lecture05-RBTree

lecture05-RBTree - Sources Dr David Luebke’s slides Dr...

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Unformatted text preview: Sources: Dr. David Luebke’s slides Dr. Dan Gildea’s slides CS 6713 Advanced Analysis of Algorithms Lecture 05 Red-Black Trees Review: Binary Search Trees ● Binary Search Trees (BSTs) are an important data structure for dynamic sets ● In addition to satellite data, elements have: ■ key : an identifying field inducing a total ordering ■ left : pointer to a left child (may be NULL) ■ right : pointer to a right child (may be NULL) ■ p : pointer to a parent node (NULL for root) Review: Binary Search Trees ● BST property: key[left(x)] ≤ key[x] ≤ key[right(x)] [all the keys in x’s left subtree] ≤ key[x] ≤ [all the keys in x’s right subtree] ● Example: F B H K D A Review: Inorder Tree Walk ● An inorder walk prints the set in sorted order: TreeWalk(x) TreeWalk(left[x]); print(x); TreeWalk(right[x]); ■ Easy to show by induction on the BST property ■ Preorder tree walk : print root, then left, then right ■ Postorder tree walk : print left, then right, then root Review: BST Search TreeSearch(x, k) if (x = NULL or k = key[x]) return x; if (k < key[x]) return TreeSearch(left[x], k); else return TreeSearch(right[x], k); Review: BST Search (Iterative) IterativeTreeSearch(x, k) while (x != NULL and k != key[x]) if (k < key[x]) x = left[x]; else x = right[x]; return x; Review: BST Insert...
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lecture05-RBTree - Sources Dr David Luebke’s slides Dr...

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