## Is deletion commutative in binary search tree?

No, deletion is not commutative. To see why, consider the tree with root 5, children 3 and 7, and 6 as a child of 7. We will delete 5 and 3: if 5 is deleted first, then we get the tree with root 6, children 3 and 7; after deleting 3 we get the tree with root 6 and right child 7.

## Is insertion in BST commutative?

Insertion in a binary search tree is “commutative”. That is, inserting x and then y into a binary search tree leaves the same tree as inserting y and then x. A red-black tree on 128 keys must have at least 1 red node. A heap with n elements can be converted into a binary search tree in O(n) time.

What are the three cases to consider when deleting node N from a binary search tree as stated in the textbook )?

There are three possible cases to consider deleting a node from BST:

• Case 1: Deleting a node with no children: remove the node from the tree.
• Case 2: Deleting a node with two children: call the node to be deleted N . Do not delete N .
• Case 3: Deleting a node with one child: remove the node and replace it with its child.

Which of the following options is not true about the binary search tree?

Which of the following is false about a binary search tree? Explanation: In order sequence of binary search trees will always give ascending order of elements. Remaining all are true regarding binary search trees.

### How do you add an element to a binary search tree?

Insertion

1. Allocate the memory for tree.
2. Set the data part to the value and set the left and right pointer of tree, point to NULL.
3. If the item to be inserted, will be the first element of the tree, then the left and right of this node will point to NULL.

### How many types of deletion are performed in a binary tree?

There are three situations of deleting a node from binary search tree.

What is the time and space complexity of deletion in a binary tree?

Time Complexity Problems on Binary Tree

Operation Worst Case Best Case
Insert O(N) O(logN)
Search O(N) O(1)
Delete O(N) O(logN)

What is false about binary search tree?

1. Which of the following is false about a binary search tree? Explanation: In order sequence of binary search trees will always give ascending order of elements. Remaining all are true regarding binary search trees.