算法分析代写 Analysis of Algorithms代写 Practice Exam代写
769CSCI-570 Analysis of Algorithms Practice Exam - 2 算法分析代写 True/False Problems 1. For every graph G and every maximum flow on G, there always exists an edge such that increasing the ...
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人工智能代考 Problem 1 The following problem is known as EXACT SET COVER: You are given a universal set U of elements and a collection W of subsets of U.
The following problem is known as EXACT SET COVER: You are given a universal set U of elements and a collection W of subsets of U. The object is to find a sub collection Y of W such that every element of U is in exactly one set in Y.
For instance, suppose that U is the set {a,b,c,d,e,f,g,h,i} and that W is the following collection:
W1 = {a,d,f,h}
W2 = {b,e,g}
W3 = {e,g}
W4= {d,e,i}
W5 = {b,d,f,h}
W6 = {a,c,i}
W7 = {c,d,e}
W8 = {b,c,f}
Then one solution would be Y={W3,W5,W6}
For instance, if S is the collection {W6}, then X is the element “b”. The successors to S are the collections {W6,W2}, and {W6,W5}. The collection {W6,W8} is not a successor to S — in fact, it is not a legitimate state at all — because both W6 and W8 contain the element “c”.
Show the part of the state space generated by a depth-first search for the above example.
Suppose that in a particular problem, there are 100 elements in U; there are 50 sets in W; each set in W has exactly 20 elements; and each element in U is covered by exactly 10 sets in W. Thus, a solution to the problem must consist of exactly 5 sets in W (100 elements total divided by 20 elements per set). What is the branching factor in the state space? What is the depth of the state space? Give an upper bound on the size of the state space.
Would it be worthwhile using iterative deepening rather than depth-fifirst search for the problem in B? Explain your answer.
Suppose that in a particular problem, there are 100 elements in U; there are 50 sets in W; each set in W has between 10 and 20 elements; and each element in U is covered by between 5 and 10 sets in W. Thus, a solution to the problem contains somewhere between 5 (=100/20) and 10 (=100/10) sets in W. Might it be worth wile using iterative deepening for this problem rather than depth-first search? Explain your answer.
Suppose that we want to solve EXACT SET COVER using hill climbing. Let us define a state to be any sub collection of W; for instance, in the above example {W3, W4, W7} would be one state. Propose a plausible neighbor relation on the state space and a plausible error function.
Convert the following sentences to CNF:
A. ~ [P ^ (Q=>R)]
B. ~[Q <=> R]
Trace the workings of the Davis-Putnam procedure on the following set of clauses. When you reach a choice point, use the alphabetically first unbound atom and try TRUE before FALSE.
1. ~P V Q V R.
2. Q V ~R V ~W.
3. P V Q V ~R
4. ~Q.
5. ~P V ~W
6. W V X
7. ~R V W V ~X.
Let U be a domain of people and books. Let L a first-order language over U with the following symbols:
B(b,p) — book b is a biography of person p
G(p1,p2,b) — person p1 gave a copy of book b to person p2.
O(p,b) — person p owns a copy of book b.
W(p,b) — person p wrote book b.
F(p1,p2) — persons p1,p2 are friends.
A,P,S — Anne, Pamela, Sam
Express the following in L
1. Sam gave a copy of a book by Anne to Pamela.
2. If person p1 gave book b to person p2 then p2 owns a copy of b.
3. Sam owns a copy of every book that Anne has written.
4. The only books that Anne has written are biographies of friends of Anne’s.
Consider the following situation. A patient arrives at a doctor’s office, complaining of symptoms. Given these symptoms, the probability is 3/4 that this is a benign situation that will go away in a week, and 1/4 that it is a serious condition that, left untreated, will not go away. There is a treatment for the condition that is always immediately effective. There is also a test for the condition, which is not all that good. It never gives false positives — that is, it never comes up positive if the patient does not have the condition — but the probability of a false negative if the patient does have the condition is 1/2.
The associated costs are:
So the doctor has the following choices:
Draw the decision tree. Label each out arc of a chance node with its probability, and every node of the tree with its utility. (Note: you may use a calculator for this purpose.)
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