Lecture10

Binary Search Tree

Properties

• Left subtree
  • The left subtree of a given node contains only nodes with keys lesser than the node's key.
• Right subtree
  • The right subtree of a given node contains only nodes with keys greater than the node's key.

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Insertion

Case 1: Empty tree

• Create a new node with new key
• Make that new node root

Case 2: Non-empty Tree

• Start at the root
• Traverse the tree to find a location for the new key(stops at a leaf node X)
• Add a new node as a child of X

Deletion

Case 1 : No Children

• It is a leaf node, we don't need to worry about "disconnecting" its children.
• "Sever" the connection between the parent node and found ndoe.
• Either delete the "stray" node or let garbage collector remove it. Done!

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if (current.leftChid == null && current.rightChid == null){
            if (current == root){
                root = null;
            }else if (isLeftChild){
                parent.leftChid = null;
            }else{
                parent.rightChid = null;
            }

Case 2: One Child

• It is not a leaf node, we NEED to worry about its child.
• FOUND node's only child should take it's place to preserve BST properties
• Connect FOUND node's parent to FOUND's child. "Old" connection "severed"
• Either delete the "stray" node or let garbage collector remove it. Done!

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else if (current.rightChid == null){
                if (current == root){
                    root = current.rightChid;
                }else if (isLeftChild){
                    parent.leftChid = current.leftChid;
                }else{
                    parent.rightChid = current.rightChid;
                }
        }else if (current.leftChid == null){
            if (current == root){
                root = current.rightChid;
            }else if (isLeftChild){
                parent.leftChid = current.leftChid;
            }else{
                parent.rightChid = current.rightChid;
            }

Case 3: Two Children

Successor a Leaf Node,Successor a Right Child

• It is not s leaf node, we NEED to worry about its children.
• Trick: find an IN-ORDER successor of FOUND node place it instead of FOUND
• FOUND's LEFT child also becomes FOUND's successor LEFT CHILD
• We can now "server" FOUND's connection to its LEFT child. Successor's got it.
• Now we need to connect FOUND'S Parent with FOUND'S successor
• Either delete the "stray" node or let garbage collector remove it. Done!

image-20210328113809441.png

Successor is a Left Descendant of Right Child

image-20210328114102618.png

Successor is a Left Descendant of Right Child , Successor has a Right Child

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