1. BSTImp: Insert, Delete

2. Inserting an Element into a BST Search for the position in the tree where the element would be found Insert the element in the position – Note: A newly inserted node is a leaf

3. Inserting an Element into a BST (cont’d)

4. Inserting an Element into a BST Search for the position in the tree where the element would be found Insert the element in the position – Note: A newly inserted node is a leaf

5. Inserting an Element into a BST (cont’d)

6. Exercise: Write a recursive version of insert Running Time?

7. Deleting an Element from a BST Algorithm: Find the node to delete, delete it When deleting a node from a BST, there are 3 cases to consider – The node is a leaf; it has no children. This is the easiest case to deal with – The node has one child. This case is not complicated – The node has two children. The most complicated case

8. Deleting a Leaf

9. Deleting a Node with One Child

10. Deleting a Node with One Child (cont’d)

11. Deleting a Node with Two Children Find the rightmost node in the left subtree (WHY?) and swap data between these 2 nodes

12. Deleting a Node with Two Children (cont’d)

13. Delete By Copy template void BST ::deleteByCopying(BSTNode *& node) { BSTNode *previous, *tmp = node; if (node->right == 0) // node has no right child; node = node->left; else if (node->left == 0) // node has no left child; node = node->right; else { tmp = node->left; // node has both children; previous = node; // 1. while (tmp->right != 0) { // 2. previous = tmp; tmp = tmp->right; } node->key = tmp->key; // 3. if (previous == node) previous->left = tmp->left; else previous->right = tmp->left; // 4. } delete tmp; // 5. } 3. the predecessor is right below the deleted node 4. When the predecessor is not right below the deleted node, after copying the predecessor to the deleted notde’s key, need to take care of the predessor’ left, note that the predecessor does not have a right child.

14. deleteByMerging template void BST ::deleteByMerging(BSTNode *& node) { BSTNode *tmp = node; if (node != 0) { if (!node->right) // node has no right child: its left node = node->left; // child (if any) is attached to its parent; else if (node->left == 0) // node has no left child: its right node = node->right; // child is attached to its parent; else { // be ready for merging subtrees; tmp = node->left; // 1. move left while (tmp->right != 0)// 2. and then right as far as possible; tmp = tmp->right; tmp->right = // 3. establish the link between the node->right; // the rightmost node of the left // subtree and the right subtree; tmp = node; // 4. node = node->left; // 5. } delete tmp; // 6. }