Tree Data Structures in Nonlinear Data Structures
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Questions and Answers

What is the name given to a tree where every internal node has exactly two children?

  • Complete Binary Tree
  • Strictly Binary Tree (correct)
  • Full Binary Tree (correct)
  • Binary tree

What is the significance of the root node in a tree data structure?

The root node is the starting point of the tree, and it does not have a parent. All other nodes in the tree are descendants of the root node.

What is the difference between a leaf node and an internal node in a tree?

A leaf node is a node without any children. An internal node, on the other hand, has at least one child.

What is the purpose of the llink and rlink fields within a node in a binary tree?

<p>The <code>llink</code> field contains the address of the left subtree, while the <code>rlink</code> field contains the address of the right subtree.</p> Signup and view all the answers

What is a 'subtree' in a tree data structure?

<p>A subtree is a subset of a tree that itself forms a complete tree structure.</p> Signup and view all the answers

What is the purpose of 'Threads' in a threaded binary tree?

<p>All of the Above (D)</p> Signup and view all the answers

What is the principle behind the 'binary search property' in a Binary Search Tree (BST)?

<p>In a Binary Search Tree (BST), the 'binary search property' ensures that all nodes in the left subtree of a node contain values less than or equal to the node's value, while all nodes in the right subtree contain values greater than or equal to the node's value.</p> Signup and view all the answers

What is the primary purpose of the 'Hash Function' in a Hash Table?

<p>All of the Above (D)</p> Signup and view all the answers

Explain the concept of 'collision' in Hash Tables.

<p>Collision occurs when two or more different keys are hashed to the same memory location within the Hash Table.</p> Signup and view all the answers

What are the two primary techniques used to address collision conflicts in Hash Tables?

<p>The two main techniques for handling collisions in Hash Tables are Open Hashing and Closed Hashing.</p> Signup and view all the answers

Hashing is used in the implementation of a Binary Search Tree.

<p>False (B)</p> Signup and view all the answers

Which of the following is NOT a common traversal approach for binary trees?

<p>Hash Traversal (B)</p> Signup and view all the answers

What is an 'Euler path' in graph theory?

<p>An Euler path is a path that traverses every edge of a graph exactly once, starting and ending at different vertices.</p> Signup and view all the answers

What is a 'Hamiltonian circuit' in graph theory?

<p>A Hamiltonian circuit is a cycle that visits each vertex of a graph exactly once, starting and ending at the same vertex.</p> Signup and view all the answers

Explain what a 'weighted graph' is and provide an example.

<p>A weighted graph is a graph where each edge has an associated weight or value representing a cost, distance, or capacity. For example, in a graph representing roads connecting cities, the weight of each edge could represent the distance between the cities.</p> Signup and view all the answers

The length of a path in a graph is determined by counting the number of vertices.

<p>False (B)</p> Signup and view all the answers

A 'self-loop' in a graph refers to an edge that connects a vertex to itself.

<p>True (A)</p> Signup and view all the answers

What is the primary difference between a 'directed graph' and an 'undirected graph'?

<p>In a directed graph, edges have a direction, indicating the flow of connections between vertices. In an undirected graph, edges do not have a specific direction, representing relationships between vertices where the connection is bidirectional.</p> Signup and view all the answers

What is the main point of using adjacency lists to represent a graph?

<p>Adjacency lists provide a more space-efficient way to represent sparse graphs, which have a low edge density, compared to adjacency matrices. They store only the edges that are present in the graph, saving memory.</p> Signup and view all the answers

What is the concept of 'component' in a 'disconnected graph'?

<p>Each individual connected subgraph within a disconnected graph is called a 'component.'</p> Signup and view all the answers

Which of the following graph representations is generally preferred for sparse graphs?

<p>Adjacency List (B)</p> Signup and view all the answers

Overflow in a hash table occurs when the hash table reaches its maximum capacity.

<p>True (A)</p> Signup and view all the answers

What is one advantage of using a 'threaded binary tree' over a traditional binary tree?

<p>One advantage of using a threaded binary tree over a traditional binary tree is the ability to traverse the tree more efficiently, especially when finding predecessors or successors of a node. This is because threads in a threaded binary tree enable upward movement in the tree, unlike a traditional binary tree, which is only capable of downward movement.</p> Signup and view all the answers

Explain one way to handle 'overflow' in a Hash Table.

<p>One effective method for handling overflow in a Hash Table is to resize the table. Increasing the table's size will create more memory space, allowing for more data storage and reducing the chances of collisions.</p> Signup and view all the answers

Given the expression: 3 + ((5+9)*2), what is the corresponding infix expression tree representation?

<p>The infix expression tree representation for the expression 3 + ((5+9)<em>2) would have a plus (+) operator as the root. Below the root, on the left, there would be a node containing the number 3. On the right, another plus (+) operator would be placed, acting as the parent node to the left and right sides. The left side would contain a multiplication (</em>) operator with '5' and '9' as its children. The final node on the right would be a '2' as the right child of the multiplication (*) operator.</p> Signup and view all the answers

Flashcards

Tree Data Structure

A finite set of nodes that shows parent-child relationships, with a designated root node and subtrees.

Root Node

The topmost node in a tree; it has no parent.

Child Node

A node that is directly connected to another node, called the parent.

Sibling Nodes

Nodes that share the same parent node.

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Ancestors

Nodes that lie on the path from a given node upwards towards the root.

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Descendants

Nodes that lie below a parent node, reachable by moving downwards.

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Left Descendants

Nodes in the left subtree of a given node.

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Right Descendants

Nodes in the right subtree of a given node.

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Left Subtree

All nodes that are left descendants of a given node.

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Right Subtree

All nodes that are right descendants of a given node.

