Given a binary search tree and a node of the binary search tree, the task is to delete the node from the Binary Search tree Iteratiely.
Here are the three cases that arise while performing a delete operation on a BST:
- Case 1: Node to be deleted is a leaf node. Directly delete the node from the tree.
10 10 / \ delete(5) / \ 7 15 ---------> 7 15 / \ / \ \ / \ 5 8 11 18 8 11 18
- Case 2: Node to be deleted is an internal node with two children. Copy the contents of the inorder successor of the node to be deleted and delete the inorder successor. The inorder successor can be found by finding the minimum element in the right subtree of the node.
inorderSuccessor(10) = 11.
10 11 / \ delete(10) / \ 7 15 ---------> 7 15 / \ / \ / \ \ 5 8 11 18 5 8 18
- Case 3: Node to be deleted is an internal node with one child. For this case, delete the node and move its child up to take its place.
10 10 / \ delete(15) / \ 7 15 ---------> 7 11 / \ / / \ 5 8 11 5 8
The intuition behind deleting the inorder successor in Case 2 is that the inorder successor of a node with two children will always be greater than all elements in the left sub-tree of the of the node since it is the smallest node in the right sub-tree of the node and the inorder successor of the node will always be smaller than all other nodes in the right sub-tree of the node.
This preserves the BST property of all nodes in the left sub-tree of a given node are smaller than the given node and all nodes in the right sub-tree of the given node are greater than the given node.
Below is the implementation of the above approach:
Inorder traversal of original BST: 5 7 8 10 11 15 18 Deletion of 11 Inorder traversal post deletion: 5 7 8 10 15 18 Deletion of 15 Inorder traversal post deletion: 5 7 8 10 18 Deletion of 10 Inorder traversal post deletion: 5 7 8 18
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- Iterative searching in Binary Search Tree
- Binary Search Tree | Set 2 (Delete)
- Binary Search Tree | Set 1 (Search and Insertion)
- Convert a Binary Search Tree into a Skewed tree in increasing or decreasing order
- Count the Number of Binary Search Trees present in a Binary Tree
- Binary Tree to Binary Search Tree Conversion
- Difference between Binary Tree and Binary Search Tree
- Binary Tree to Binary Search Tree Conversion using STL set
- Deleting a binary tree using the delete keyword
- Floor in Binary Search Tree (BST)
- Sum of all the levels in a Binary Search Tree
- Optimal Binary Search Tree | DP-24
- Make Binary Search Tree
- How to handle duplicates in Binary Search Tree?
- Double Threaded Binary Search Tree
- Print Binary Search Tree in Min Max Fashion
- Threaded Binary Search Tree | Deletion
- Print all odd nodes of Binary Search Tree
- Number of pairs with a given sum in a Binary Search Tree
- Print all even nodes of Binary Search Tree
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