Lecture11 - Lecture 11 Deletion 3 Cases No children simple...

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1 124 Deletion 3 Cases: » No children – simple delete, replace pointer from parent with null » 1 child – delete, redirect pointer from parent to point to child » 2 children – cannot simply delete 3rd case: put successor(x) instead of x. » Binary Tree property satisfied. » Delete “hole” using case 1 or 2. » Why ?? » (successor does not have left child !) Lecture 11, Oct 26 2010 Summary Data structure implements insert/delete/search/pred/successor Speed depends on height of the tree, in general can be large Need a way to “rebalance the tree” Possible to rebalance so that height < 2log n Basic operation: “Rotation” 125
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2 132 Skip List Simple data structure, easier to implement than red/black trees. Sorted doubly-linked list with “skip” pointers. Construction: » Every element in the “bottom list” (list 0) » Element passed to list 1 with probability 1/2 . » In general, element in list i is promoted/added to list i+1 with prob. 1/2 .
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