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7.5-avl - CMPT 225 Self-Balancing Trees CMPT 225 AVL Trees...

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CMPT 225 Self-Balancing Trees
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CMPT 225 AVL Trees
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CMPT 225 BST Activity - 1 Build BST #1 by performing the following operations: Insert K, F, G, C, H, A, R, T, U, S, P, D, L, M, N Remove G and R Build BST #2 by performing the following operations: Insert A, C, D, F, H, K, L, M, G, N, P, S, T, U, R Remove G and R Draw the resulting BST’s
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CMPT 225 BST Activity - 2 Exercises: How many elements are contained in each resulting BST? Determine the height of each resulting BST. Determine the number of levels of each resulting BST. Which element would you be searching for if you were to perform the “best case” scenario of the search operation in each of these BST's? What would be the time complexity of this scenario? Which element would you be searching for if you were to perform the “worst case” scenario of the search operation in each of these BST's? What would be the time complexity of this scenario?
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CMPT 225 Some Conclusions BST insertion and removal algorithms Only preserve the sort ordering property of the BST These algorithms do not keep the BST balanced Therefore, if we insert n elements into a BST and these elements are already in a sorting order (sort ordered by key value), these insertions will produce an unbalanced BST, i.e., a linear data structure, and the search time complexity will degrade to O (n)
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CMPT 225 To avoid degeneration of BST into linear data structure, let’s consider a variation of a BST that self-balances itself when insertion/removal operation are performed ...
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CMPT 225 AVL Definition : An AVL tree is a binary search tree with an
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