Tree Data Structures
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Questions and Answers

What is the order of node visitation in Inorder Traversal?

  • Root -> Left -> Right
  • Left -> Root -> Right (correct)
  • Left -> Right -> Root
  • Right -> Left -> Root

    • What is the time complexity of Inorder Traversal?

  • O(1)
  • O(N log N)
  • O(log N)
  • O(N) (correct)

    • Which traversal method processes nodes in the order: Root -> Left -> Right?

  • Inorder Traversal
  • Preorder Traversal (correct)
  • Level Order Traversal
  • Postorder Traversal

    • Which traversal method is primarily used for breadth-first search?

    <p>Level Order Traversal</p> Signup and view all the answers

    What is a common application of trees in computer science?

    <p>Hierarchical data representation</p> Signup and view all the answers

    What is the traversal order for Postorder Traversal?

    <p>Left -&gt; Right -&gt; Root</p> Signup and view all the answers

    Which operation allows you to locate a specific value within a binary search tree?

    <p>Search</p> Signup and view all the answers

    What scenario best describes the function of network routing algorithms in relation to trees?

    <p>Determining the shortest path</p> Signup and view all the answers

    Which of the following traversal methods visits nodes level by level?

    <p>Level Order Traversal</p> Signup and view all the answers

    In the context of binary search trees, what is a benefit of using trees for data representation?

    <p>Efficient searching and sorting</p> Signup and view all the answers

    What defines a root node in a tree structure?

    <p>The first node from which the tree originates.</p> Signup and view all the answers

    How many edges are there in a tree with n nodes?

    <p>n-1 edges</p> Signup and view all the answers

    Which of the following correctly describes leaf nodes?

    <p>Nodes that do not have any child.</p> Signup and view all the answers

    What is the definition of the degree of a node?

    <p>The total number of children of that node.</p> Signup and view all the answers

    What does the height of a tree represent?

    <p>The number of edges from the root to the highest leaf.</p> Signup and view all the answers

    Which statement is true about sibling nodes?

    <p>They belong to the same parent node.</p> Signup and view all the answers

    In tree terminology, what are internal nodes?

    <p>Nodes that have at least one child.</p> Signup and view all the answers

    How is the level of a node defined in a tree structure?

    <p>The number of edges on the path from the root to the node.</p> Signup and view all the answers

    Which of the following statements is incorrect regarding the structure of trees?

    <p>Internal nodes are also called terminal nodes.</p> Signup and view all the answers

    What is true about the nodes in a tree except the root node?

    <p>All nodes can be either internal or leaf nodes.</p> Signup and view all the answers

    What defines the depth of a tree?

    <p>The length of the path from the root to a specific node, measured in edges.</p> Signup and view all the answers

    What is a subtree in a tree structure?

    <p>A portion of the tree that includes a node and all its descendants.</p> Signup and view all the answers

    Which statement best describes a binary tree?

    <p>It is defined as a tree where each node has at most two children.</p> Signup and view all the answers

    Which type of tree guarantees that all leaf nodes are at the same depth?

    <p>Perfect binary tree</p> Signup and view all the answers

    What characterizes a binary search tree (BST)?

    <p>The left child contains values less than the parent and the right child contains values greater.</p> Signup and view all the answers

    Which of the following is NOT true about the ancestors of a node?

    <p>All sibling nodes are ancestors of each other.</p> Signup and view all the answers

    In a full binary tree, what is the maximum number of children a node can have?

    <p>Two children</p> Signup and view all the answers

    Which of the following statements about paths in a tree is accurate?

    <p>The length of a path is defined as the number of edges in the path.</p> Signup and view all the answers

    What distinguishes a complete binary tree from other types?

    <p>All levels are filled from left to right.</p> Signup and view all the answers

    Which of the following tree types can have more than two children per node?

    <p>Generic trees</p> Signup and view all the answers

    Study Notes

    Tree Data Structures

    • A tree is a non-linear data structure that organizes data hierarchically.
    • Trees consist of nodes, which are connected by edges.
    • Trees have a root node, which is the starting point.
    • Branches (edges) connect nodes to their children.

    Tree Terminology

    • Root: The top node of the tree.
    • Node: A data item in the tree.
    • Edge: The link between two nodes.
    • Parent: A node that has children.
    • Child: A node that has a parent.
    • Sibling: Nodes that share a common parent.
    • Degree: The total number of children of a node.
    • Leaf Node: A node with no children.
    • Internal Node: A node that has at least one child.
    • Level: The position of a node in the tree.
    • Subtree: A part of a tree rooted at a node.
    • Height: The maximum level in the tree (highest degree).
    • Depth: The number of edges on the path from the root to a node.
    • Path: Sequence of nodes and edges from one node to another.
    • Forest: A set of trees; or a tree structure without a root.

    Root

    • The initial node from which the tree originates.
    • A tree must have only one root.

    Edge

    • The connecting link between any two nodes.
    • In a tree with n nodes, there are exactly n - 1 edges.

    Parent

    • The node that has children.
    • A parent can have any number of children.

    Child

    • A node that has a parent.

    Siblings

    • Nodes that share a common parent.

    Degree

    • The total number of children of a node.
    • The tree's degree is the highest degree of a node.

    Internal Node

    • A node with at least one child.
    • All non-leaf nodes are internal nodes.

    Leaf Node

    • A node with no children.
    • Leaf nodes are also external nodes or terminal nodes.

    Level

    • The position of a node in the tree, measured by the number of edges away from the root node.
    • The root node is at level 0.

    Height

    • Equivalent to the maximum level in the tree.

    Depth

    • Measured by the number of edges between a node and the root.

    Subtree

    • A subsection of a tree rooted at a node, containing the node and all its descendants.
    • Every child of a node forms a subtree.

    Path

    • The sequence of nodes and edges between two specified nodes in a tree.
    • The length of a path is equal to the number of nodes in the path.

    Ancestor

    • Any node on the path between the root and a specific node.

    Types of Trees

    • Binary Tree: A tree where each node has at most two children.
      • Complete Binary Tree: All levels are completely filled.
      • Full Binary Tree: Every node has either zero or two children.
      • Perfect Binary Tree: All leaf nodes are at the same depth, and all non-leaf nodes have two children.
    • Ternary Tree: Each node has at most three children.
    • N-ary Tree: A node can have any number of children.

    Binary Search Tree (BST)

    • A binary tree where the value of each node's left child is less than the node's value, and the value of each node's right child is greater than the node's value
    • Enables efficient searching, insertion and deletion of data

    Basic Operations of BST

    • Tree Traversal
    • Insert
    • Search
    • Deletion

    Tree Traversal Techniques

    • Inorder (Left-Root-Right)
    • Preorder (Root-Left-Right)
    • Postorder (Left-Right-Root)
    • Level Order (Breadth-First)

    Applications

    • Hierarchical data representation (file systems, databases)
    • Network routing algorithms (determining shortest paths)
    • Artificial intelligence (decision trees)

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    Tree Data Structure PDF

    Description

    This quiz covers the fundamental concepts of tree data structures, including their hierarchical organization and various terminologies associated with trees. You will learn about important terms like root, node, edge, degree, and more, essential for understanding tree structures in computer science.

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