# hw1KEY - COP 3530 Homework Problems#1 Summer 2002 SOLUTION...

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COP 3530 – Homework Problems #1 – Summer 2002 SOLUTION KEY 1. Shown below is a BST which is unbalanced. Use the DSW algorithm to create a perfectly balanced version of this tree. Show all intermediate steps in both the creation of the backbone as well as the rotations that will occur to convert the backbone into the perfectly balanced tree. Part 1: Establishing the backbone. To see the creation of the backbone, see page 10. Part 2: Perform required number of initial rotations. There are 12 nodes in this tree so n = 12. m = 2 log 2 (n+1) - 1; m = 2 log 2 (12+1) - 1 = 2 3 -1 = 7 Perform a total of n – m = 12 – 7 = 5 initial rotations on the backbone. 1 45 40 55 25 15 35 85 30 38 70 65 60 15 25 30 35 38 40 45 55 60 65 70 85 15 25 30 35 38 40 45 55 60 65 70 85

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backbone above) produces the following backbone. The backbone after the initial rotations Part 3: Perform required number of rotations to perfectly balance the tree. Since m=7 and its value is halved after every rotation and rotation stops when m=1, we will perform a total of 4 rotations (when m = 7 do 3: 35 about 25, 55 about 40, and 70 about 65, when m = 3 do 1: 55 about 35). First 3 rotations
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hw1KEY - COP 3530 Homework Problems#1 Summer 2002 SOLUTION...

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