Tutorial 7 - binary search tree 6 Draw a graph having the...

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DCS5028 DISCRETE STRUCTURES TUTORIAL 7 1 CHAPTER 7: Trees 1. Refer to the tree diagram below. With “i” as the root w hat is the height of the tree? b i d j k h a e c f g 2. Refer to the tree diagram below. With “a” as the root, what is the height of the resulting tree? d a i g e b j c f h 3. For questions (i-iii), refer to the tree diagram below: a b c d e f h i j k l m n o p q r (i) Find the parents of c and h (ii) Find the ancestors of c and j (iii)Find the children of d and e (iv) Find the descendants of c and e (v) Find the siblingsof f and h (vi) Find the leaf vertices (vii)Find the internal vertices
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DCS5028 DISCRETE STRUCTURES TUTORIAL 7 2 (vii) Draw the subtree rooted at j (xi) Draw the subtree rooted at e 4. Redraw the following tree with V6 as the root: (a) Use the newly drawn three in question 4 to answer the following questions: 1. What are the descendants of V4? 2. List all level-4 vertices. 3. List all internal vertices. 5. Place the words FOUR SCORE AND SEVEN YEARS AGO OUR FOREFATHERS BROUGHT FORTH in the order in which they appear in a
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Unformatted text preview: binary search tree. 6. Draw a graph having the given properties: Full binary tree, nine terminal (leaf) vertices, height = 3 . Explain why no such graph exists. 7. Given the following alphabets P T D H X M S J B E N K a) Create a binary search tree from the above alphabets. b) Write the traversal for Depth First Search in finding the letter ‘ M ’ based from the answer in question 7(a). c) Write the traversal for Breath First Search in finding the letter ‘ S ’ based from the answer in question 7(a). V2 V1 V3 V4 V5 V8 V6 V9 V7 V10 DCS5028 DISCRETE STRUCTURES TUTORIAL 7 3 8. Find the minimal spanning tree by using Prim’s algorithm for the graph below: 2 3 1 3 4 2 3 3 2 9. Find the minimal spanning tree by using Kruskal’s algorithm for the graph below: 4 1 12 6 7 5 11 14 8 13 3 9 2 10 10. Based on the tree diagram below, list the order in which the vertices are processed using preorder, inorder and postorder traversal. A B C D E F 1 2 3 4 5 6 1 2 3 4 5 6 7 8 9...
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