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Chapter 11: Trees

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Discrete Mathematics and its Applications
Pages: 745 - 805
Discrete Mathematics and its Applications

Discrete Mathematics and its Applications

Book edition 7th
Author(s) Kenneth H. Rosen
Pages 808 pages
ISBN 9780073383095

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Illustration

284 Questions for Chapter 11: Trees

  1. One of four coins may be counterfeit. If it is counterfeit, it may be lighter or heavier than the others. How many weighing’s are needed, using a balance scale, to determine whether there is a counterfeit coin, and if there is, whether it is lighter or heavier than the others? Describe an algorithm to find the counterfeit coin and determine whether it is lighter or heavier using this number of weighing.

    Found on Page 769

  2. Draw the subtree of the tree in Exercise \(4\)that is rooted at

    Found on Page 755

  3. A minimum spanning forest in a weighted graph is aspanning forest with minimal weight. Explain how Prim’sand Kruskal’s algorithms can be adapted to construct minimum spanning forests.

    Found on Page 802

  4. In Exercises 8–10 draw all the spanning trees of the given simple graphs.

    Found on Page 795

  5. In which order are the vertices of the ordered rooted tree in Exercises 7 visited using an in order traversal?

    Found on Page 783

  6. a) Define pre-order, in-order, and post-order tree traversal.

    Found on Page 805

  7. Draw three different B-trees of degree 3 with height 4.

    Found on Page 805

  8. Found on Page 755

  9. Find the least number of comparisons needed to sort four elements and devise an algorithm that sorts these elements using this number of comparisons.

    Found on Page 769

  10. How many different spanning trees does each of thesesimple graphs have?

    Found on Page 795

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