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1) List allofthe following a) Level- vertices b) Leaves c) Siblings ofv, d) Descendants of v2 2) Isthis an n-tree? 1so for what integer n? 3) Explain how many vertices would need be added to each existing vertex to create a complete 3-tree For example, writing "Vs would mean that two vertices need te be added tothe existing Vo vertex Writing 0 would mean that no vertices need be added the existing vertex 4) Compute the tree T(v2). You may use (copy paste move resize etc) the images below to create your graph 5) Give height each Explain your answers a) T(v). b) T(v>) 6) Construct the tree of the algebraid expression below. Note that problems refer to the tree that you construct nthis problem. You may use (copy paste move /resize/etc) the images below to create your graph 0000000000000000 tree below for 7) Decode the message 110001000111 Show your calculations. 8) Find the string that represents EAST. Show your calculations 9) Use the tree that you constructed problem the result of performing a preorder search for ((z y]) (w your answer 10) Use the tree that you constructed problem above Show the result of performing an inorder search for ((z v)) (w-(z- 7)). Explain your answer 11) Use the tree that you constructed problem above Show the result of performing a an postorder search 3)+(2- 7)) Explain your answer 12) Draw the digraph of the binary positional tree that corresponds Figure HW (which was used problems above, at the top of page 21. You mayuse (copy paste move / resize etc. the images below create your graph. 13) Use vertex the initial vertex anduse Prim's algorithm to find minimal spanning tree What sthe total weight of your tree? You do not need to draw the tree.but dolist the edges (as an ordered pair)ir the order which they are chosen K H 14) Use Kruskal algorithm to finda minimal spanning tree What thetotal weight of your tree? You do not need to draw the tree, but do list the edges (as an ordered pair) ir the order in which they are chosen. This is the same graphs problem 13 D

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1) List all of the following.
a) Level-2 vertices: v1,v2,v3
b) Leaves: v4,v5,v8,v9,v7
c) Siblings of v2 :v1 and v3
d) Descendants of v2 : v5,v6,v8,v9

2) Is this an n-tree? If so, for what integer n? it is a 3-tree since the maximal degree is 3: no node has more than 4 children.

3) Explain how many vertices would need to be added to each existing vertex to create a complete 3-tree. For example, writing “v0: 2” would mean that two vertices need to be added to the existing v0 vertex. Writing “v0: 0” would mean that no vertices need to be added to the existing v0 vertex.

v0: 0 v1: 2 v2: 1 v3: 2 v4: 3

v5: 3 v6: 1 v7: 3 v8: 0 v9: 0...

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