Binary Search Tree Concepts Quiz

A data structure that efficiently stores data, allowing for quick insertion, deletion, and retrieval operations. It is organized in a manner that leverages a sorted structure, enabling logarithmic time complexity (O(log n)) for most operations.

The basic building block of a Binary Search Tree. Each node contains a value and pointers to two child nodes: a left node and a right node. These pointers can be either null (representing the absence of a child) or point to other Binary Search Tree nodes, forming a tree structure.

A node in a Binary Search Tree that doesn't have any child nodes. In other words, both its left and right pointers are null.

The special node at the top of a Binary Search Tree. It is the starting point for traversing the entire tree, and its pointers connect to the rest of the tree structure.

The process of inserting a new value into a Binary Search Tree, maintaining the sorted structure. It involves comparing the new value with existing node values and placing it in the appropriate location based on its value (left for smaller values, right for larger values).

The process of removing a given value from a Binary Search Tree, while preserving the sorted structure. It involves finding the node with the value, replacing it with its successor or predecessor (to maintain the sorted order), and adjusting the tree structure accordingly.

The process of searching for a particular value within a Binary Search Tree. It utilizes the tree's sorted structure to efficiently navigate through the nodes, comparing the target value with node values to locate the desired value. The algorithm starts at the root node and branches left or right based on value comparisons.

A representation of the time complexity of a Binary Search Tree operation. It is typically logarithmic (O(log n)), indicating that the time required for operations increases proportionally to the logarithm of the number of nodes in the tree. This efficiency is a key advantage of using Binary Search Trees for data storage, but in some scenarios, the tree can degenerate into a linear structure, resulting in linear time complexity (O(n)).

A tree where every level, except the bottom level, is completely filled with nodes, and the nodes on the bottom level are as far left as possible.

The maximum number of nodes that can be present at a specific level in a complete binary tree. For level 0 (root), the width is 1. For level 1, the maximum width is 2. For level 2, the maximum width is 4, and so on.

The maximum number of nodes that can be present in a specific level in a complete binary tree.

The length of the longest path from the root node to a leaf node in a complete binary tree. This is also the number of levels in the tree.

The number of nodes on the longest path from the root to a leaf node in a complete binary tree.

A data structure where each node has a value and can have up to two child nodes, a left child and a right child. The nodes are organized in a way that maintains a specific order based on their values.

A method used to insert a new node into a binary search tree. The method ensures that the tree's ordering is maintained.

A recursive method used in conjunction with the public add method to insert a new node into a binary search tree.

A tree traversal method where the current node's value is printed first, followed by the left subtree, and lastly the right subtree. Think of it as a "root-left-right" order.

A tree traversal method that visits nodes in a specific order: left subtree, current node, and then right subtree. This order ensures that nodes are visited in ascending order for a binary search tree.

A tree traversal method where the left subtree is visited first, then the right subtree, and lastly the current node's value is printed. This results in printing the subtree nodes before the root node.

A way to visualize the order in which the algorithm visits nodes during a traversal. It's useful for understanding the steps involved and tracking the current node's position.

The process of visiting or processing each node in a tree in a specific order.

A method that removes a target value from a binary search tree. It returns the removed node, which is detached from the tree.

A node in a binary search tree with only one child.

A node in a binary search tree with two children.

A temporary variable used to store a reference to the node being removed. It ensures that the removed node remains accessible even after being detached from the tree.

The situation where the root node is the target for removal.

A special case of removing a node when the tree is empty.

A traversal method for binary trees that visits all nodes in a level-by-level manner, starting from the root node. It uses a queue to store nodes for processing and adds a node's children to the queue after visiting the node itself.

A queue data structure used in level order traversal to hold the nodes that need to be processed. It ensures nodes are visited in a breadth-first manner.

A method in a binary tree class that returns a string representation of the tree using the level order traversal. The string contains all node values, separated by spaces, in level order.

The root of a binary tree is the starting node from which all other nodes can be reached through pointers. In level order traversal, the root node is the first node to be processed.

Each node's left child (if not null) is added to the queue after the node itself has been processed. This ensures that the left child will be visited before the right child.

Each node's right child (if not null) is added to the queue after the left child has been added (or if the left child is null). This ensures that the right child will be visited after the left child.

The process of extracting a node from the front of the queue in level order traversal. The extracted node's value is added to the output string, and its children (if not null) are added to the queue for further processing.

The loop in the level order traversal algorithm continues until the queue is empty, indicating that all nodes have been visited and processed.

This method removes a node from a binary search tree with the given target value.

It's a temporary node used to hold the reference to the current node being considered for removal. This reference is crucial for updating the tree structure after removal.

This variable stores the successor node of the current node, which is the next node in sorted order. Used for removing nodes with two children.

This condition checks if the root node itself needs to be removed.

When the node to be removed is a leaf node, meaning it has no children, simply set the reference in its parent to null.

If the node to be removed has only a right child, replace the node with its right child.

If the node has only a left child, replace the node with its left child.

This part handles the scenario where the node to be removed has two children. It finds the inorder successor, swaps it with the node to be removed, and then removes the successor from its original position.