Binary Search Trees Quiz

A type of binary tree where data is organized in a specific order. Each node's left subtree contains values smaller than its own, and the right subtree contains values larger than its own.

A data structure where each node has a maximum of two children (left and right).

The topmost node in a tree structure.

A node that has no children.

The process of locating a specific value within a binary search tree.

A recursive process that starts at the root node and traverses down based on comparisons.

Adding a new node to a binary search tree while maintaining the order property.

Removing a node from a binary search tree while maintaining the order property.

A recursive algorithm that searches for a given key in a binary search tree (BST). It starts from the root and compares the key with the current node's key. If they are equal, the node is returned. If the key is less than the current node's key, it searches the left subtree. If the key is greater, it searches the right subtree.

An iterative algorithm for searching a key in a BST. It keeps moving down the tree, left or right based on the comparison with the current node's key, until the key is found or a null node is reached.

The most efficient way to find the minimum element in a binary search tree (BST). It traverses the tree, always moving to the left child, until it reaches the leftmost node, which holds the minimum value.

The most efficient way to find the maximum in a binary search tree (BST). It traverses the tree, always moving to the right child, until it reaches the rightmost node, which holds the maximum value.

This case deals with the termination condition of the recursive function. In BST insertion, it happens when an empty subtree is encountered, meaning a new node needs to be added.

This case handles the recursive part of the insertion process. It checks if the new value is smaller than the current node's value and calls the function recursively on the left subtree, or if it's larger, it calls it recursively on the right subtree.

The order in which you insert elements into a BST can significantly impact its height and efficiency. Inserting in a specific order can lead to a tree with a height equal to the number of nodes, making searches inefficient.

Unbalanced BSTs with a height close to the number of nodes result in longer search times, as the algorithm has to traverse more levels. Balanced trees, like AVL or red-black trees, provide better search performance by maintaining a certain depth.

A function that finds a specific value in a Binary Search Tree (BST) iteratively. It starts at the root node and traverses down, comparing the value to be found with the current node's value. It moves left if the value is smaller, right if it's larger. If the value matches, it returns the found value. If null is reached, it returns null, indicating the value is not found.

A function that finds a specific value in a Binary Search Tree (BST) recursively. It starts at the root node and compares the value to be found with the current node's value. The function calls itself recursively with appropriate subtree to continue the search.

The time it takes for a search function to complete, measured in the number of operations. It describes the efficiency of the algorithm in finding a specific value in a BST.

A function that inserts a new node into a Binary Search Tree (BST) at the correct position while maintaining the BST property. It ensures that the left subtree contains values smaller than the current node, and the right subtree contains values larger than the current node.

The size of the subproblem tackled within a recursive function call in BST InsertItem. It refers to the number of elements the function is currently dealing with in the subtree being considered.

Deleting a node from a binary search tree with no children (leaf node).

Deleting a node with only one child; either left or right. The remaining child replaces the deleted node.

Deleting a node with two children. Finding the predecessor (the rightmost node in the left subtree) and replacing the data of the deleted node. Then deleting the predecessor.

The process of finding the rightmost node in a binary search tree's left subtree.

The part of the DeleteItem function that handles deleting a node based on its child count.

A recursive function that handles deleting a specific item from a binary search tree.

The function that kicks off the item deletion process in a binary search tree.

A function for finding the predecessor of a node in a binary search tree.

The base case of the Delete function, where the item to be deleted has been found.

Choosing the appropriate subtree (left or right) based on comparison with the target item.