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Trees - Part II

© Dave Bockus

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Building a Binary Search Tree

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Input: i h b m e c f a d k

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Code for BST InsertionUsing Recursion

BinaryNode Insert(Comparable x, BinaryNode t) {if (t == null) Null ptr, Create new Node. t = new BinaryNode(X, null, null);

else if (x.compareTo(t.element < 0) If element is < then descend left t.left = Insert(x, t.left); else if (x.compareTo(t.element > 0) If element is > then descend right t.right = Insert(x, t.right); else ; Equal i.e. Duplicate - do nothing return t;}

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BST Insertion Using Iteration - page 308 Lafore public void insert(int id, double dd) { Node newNode = new Node(); // make new node newNode.iData = id; // insert data newNode.dData = dd; if(root==null) // no node in root root = newNode; else { // root occupied Node current = root; // start at root Node parent; while(true) { // (exits internally) parent = current; if(id < current.iData){ // go left? current = current.leftChild; if(current == null) { // if end of the line parent.leftChild = newNode; // insert on left return; } } // end if go left else { // or go right? current = current.rightChild; if(current == null){ // if end of the line parent.rightChild = newNode; // insert on right return; } } // end else go right } // end while } // end else not root } // end insert()

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Modified BST Insertion Using Iteration public Node insert(int id) //Data is modified outside of { // insert via returned ptr Node newNode = new Node(); // make new node newNode.iData = id; // insert key data if(root==null) // no node in root root = newNode; return root; else { // root occupied Node current = root; // start at root Node parent; while(true) { // (exits internally) parent = current; if (id == current.iData) return current; if(id < current.iData){ // go left? current = current.leftChild; if(current == null) { // if end of the line parent.leftChild = newNode; // insert on left return parent.leftChild; } } // end if go left else { // or go right? current = current.rightChild; if(current == null){ // if end of the line parent.rightChild = newNode; // insert on right return parent.rightChild; } } // end else go right } // end while } // end else not root } // end insert()

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Building an AVL Tree

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Input: M J B F E G

Single Right

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Double RightF

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Deletions in a Binary Tree

• 3 Cases - if we delete node pointed to by ptr– Leaf Node

• Just Delete it– Node with 1 null sub-tree.

• Ptr’s Parent points to non-null sub-tree.– Node with 2 non-null sub-trees.

• Find successor• Copy successor into node pointed to by ptr.• Delete successor - simple case i.e. null left sub-tree

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Deletion Case 1 - A leaf node

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aLeaf nodes can be deleted

without any problems

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Deletion Case 2 - 1 non-null sub-tree

Parent points to non-null subtree

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Node pointed to by ptr is deleted

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Deletion Case 2 - 2 non-null sub-trees

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Find the successor

Replace data of ptr with data of qtr

Deleting node qtr is a simple case

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Code to Delete from a BSTBinaryNode remove(Comparable x, BinaryNode t) {

if (t == null) Null ptr, node not found return t;if (x.compareTo(t.element) < 0) Descend left branch t.left = remove(x, t.left);else if(x.compareTo(t.element) > 0) Descend right branch t.right = remove(x, t.right);else if (t.left != null && t.right != null) { t.element = successor(t).element; Copy successor into current t.right = remove(t.element, t.right); node and recursively remove} the successor.else if (t.left != null) Simple case: found x pointed to by t = t.left; t, so point around it to the non- else null sub-tree. If t is a leaf then t = t.right; t.left is null so we point around toreturn t; t.right which is null also, this

} null is returned.