14. BinarySearchTrees_outside

# An inorder traversal of a binary search trees visits

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An inorder traversal of a binary search trees visits the keys in increasing order 6 9 2 4 1 8 © 2010 Goodrich, Tamassia

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Binary Search Trees 6 Search To search for a key k , we trace a downward path starting at the root The next node visited depends on the comparison of k with the key of the current node If we reach a leaf, the key is not found Example: get (4): Call TreeSearch(4,root) The algorithms for floorEntry and ceilingEntry are similar Algorithm TreeSearch ( k , v ) if v.isExternal () return v if k < v.key () return TreeSearch ( k , v.left ()) else if k = v.key () return v else { k > v.key () } return TreeSearch ( k , v.right ()) 6 9 2 4 1 8 < > = © 2010 Goodrich, Tamassia
Binary Search Trees 7 Insertion To perform operation put (k, o), we search for key k (using TreeSearch) Assume k is not already in the tree, and let w be the leaf reached by the search We insert k at node w and expand w into an internal node Example: insert 5 6 9 2 4 1 8 6 9 2 4 1 8 5 < > > w w © 2010 Goodrich, Tamassia

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Binary Search Trees 8 Deletion To perform operation erase ( k ), we search for key
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