3. Suppose you are given an n x n checkerboard with some of the squares deleted....
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
3. Suppose you are given an n x n checkerboard with some of the squares deleted. You have a large set of dominos, each just the right size to cover two neighboring squares of the checkerboard. Tiling the board with dominos means placing dominos so each domino covers exactly two squares and each undeleted square is covered by exactly one domino. A checkerboard tiled with dominos. We will design an algorithm to determine whether one can tile a board with dominos by reducing to maximum matching in a bipartite graph. (a) A bipartite graph G has two sets of vertices U and W. What should we use for each of the sets U and W? [Hint: Our goal is to cover all the undeleted squares of the checkerboard. You may want to check what the squares of a checkerboard look like.] (b) What should we use for our set of edges? [Hint: A matching is a subset of edges that is incident to each vertex at most once.] (c) What should the size of the maximum matching be if we can tile the given checker- board? (d) In terms of n, how long does it take to determine if we can tile the checkerboard using this reduction? 3. Suppose you are given an n x n checkerboard with some of the squares deleted. You have a large set of dominos, each just the right size to cover two neighboring squares of the checkerboard. Tiling the board with dominos means placing dominos so each domino covers exactly two squares and each undeleted square is covered by exactly one domino. A checkerboard tiled with dominos. We will design an algorithm to determine whether one can tile a board with dominos by reducing to maximum matching in a bipartite graph. (a) A bipartite graph G has two sets of vertices U and W. What should we use for each of the sets U and W? [Hint: Our goal is to cover all the undeleted squares of the checkerboard. You may want to check what the squares of a checkerboard look like.] (b) What should we use for our set of edges? [Hint: A matching is a subset of edges that is incident to each vertex at most once.] (c) What should the size of the maximum matching be if we can tile the given checker- board? (d) In terms of n, how long does it take to determine if we can tile the checkerboard using this reduction?
Expert Answer:
Related Book For
Artificial Intelligence A Modern Approach
ISBN: 9780134610993
4th Edition
Authors: Stuart Russell, Peter Norvig
Posted Date:
Students also viewed these programming questions
-
can someone solve this Modern workstations typically have memory systems that incorporate two or three levels of caching. Explain why they are designed like this. [4 marks] In order to investigate...
-
CANMNMM January of this year. (a) Each item will be held in a record. Describe all the data structures that must refer to these records to implement the required functionality. Describe all the...
-
Terri is single and age 32. She reported AGI of $70,000 in tax year 2021. She is an active participant in her employers pension plan. What is the maximum deductible IRA contribution she can make for...
-
On January 1, 2017, Copeland Ltd. (a public company) had the following shareholders' equity accounts: Preferred shares, $5 non-cumulative, unlimited number authorized, none issued .......... -0-...
-
Using Figure 14.1, answer the following questions: a. How many exchanges trade wheat futures contracts? b. If you have a position in 10 gold futures, what quantity of gold underlies your position? c....
-
For the vapour-phase hydration of ethylene to ethanol \[ \mathrm{C}_{2} \mathrm{H}_{4}+\mathrm{H}_{2} \mathrm{O} ightarrow \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH} \] The equilibrium constants were...
-
Lindas Boards sells a snowboard, Xpert,that is popular with snowboard enthusiasts. Information relating to Lindas purchases of Xpert snowboards during September is shown below. During the same month,...
-
"Better blow the whistle," says Roy, your friend and project teammate at Final Four Industries. "The project is out of control, and you know it!" "Maybe so," you respond, "But that's not my call I'm...
-
Miras portfolio includes a bond with the following characteristics: Current Value $127,325 Average historical return 5% Standard deviation 7% Current YTM 5% Duration 8 years What would the new value...
-
Describe what is meant by corporate culture. Identify and briefly describe the four different types of cultures that companies may adopt after a merger or acquisition.
-
An 8-metre by 12-metre swimming pool is filled with water. The depth is measured at 2-metre intervals, starting at one corner of the pool, and the values are recorded in the table. Estimate the...
-
A friend plans to purchase a 72-inch tv at a particular store for a cost of $1500. The storeis offering 25% off any one item. He also has an internet coupon for an additional 10%off any...
-
Example 8: The members of a marching band were asked which musical instruments they play. A total of 23 said that they played trumpet, 19 said they played drums and 11 said that they played both....
-
(b) Given complex numbers, x y 1-i + -3+i 3-i 1+3i where x and y are real numbers. Find the values of x and y.
-
Consider the material structure tree for item A above. If 20 units are needed, how many units of D are needed if there are already 10 B's and 10 C's in inventory?
-
(a) Consider the polynomial p = r - 8r + 26.r 40.r + 25 (i) Find all the multiple roots of the polynomial p or show that it has none. (i) Do there exist polynomials q,r e Qlr] such that dp = 1? IP...
-
The manager of a local convenience store is expanding his line of small toy items. To price these new items, the manager is looking at the prices being charged by competing retailers in his area. For...
-
The vast majority of academic publications and media articles report on successes of AI. Examine recent articles describing failures of AI. (? (?) and ? (?) are good examples, but feel free to find...
-
Figure 17.13 shows two MDPs: one, M, represents a two-armed bandit where one has the choice to continue with the first arm or to switch permanently to a second arm with fixed reward ; the other, a...
-
In a minimax tree with a branching factor of 3 and depth 2 (one max layer, one min layer with 3 nodes, and a leaf layer with 9 total nodes) what is the maximum number of nodes that can be pruned by...
-
What do you mean by phase of a system?
-
Explain the term Energy. Discuss its various forms.
-
Define work. Show that work is a path function.
Study smarter with the SolutionInn App