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Questions and Answers
What is the correct order of nodes visited in postorder traversal?
What is the correct order of nodes visited in postorder traversal?
Which property is unique to a perfect binary tree?
Which property is unique to a perfect binary tree?
What distinguishes a binary search tree (BST) from a regular binary tree?
What distinguishes a binary search tree (BST) from a regular binary tree?
In level order traversal, what is the order of node visits?
In level order traversal, what is the order of node visits?
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Which type of binary tree requires that every parent node has either two children or no children?
Which type of binary tree requires that every parent node has either two children or no children?
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What is a defining characteristic of a binary heap?
What is a defining characteristic of a binary heap?
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In inorder traversal, what is the sequence in which nodes are visited?
In inorder traversal, what is the sequence in which nodes are visited?
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What is the main criterion for a complete binary tree?
What is the main criterion for a complete binary tree?
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What characteristic of a binary search tree (BST) dictates where to insert a new node?
What characteristic of a binary search tree (BST) dictates where to insert a new node?
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Which operation on a binary search tree requires traversing from the root to a leaf?
Which operation on a binary search tree requires traversing from the root to a leaf?
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What happens when searching for a value that is equal to the current node's value in a BST?
What happens when searching for a value that is equal to the current node's value in a BST?
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In the insertion process of a BST, which condition is used to determine whether to move left or right?
In the insertion process of a BST, which condition is used to determine whether to move left or right?
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Which of the following statements about a binary tree node is incorrect?
Which of the following statements about a binary tree node is incorrect?
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What is the primary purpose of the binary search algorithm within a binary search tree?
What is the primary purpose of the binary search algorithm within a binary search tree?
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When traversing a binary search tree, if the search key is greater than the current node's value, what is the next step?
When traversing a binary search tree, if the search key is greater than the current node's value, what is the next step?
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What is the initial step when inserting a new value into a binary search tree?
What is the initial step when inserting a new value into a binary search tree?
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What is a key characteristic of a node in a tree data structure?
What is a key characteristic of a node in a tree data structure?
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Which term describes the highest node in a tree?
Which term describes the highest node in a tree?
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What does the height of a tree refer to?
What does the height of a tree refer to?
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In terms of tree traversal, which method visits the root node before its child nodes?
In terms of tree traversal, which method visits the root node before its child nodes?
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What defines the degree of a node in a tree structure?
What defines the degree of a node in a tree structure?
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What is a leaf node in the context of a tree data structure?
What is a leaf node in the context of a tree data structure?
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How is the depth of a node defined?
How is the depth of a node defined?
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What is a subtree?
What is a subtree?
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Study Notes
Tree Data Structure
- A tree is a non-linear hierarchical data structure
- It consists of nodes connected by edges
- Trees are used extensively in computational settings
- Linear structures like arrays, linked lists, stacks, and queues store data sequentially
- Linear structures' time complexity increases with data size, which is not suitable for today's computational needs
Tree Terminologies
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Node: An entity containing a key or value and pointers to its child nodes. Can have zero or more children.
- Leaf nodes (or external nodes) are the last nodes on each path. They do not connect to child nodes.
- Internal nodes have at least one child node.
- Edge: The link between any two nodes.
- Root: The topmost node of the tree.
Tree Data Structure: Tree Terminologies
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Level/Depth: The level of a node is the number of edges from the root to that node.
- The root is level 0, its children are at level 1, etc.
- Height of a node: The number of edges on the longest path from the node to a leaf node.
- Height of the tree: The height of the root node. This is the length of the longest path from the root to a leaf node.
Tree Data Structure: Tree Terminologies
-
Subtree: A tree formed by a node and all its descendants in the tree.
- Each node in a tree can be considered the root of its own subtree.
- Degree of a Node: The total number of branches (or children) of a node.
- Degree of a Tree: The maximum degree of all nodes.
- Size of the tree: The overall number of nodes within the tree.
Tree Traversal: Inorder-Preorder-postorder
- Linear data structures (arrays, stacks, queues, and linked lists) only have one way to read data.
- Trees can be traversed in multiple ways like inorder, preorder, and postorder.
- A tree's structure is a combination of a node containing data and two subtrees.
Inorder Traversal
- Visit recursively all nodes in the left subtree.
- Then visit the root node.
- Visit recursively all nodes in the right subtree.
Preorder Traversal
- Visit the root node.
- Visit recursively all nodes in the left subtree.
- Visit recursively all nodes in the right subtree.
Postorder Traversal
- Visit recursively all nodes in the left subtree.
- Visit recursively all nodes in the right subtree.
- Visit the root node.
Example Traversal
- Inorder: 12, 22, 32, 54, 55, 61, 78
- Preorder: 54, 22, 12, 32, 61, 55, 78
- Postorder: 12, 32, 22, 55, 78, 61, 54
Level Order Traversal
- Traverses nodes level by level, left to right
- The nodes in each level are traversed entirely before moving to the next level.
- Example output: 54, 22, 61, 12, 32, 55, 78
Binary Tree
- A tree data structure in which each parent node can have at most two children.
- Each node has a data item and addresses for its left and right child.
Binary Tree: Types
- Complete Binary Tree: Every level is filled completely, except possibly the last level. Nodes are filled from left to right on the last level.
- Full Binary Tree: Each parent node has either two children or no children.
- Perfect Binary Tree: Every internal node has exactly two children and all leaf nodes are at the same level.
- Heap Tree: A complete binary tree in which the value of each node is either greater than or equal to (Min Heap) or less than or equal to (Max Heap) the values of its children.
Binary Search Tree (BST)
- A binary tree with special properties ensuring:
- All nodes in the left subtree are less than the root node
- All nodes in the right subtree are greater than the root node
- Both subtrees of every node are also binary search trees
Binary Search Tree Representation
- A node in a binary tree is represented using a structure that contains data and pointers to its left and right subtrees/children.
Binary Search Tree Implementation
- Code snippets showing how to create a new node, initiate a BST, etc.
Binary Tree Operations: Searching
- Techniques for finding a specific node in a BST
Binary Tree Operations: Insertion
- Techniques for adding a new node to a BST
Binary Tree Operations: Deletion
- Methods to remove a node from a BST. Different cases are illustrated: deleting a leaf node, a node with one child, and a node with two children.
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Description
Test your knowledge of tree data structures and their terminologies with this quiz. Explore concepts such as nodes, edges, and the importance of trees in computational settings. Ideal for students learning about data structures in computer science.
