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lec0318-BSTbalance

# lec0318-BSTbalance - delete traverse something new… which...

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MP5 available. Due 4/1 (EC due 3/18). Today: Binary Search Trees – analysis, balance, and rotations. Announcements:

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Binary Tree - the height of a Binary Tree height(T) is: • ______ if T is empty • 1 + max{height(T L ), height(T R )}, otherwise The algorithms on BST depend on the height (h) of the tree. The analysis should be in terms of the amt of data (n) the tree contains. So we need a relationship between h and n. h f(n) h g(n)
Binary Tree (theory moment #2) what is minimum number of nodes (n) in a tree of height h? what is the greatest possible height (h) for a tree of n nodes?

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Binary Search Tree - The height of a BST depends on the order in which the data is inserted into it. 1 3 2 4 5 7 6 vs. 4 2 3 6 7 1 5 operation avg case worst case sorted array sorted list find insert

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Unformatted text preview: delete traverse something new… which tree makes you happiest? 50 70 90 50 70 90 The “height balance” of a tree T is: b = height(T L ) - height(T R ) A tree T is “height balanced” if: • • Binary Search Tree - is this tree “height balanced”? balanced trees - rotations 50 90 99 95 80 60 85 40 20 30 balanced trees - rotations 70 60 80 50 20 40 balanced trees - rotations 70 60 80 50 20 40 balanced trees - rotations summary: 1. there are 4 kinds: left, right, left-right, right-left (symmetric!) 2. local operations (subtrees not affected) 3. constant time operations 4. BST characteristic maintained height balanced trees - we have a special name: Three issues to consider as we move toward implementation: Rotating Maintaining height Detecting imbalance...
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