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Binary search: Algorithms

We have discussed BST search and insert operations. In this post, delete operation is discussed. When we delete a node, three possibilities arise.
1) Node to be deleted is leaf: Simply remove from the tree.

2) Node to be deleted has only one child: Copy the child to the node and delete the child

3) Node to be deleted has two children: Find inorder successor of the node. Copy contents of the inorder successor to the node and delete the inorder successor. Note that inorder predecessor can also be used.

The important thing to note is, inorder successor is needed only when right child is not empty. In this particular case, inorder successor can be obtained by finding the minimum value in right child of the node.

Time Complexity: The worst case time complexity of delete operation is O(h) where h is height of Binary Search Tree. In worst case, we may have to travel from root to the deepest leaf node. The height of a skewed tree may become n and the time complexity of delete operation may become O(n)

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