Deletion of a node from a binary search tree, Data Structure & Algorithms

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The algorithm to delete any node having key from a binary search tree is not simple where as several cases has to be considered.

If the node to be deleted contains no sons, then it might be deleted without further adjustment to the tree.
If the node to be deleted contains only one subtree, then its only son may be moved up to take its space.
The node p to be deleted contain two subtrees, then its inorder successor s have to take its place. The inorder successor could not contain left subtree. Hence, right son of s can be moved up to gain the place of s.

Example: Assume the following cases wherein node 5 have to be deleted.

1. The node to be deleted has no children.

2390_Deletion of a node from a Binary Search Tree.png

3. The node to be deleted contains two children. This case is complicated. The order of the binary tree has to be kept intact.

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