats when using Terraform and the provider for OCI? A. Terraform .tf configuration files B. CLI commands C. Terraform .tf.json configuration files D....
-
Tech Company sells personal computers, mainframes, and software in more than seven countries. The company is required to file financial statements annually with a securities commission. The...
-
What are the biological bases of memory?
-
How do psychologists establish cause-and-effect relationships in research studies?
-
The price P of a certain computer system decreases immediately after its introduction and then increases. If the price P is estimated by the formula P=120t^(2)-2,200t+6,400, where t is the time in...
-
Synthesize the products by drawing out reagents and intermediates along the way. `N H. OH HO HO
-
A large sample of lenses was randomly selected and evaluated for a particular lens dimension. It was then compared to its specification range of nominal (0.000) ± 0.030 units. One hundred ten...
-
The California Department of Education gives an annual report on the Advanced Placement test results for each year. In the 20072008 school year, Hughson Unified in Stanislaus County had students with...
-
Find the area under the standard normal curve between - 1.39 and the mean, P(_1.39
-
Use Bluetooth to connect a simple sensor, such as an electric eye, to a database.
-
Use a temperature sensor and a motion sensor to determine the average temperature in a room when a person is present.
-
Design a database schema for a smart classroom. Identify the features of the smart classroom and design the schema to support to support those use cases.
Study smarter with the SolutionInn App