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31. Assume that the binary tree T shown below was produced as a result of an execution on RandQS. Which sequences of picking pivot elements can lead to ?
3, 2, 1, 5, 4, 8, 7, 6, 9
3, 5, 8, 9, 7, 6, 4, 2, 1
3, 2, 5, 1, 4, 8, 7, 9, 6
3, 5, 8, 9, 2, 4, 7, 1, 6
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32. Consider the graph G given below. Which of the following statements are true?
G doesn't have a cut of size
Mincut in G is of size
G has a mincut of size .
G doesn't have a unique mincut
33. Consider the input graph G as given below. Assume that we contract uniformly at random the edges of G until only two vertices remain. Which of the following statements are true?
The probability that the randomized algorithm returns a mincut is greater than 1/100
The probability that the randomized algorithm returns a mincut is less than 1/8
For any choice of the first edge to contract, there is a non zero probability that randomized algorithm returns the correct answer
34. Consider the input graph G as given below. Assume that we contract uniformly at random the edges of G until only two vertices remain. Further assume that G1 is the resultant graph after the first four edge contractions. Which of the following statements are true?
If the edges contracted were (a1, b1), (b1, c1), (a3, b3) and (b3, c3), then G1 will have 18 edges.
If the edges contracted were (a1, b1), (b1, c1), (a3, b3) and (b3, c3), then G1 will have 20 edges.
G1 will have at least 12 edges
The mincut in G1 could be smaller than the mincut in G.
35. Let G be a graph with vertices. Let the mincut in G be of size. Which of the following statements are true?
There is a vertex in G with degree 10.
G does have any cycles
G has at least 50 edges
Every vertex in G has degree at least 5.
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