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Parent Node

A node that has at least one child node.

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Degree of a Node

The number of subtrees of a node.

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Leaf Node

A node with no children.

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Internal Nodes

Nodes in a tree that are not leaf nodes.

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Binary Tree

A special kind of tree where each node has at most two children.

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Strictly Binary Tree (Full Binary Tree)

A binary tree where every node has exactly two children or none.

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Complete Binary Tree

A binary tree where every level, except possibly the last, is fully filled.

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Skewed Tree

A binary tree with only left or right subtrees.

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Expression Tree

A binary tree used to represent mathematical expressions; operators are internal nodes, operands are leaf nodes.

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Binary Search Tree (BST)

A binary tree that maintains sorted data. The left subtree has values less than the node; the right subtree has values greater.

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Linked Representation of a Tree

Storing a tree in memory using linked lists; each node contains pointers to its children.

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Array Representation of a Tree

Storing a tree in memory using an array; nodes are placed in specific array positions.

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Preorder Traversal (Root Left Right)

A traversal of a binary tree where the root is processed first, followed by the left subtree and then the right subtree.

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Postorder Traversal (Left Right Root)

A traversal of a binary tree where the left subtree is processed, followed by the right subtree and then the root.

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Inorder Traversal (Left Root Right)

A traversal of a binary tree where the left subtree is processed, followed by the root, and then the right subtree.

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Threaded Binary Tree

A binary tree that uses 'threads' to allow for efficient upward movement in the tree.

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Directed Graph (Digraph)

A graph where every edge has a direction, representing a one-way relationship.

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Undirected Graph

A graph where every edge is undirected, representing a two-way relationship.

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Self-Loop

An edge that starts and ends at the same vertex.

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Multigraph

A graph that allows multiple edges between the same pair of vertices.

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Complete Graph

A graph where there is an edge between every pair of vertices.

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Walk

A sequence of vertices and edges in a graph, representing a path through the graph.

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Simple Path

A walk where all vertices are distinct, except possibly the first and last.

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Length of a Path

The number of edges in a path.

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Euler Circuit

A path that starts and ends at the same vertex and visits every edge exactly once.

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Euler Path

A path that visits every edge of a graph exactly once, but starts and ends at different vertices.

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Hamiltonian Circuit

A circuit that visits every vertex exactly once, starting and ending at the same vertex.

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Hamiltonian Path

A path that visits every vertex exactly once, but does not need to start and end at the same vertex.

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Study Notes

Nonlinear Data Structures - Tree Data Structures

  • A tree is a finite set of one or more nodes that shows a parent-child relationship.
  • There's a designated node called the root.
  • Remaining nodes are partitioned into disjoint subsets (subtrees).
  • Subtrees are the children of the root node.

Terminology

  • Root Node: The topmost node in a tree, having no parent.
  • Child: A node directly connected to a parent node.
  • Siblings: Nodes sharing the same parent.
  • Ancestors: Nodes on the path from a specific node to the root.
  • Descendants: Nodes reachable from a specific node moving downward.
  • Left Subtree: All nodes to the left of a specified node.
  • Right Subtree: All nodes to the right of a specified node.
  • Parent: A node having a subtree/subtrees connected to it.
  • Degree: The number of subtrees a node has.
  • Leaf Node / Terminal Node: A node with a degree of zero, meaning no children.
  • Internal Node: A node with at least one child.

Binary Trees

  • A finite set of nodes that has a root node and two subtrees (left and right).
  • The left subtree contains values less than the root, and the right subtree contains values greater than the root.
  • A binary tree can be:
    • Empty
    • Consists of a root node with two subtrees (left and right)
  • Each node in a binary tree has at most two children.

Binary Tree Representation

  • Node: The data structure consists of three fields:
    • Ilink: Address of the left subtree
    • Info: Actual data or information to be manipulated
    • Rlink: Address of the right subtree

Binary Tree Traversals

  • Preorder: Visit root, traverse left subtree, traverse right subtree.
  • Postorder: Traverse left subtree, traverse right subtree, visit root.
  • Inorder: Traverse left subtree, visit root, traverse right subtree.

Types of Binary Trees

  • Strictly Binary Tree (Full Binary Tree): Every node has either zero or two children.
  • Complete Binary Tree: All levels except possibly the last are completely filled, and the last level is filled from left to right.
  • Skewed Tree: A tree consisting of only left or right subtrees.
  • Expression Tree: Internal nodes are operators; leaf nodes are operands.

Graph Theory

  • Vertex: A node in a graph.
  • Edge: A connection between two vertices.
  • Self-Loop: An edge from a vertex to itself.
  • Multigraph: A graph with multiple edges between two vertices.
  • Complete Graph: A graph with an edge between every pair of vertices.
  • Path: A sequence of vertices connected by edges.
  • Cycle (Circuit): A path in which the first and last vertices are the same.
  • Connected Graph: A graph where there is a path between every pair of vertices.
  • Disconnected Graph: A graph with multiple connected components.

Hashing

  • Used in data structures for efficient searching.
  • Time to search an element doesn't depend on total number of elements.
  • Hash table stores data.
  • Hash function converts keys into indices within the hash table.
  • Collision occurs when two or more keys produce the same hash address.
  • Techniques for collision avoidance include open hashing (chaining) and closed hashing (probing).
  • Overflow handling addresses issues when the hash table is full or the collision handling structure is too large.

Practice: Algorithms & Functions based on Trees/graphs operations

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Trees PPT PDF

Description

Explore the fundamentals of tree data structures, including key terminology and relationships among nodes. Learn about concepts like root nodes, child nodes, and the various types of subtrees that exist in a tree framework. This quiz will deepen your understanding of how trees function within nonlinear data structures.

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