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To insert a new node at the root position in a binary search tree, the tree must be restructured by following these steps:
- Create a new node with the desired value.
- Compare the value of the new node with the value of the current root node.
- If the new node's value is less than the root node's value, set the left child of the root node to be the current root node, and set the left child of the new node to be the previous left child of the root node.
- If the new node's value is greater than the root node's value, set the right child of the root node to be the current root node, and set the right child of the new node to be the previous right child of the root node.
- Set the new node as the new root of the binary search tree.
By following these steps, a new node can be inserted at the root position of a binary search tree while maintaining the binary search tree properties.
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What is the height of a binary search tree?
The height of a binary search tree is the maximum number of edges from the root node to a leaf node. It represents the longest path from the root to a leaf in the tree.
What are the key differences between a heap and a binary search tree (BST)?
A heap is a complete binary tree where each node has a value greater than or equal to its children (max heap) or less than or equal to its children (min heap). A binary search tree is a binary tree where the left child of a node has a value less than the node and the right child has a value greater than the node. The key difference is that a heap does not have a specific order between parent and child nodes, while a binary search tree maintains a specific order for efficient searching.
How does binary tree insertion work and what are the key steps involved in inserting a new node into a binary tree?
Binary tree insertion involves adding a new node to a binary tree while maintaining the tree's structure. The key steps in inserting a new node are: Start at the root node and compare the value of the new node with the current node. If the new node's value is less than the current node, move to the left child node. If it is greater, move to the right child node. Repeat this process until reaching a leaf node (a node with no children). Insert the new node as the left or right child of the leaf node, depending on its value compared to the leaf node's value.
Are binary search trees always balanced?
No, binary search trees are not always balanced. Balancing a binary search tree involves ensuring that the height difference between the left and right subtrees of each node is at most 1. Unbalanced binary search trees can lead to inefficient search and insertion operations.
What is the process of traversing a binary tree level by level, starting from the root node, known as?
The process of traversing a binary tree level by level, starting from the root node, is known as breadth-first search (BFS).
When we insert a new node in a binary search tree will it become an internal node or terminal node?
It will be come a terminal node. Normally we call terminal nodes leaf nodes because a leaf has no branches other than its parent.
What is the height of a binary search tree?
The height of a binary search tree is the maximum number of edges from the root node to a leaf node. It represents the longest path from the root to a leaf in the tree.
Write an iterative function to search an element in a binary search tree?
_node* search (_node* head, _key key) { _node* node; for (node=head; node != NULL;;) { if (key == node->key) return node; else if (key < node.>key) node = node->left; else node = node->right; } return node; }
What is cprogram code to insert a node in single link list?
Write Code to Insert a Node in a Single Linked List at any given Position.
What are the key differences between a heap and a binary search tree (BST)?
A heap is a complete binary tree where each node has a value greater than or equal to its children (max heap) or less than or equal to its children (min heap). A binary search tree is a binary tree where the left child of a node has a value less than the node and the right child has a value greater than the node. The key difference is that a heap does not have a specific order between parent and child nodes, while a binary search tree maintains a specific order for efficient searching.
How does binary tree insertion work and what are the key steps involved in inserting a new node into a binary tree?
Binary tree insertion involves adding a new node to a binary tree while maintaining the tree's structure. The key steps in inserting a new node are: Start at the root node and compare the value of the new node with the current node. If the new node's value is less than the current node, move to the left child node. If it is greater, move to the right child node. Repeat this process until reaching a leaf node (a node with no children). Insert the new node as the left or right child of the leaf node, depending on its value compared to the leaf node's value.
What is the algorithm to find largest node in a binary search tree?
Since a binary search tree is ordered to start with, to find the largest node simply traverse the tree from the root, choosing only the right node (assuming right is greater and left is less) until you reach a node with no right node. You will then be at the largest node.for (node=root; node!= NULL&&node->right != NULL; node=node->right);This loop will do this. There is no body because all the work is done in the control expressions.
What is the difference between extended binary tree and a binary search tree?
A strictly binary tree is one where every node other than the leaves has exactly 2 child nodes. Such trees are also known as 2-trees or full binary trees. An extended binary tree is a tree that has been transformed into a full binary tree. This transformation is achieved by inserting special "external" nodes such that every "internal" node has exactly two children.
Are binary search trees always balanced?
No, binary search trees are not always balanced. Balancing a binary search tree involves ensuring that the height difference between the left and right subtrees of each node is at most 1. Unbalanced binary search trees can lead to inefficient search and insertion operations.
Where Inorder Predecessor of a non leaf node is present in a Binary Search Tree?
left side
Difference between binary search tree and heap tree?
A binary search tree uses the definition: that for every node,the node to the left of it has a less value(key) and the node to the right of it has a greater value(key).Where as the heap,being an implementation of a binary tree uses the following definition:If A and B are nodes, where B is the child node of A,then the value(key) of A must be larger than or equal to the value(key) of B.That is,key(A) ≥ key(B).
What is the process of traversing a binary tree level by level, starting from the root node, known as?
The process of traversing a binary tree level by level, starting from the root node, is known as breadth-first search (BFS).
