4. There are 4 boys (A, B, C, D) and 4 girls (a, b, c, d)...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
4. There are 4 boys (A, B, C, D) and 4 girls (a, b, c, d) who want to date. Each boy has a preference list, and so does each girl. A pair of a boy and a girl is called unstable if the boy has another girl he likes better, and so does the girl. For example, if the preference list of A is b> c> a>d and that of a is B > A>D> C, then the pair of A and a is unstable since A likes b better than a, and a likes B better than A. The aim is to find a stable matching of all 4 boys and 4 girls such that there is no unstable pairing. Consider the following proposal : Morning Each girl stands on her balcony. Each boy stands under the balcony of his favorite girl on his list and serenades her. If no girl on his list, he stays home. Afternoon: Each girl who has one or more suitors serenading her asks her favorite suiters out tomorrow. She tells the others she is not available. Evening Each shunned boy crosses the girl on his list. How many days (at most) does the above proposal end? Does it give a stable matching? Explain your answers. 4. There are 4 boys (A, B, C, D) and 4 girls (a, b, c, d) who want to date. Each boy has a preference list, and so does each girl. A pair of a boy and a girl is called unstable if the boy has another girl he likes better, and so does the girl. For example, if the preference list of A is b> c> a>d and that of a is B > A>D> C, then the pair of A and a is unstable since A likes b better than a, and a likes B better than A. The aim is to find a stable matching of all 4 boys and 4 girls such that there is no unstable pairing. Consider the following proposal : Morning Each girl stands on her balcony. Each boy stands under the balcony of his favorite girl on his list and serenades her. If no girl on his list, he stays home. Afternoon: Each girl who has one or more suitors serenading her asks her favorite suiters out tomorrow. She tells the others she is not available. Evening Each shunned boy crosses the girl on his list. How many days (at most) does the above proposal end? Does it give a stable matching? Explain your answers.
Expert Answer:
Answer rating: 100% (QA)
All this will take at most 24 days Explanation I think that the n... View the full answer
Related Book For
College Algebra Graphs and Models
ISBN: 978-0321845405
5th edition
Authors: Marvin L. Bittinger, Judith A. Beecher, David J. Ellenbogen, Judith A. Penna
Posted Date:
Students also viewed these general management questions
-
In a group of 100 adults, 70 say they are most likely to do spring housecleaning in March, April, or May. Of these 70, the number who cleans in April is 14 more than the total number who cleans in...
-
A group of 100 workers were asked whether they were college graduates and whether they belonged to a union. According to their responses, 60 were not college graduates, 20 were nonunion college...
-
Suppose that in a large lot containing T manufactured items, 30 percent of the items are defective and 70 percent are nondefective. Also, suppose that ten items are selected at random without...
-
In Exercises, use the alternative form of the derivative to find the derivative at x = c (if it exists). f(x) = 1 x + 4' c = 3
-
There has recently been discussion on the Internet concerning whether the Shuffle feature on your iPod is truly random. (Well, some things really are more important than others!) How would you go...
-
During your audit of the financial statements of The Gary Manufacturing Company for the year ended December 31, 1999, you find that at January 1, 1999, the company had installed the following...
-
Place the corresponding letter of the definition next to the term. a. An organization that stands as a separate economic unit must not have its financial affairs confused with that of other entities....
-
Develop a subprogram for the bisection method that minimizes function evaluations based on the pseudocode from Figure Determine the number of function evaluations (n) per total iterations. Test the...
-
Consider the idea of Equality . Are we really equal? How do some people treat others who are different than them? Are there visual timelines of some various times when inequality stands out,...
-
Complete the following schedule by using the retail method to estimate ending inventory for September and October. September Cost October Retail Cost Retail Beginning inventory.74,950 112,000 Cost of...
-
If a product's price changes from $1,800 to $1,620, and the market demand changes from 300 per month to 315 per month (a) what is the price elasticity of demand for this product? (b) Interpret this...
-
Capes Corporation is a wholesaler of industrial goods. Data regarding the store's operations follow: Sales are budgeted at $300,000 for November, $310,000 for December, and $290,000 for January....
-
On September 1, 2015, Evansville Lumber Company issued $80 million in 20-year, 10 percent bonds payable. Interest is payable semiannually on March 1 and September 1. Bond discounts and premiums are...
-
Following is Information on two alternative Investments being considered by Tiger Co. The company requires a 7% return from its Investments. Initial investment Expected net cash flows in: Year 1 Year...
-
Suppose you have a 1-year old son and you want to provide $200,000 in 17 years towards his college education. You currently have $25,000 to invest. What interest rate must you earn to have the...
-
Great Bay Company manufactures cordless telephones. During 2022, total costs associated with manufacturing 18,500 of the AB- 2000 model (introduced this year) were as follows: Raw materials Direct...
-
Assume Miami Fiber Optics contracted to provide a customer with Internet infrastructure for $4,000,000. The project began in Year 1 and was completed in Year 2. Data relating to the contract are...
-
Find the center of mass of a thin triangular plate bounded by the y-axis and the lines y = x and y = 2 - x if (x, y) = 6x + 3y + 3.
-
In each of the following, a polynomial P(x) and a divisor d(x) are given. Use long division to find the quotient Q(x) and the remainder R(x) when P(x) is divided by d(x). Express P(x) in the form...
-
Shirts.com advertises a limited time sale, offering 1 turtleneck for $15 and 2 turtlenecks for $25. A total of 1250 turtlenecks are sold and $16,750 is taken in. How many customers ordered 2...
-
Find a polynomial function of degree of 3 with the given number as zeros. a. - 4, - 1, 2 b. - 3, 1 - i, 1 + i c. , 1 - (2, 1 + (2
-
The inversion point of a gas can be mathematically expressed as (a) \(T_{i}=\frac{2 a b}{R}\) (b) \(T_{i}=\frac{2 b}{R a}\) (c) \(T_{i}=\frac{2 a}{R b}\) (d) None of these.
-
Residual free energy is defined as (a) \(G^{R}=G-G^{\mathrm{ig}}\) (b) \(G^{R}=G^{\mathrm{ig}}-G\) (c) \(G^{R}=G+G^{\mathrm{ig}}\) (d) None of these.
-
Departure functions are useful to calculate the thermodynamic property of real fluids (a) When the \(P-V-T\) data of the substance is unavailable (b) When the \(P-V-T\) data of the substance is...
Study smarter with the SolutionInn App