Binary Trees and Heaps Quiz
42 Questions
1 Views

Choose a study mode

Play Quiz
Study Flashcards
Spaced Repetition
Chat to Lesson

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

What is the time complexity for operations in a complete binary tree?

  • O(N)
  • O(1)
  • O(N logN)
  • O(logN) (correct)

When a node with two children needs to be deleted, what is the appropriate step to take?

  • Replace it with the inorder successor and delete the successor. (correct)
  • Delete the node directly without making any changes.
  • Replace it with the inorder predecessor and delete the predecessor.
  • Move it to a leaf position before deletion.

What does the 'up_heapify()' operation ensure in a heap?

  • That the max or min property of the heap is maintained. (correct)
  • That all nodes are sorted in ascending order.
  • That the inserted node becomes the root of the heap.
  • That the heap maintains a complete binary tree structure.

In a max-heap, which operation is performed to find the maximum item?

<p>Find-max (B)</p> Signup and view all the answers

What happens during the deletion of a node in a binary tree if it has only one child?

<p>The node is replaced by its child. (C)</p> Signup and view all the answers

What is one characteristic of logical-physical independence in file structure?

<p>Key values maintain their integrity despite changes to the directory address entries. (C)</p> Signup and view all the answers

Which hashing scheme primarily deals with collisions by using separate data structures for overflow?

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

What is the load factor in a hashing scheme defined as?

<p>The ratio of the number of key values to the number of available slots. (A)</p> Signup and view all the answers

What is the primary distinction between an adjacency matrix and an adjacency list in graph representation?

<p>An adjacency matrix explicitly shows the edges using a grid format. (A)</p> Signup and view all the answers

Which method is NOT a common collision handling scheme in hashing?

<p>Sequential search (D)</p> Signup and view all the answers

In graph theory, what defines two nodes as adjacent?

<p>They are connected by a direct edge without intermediaries. (A)</p> Signup and view all the answers

Which of the following is a characteristic of absolute addresses?

<p>They depend on the device and address space for values. (D)</p> Signup and view all the answers

What is the order of operations when performing a Depth First Search (DFS) on a graph?

<p>Visit the node, push adjacent nodes, pop another node, repeat. (A)</p> Signup and view all the answers

What is the significance of folding in hashing?

<p>It involves combining parts of the key values to create a new hash code. (C)</p> Signup and view all the answers

Which of the following statements is true about graph traversal methods?

<p>DFS explores all neighboring nodes before visiting the next level. (A)</p> Signup and view all the answers

Which of the following is not an approach to collision resolution in hashing?

<p>Queue management (C)</p> Signup and view all the answers

What is a crucial factor when selecting an appropriate file organization method in hashing?

<p>The frequency of collisions in the hashing process. (D)</p> Signup and view all the answers

What basis does the 'Prime-Number Division Remainder' hashing method rely on?

<p>Dividing the key value by a prime number to obtain a remainder. (B)</p> Signup and view all the answers

Which of these techniques is primarily addressed by the concept of 'bucket addressing' in hashing?

<p>Reducing collision through subdivided storage units. (D)</p> Signup and view all the answers

What does it mean if a graph is represented as undirected?

<p>Edges can be traversed in both directions without any constraints. (C)</p> Signup and view all the answers

What is the complexity of searching for a value in an optimal hashing structure?

<p>O(1) in average cases under ideal conditions. (C)</p> Signup and view all the answers

In a graph represented by a vertex list, what happens to the representation if an edge is added between two non-adjacent vertices?

<p>The adjacency list representing each vertex must also be modified. (C)</p> Signup and view all the answers

What is the primary purpose of the down_heapify() operation in a heap?

<p>To maintain heap structure when the last element is placed in a position. (A)</p> Signup and view all the answers

Which statement correctly describes a binary tree?

<p>Each node in a binary tree can have up to two children. (B)</p> Signup and view all the answers

What is an advantage of a binary search tree (BST) over a binary tree?

<p>A BST maintains a sorted order of elements. (A)</p> Signup and view all the answers

Which of the following accurately defines a Min Heap?

<p>The parent node is the smallest element in the heap. (D)</p> Signup and view all the answers

How can one verify if a given binary tree is a binary search tree?

<p>Ensure that for every node, values in the left subtree are greater and right subtree are lesser. (D)</p> Signup and view all the answers

What does the height of a tree represent?

<p>The number of edges in the longest path from root to leaf. (D)</p> Signup and view all the answers

Which traversal method visits nodes in the order of Root, Left, Right?

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

What differentiates a Max Heap from a Min Heap?

<p>Max Heap has the parent node as the largest element and Min Heap has the smallest. (D)</p> Signup and view all the answers

What notation is commonly used to represent the process of inserting an element into a heap?

<p>Sift-Up (D)</p> Signup and view all the answers

Which statement is accurate regarding tree traversals?

<p>Different tree traversals can yield different node visit orders. (C)</p> Signup and view all the answers

What is the primary significance of maintaining a balanced tree height?

