Discrete Structures Questions

2. A seven-person committee composed of Adam, Betty, Cameron, David, Edward, Fritz, and Grace is to select a chairperson, secretary, and treasurer. How many selections are there where Betty is the chairperson, and Adam and Edward are not officers? 12 20 24 210 None of the above ...continues

Discrete Structures Questions

1. By using the Pigeonhole Principle, we can show that if you take six classes in a term and classes do not meet on the weekend, then at least three of the classes must meet on the same day. True False 2. By using the Pigeonhole Principle, it can be shown that if you are paid bi-weekly (every two weeks) duri ...continues

Find level numbers and ancestors of vertices in the given tree.

Attached figure [lib1312061.jpg] shows a subtree rooted at vertex p. Given that the level number for vertex u is 37, (a) What are the level numbers for vertices p, s, t, v, w, x, y and z? (b) How many ancestors do vertices u and y have?

List the vertices of given tree under Preorder and Postorder traversals.

List the vertices of tree in attachment lib1312062.jpg, when they are visited in a preorder traversal and in a postorder traversal.

Draw the splitting and merging trees obtained during sorting of given sequence of numbers using merge sort.

Sort the given sequence of numbers using merge sort. Draw the splitting and merging trees for each application of the procedure. -1, 0, 2, -2, 3, 6, -3, 5, 1, 4

Encoding word using given Huffman code tree, and other tree related problems.

[1] Encode "LEADEN" using the Huffman code tree given in the attachment. [2] What can you say about a vertex in a rooted tree that has no descendants? Please see the attachment for more tree related problems.

Find a minimal spanning tree (MST) for the given graph using Prim's algorithm.

Find a minimal spanning tree for the connected weighted graph, following Prim's algorithm. Please see attached 4.doc for the details on graph and Prim's algorithm for finding a minimal spanning tree.

Encode and decode strings using given Huffman code tree.

Using the Huffman code given in the attached image, (a) encode the string "NEEDLE". (b) decode the bit string "01111001001110".

Find the bad coin out of given 8 coins using only a pan balance.

Eight coins are identical in appearance, but one coin is either heavier or lighter than the others, which all weigh the same. Describe an algorithm that identifies the bad coin in at most three weighings and also determines whether it is heavier or lighter than the others, using only a pan balance.

Solve for coefficient.

When (x-2)^17 is expanded, what is the coefficient of x^12? Be careful, don’t forget about the –2.