<p>To ensure logarithmic time complexity for search operations (C)</p> Signup and view all the answers

Which of the following statements accurately distinguishes a B-tree from an AVL tree?

<p>A B-tree can have multiple keys per node, while an AVL tree has only one key. (C)</p> Signup and view all the answers

In a directed graph, what does it indicate if an edge points from node A to node B?

<p>Node A influences node B only. (A)</p> Signup and view all the answers

Which of the following best describes a cyclic graph?

<p>A graph that contains a path starting and ending at the same vertex. (D)</p> Signup and view all the answers

What is the defining characteristic of a weighted graph?

<p>Each edge has an associated weight or cost. (C)</p> Signup and view all the answers

What does it mean for a graph to be acyclic?

<p>There are no paths returning to a starting vertex. (C)</p> Signup and view all the answers

Which of the following accurately describes the properties of nodes in a graph?

<p>Nodes are the entities connected by edges in the graph. (D)</p> Signup and view all the answers

What is one primary use of a hash map in computer science?

<p>To efficiently perform key-value pair lookups. (D)</p> Signup and view all the answers

Which sorting algorithm is most suitable for partially sorted datasets?

<p>Insertion Sort (D)</p> Signup and view all the answers

What is the result of deleting an edge in a directed graph?

<p>The specific relationship represented by that edge is lost. (D)</p> Signup and view all the answers

Flashcards

What is a graph?

A graph is a data structure that represents a set of objects (vertices or nodes) connected by links (edges or arcs).

How are graphs similar to trees? How are they different?

Both graphs and trees are hierarchical data structures, but trees have a single root node and a directed path from the root to all other nodes. Graphs, on the other hand, can have multiple starting points and can have cycles.

If two graph nodes are connected by an edge, what are they called?

Nodes that are connected by an edge are called adjacent nodes.

How can you tell if two graph nodes are adjacent?

Two nodes are adjacent if there is an edge connecting them directly. This can be checked in an adjacency matrix (where '1' represents an edge) or an adjacency list (which lists the neighbors of each node).

Signup and view all the flashcards

Load Factor

It indicates how efficiently the hash function maps keys to addresses. A higher load factor implies a higher risk of collisions.

Signup and view all the flashcards

Hash Function

A hash function is a mathematical function that takes a key as input and generates a unique index value, known as the hash value, which is used to identify the location of the corresponding record in a hash table.

Signup and view all the flashcards

Collision

The hash function maps different keys to the same address, leading to a potential conflict in the hash table.

Signup and view all the flashcards

What is a Collision?

A collision is a situation where two or more keys are mapped to the same address by the hash function.

Signup and view all the flashcards

Open Addressing

Open addressing is a collision resolution technique where, if a collision occurs, the algorithm searches for the next available address in the hash table to store the colliding key.

Signup and view all the flashcards

Separate Chaining

Separate Chaining is a collision resolution technique where, when a collision occurs, the algorithm creates a linked list at the colliding address to store all the colliding keys.

Signup and view all the flashcards

Linear Probing

Linear probing is a type of open addressing where the algorithm checks consecutive addresses in the hash table for an empty spot, starting from the original address.

Signup and view all the flashcards

Double Hashing

Double hashing is a type of open addressing where the algorithm uses a second hash function to calculate the step size for probing the hash table for an empty address.

Signup and view all the flashcards

Synonym Chaining

Synonym chaining is a type of separate chaining where each address in the hash table points to a linked list, and each list element stores a key and its corresponding data.

Signup and view all the flashcards

Bucket Addressing

Bucket addressing is a method to address collisions where multiple key values are mapped to the same bucket. Each bucket is essentially a small hash table.

Signup and view all the flashcards

What is a directed graph?

A graph where edges have a direction; they point from one node to another, representing a one-way relationship.

Signup and view all the flashcards

What is an undirected graph?

A graph where edges have no direction; they connect two nodes in both directions, representing a two-way relationship.

Signup and view all the flashcards

What is a weighted graph?

Each edge in a weighted graph is assigned a weight or cost, often representing a distance, time, or cost associated with that connection.

Signup and view all the flashcards

What is a cyclic graph?

A graph is cyclic when it contains a path starting and ending at the same vertex, forming a closed loop.

Signup and view all the flashcards

What is an acyclic graph?

A graph is acyclic when it doesn't contain any cycles; there are no paths that start and end at the same vertex.

Signup and view all the flashcards

What causes a node to be isolated?

A node in a graph is considered isolated if it has no edges connected to it; it's not connected to any other node.

Signup and view all the flashcards

What is a connected graph?

A graph is considered connected when there is a path between every pair of nodes in the graph.

Signup and view all the flashcards

What is a disconnected graph?

A graph is considered disconnected when there is at least one pair of nodes that cannot be reached by following the edges.

Signup and view all the flashcards

What is a complete graph?

A graph is called a complete graph when there is an edge connecting every pair of distinct nodes in the graph.

Signup and view all the flashcards

Heapify

The process of rearranging a heap to maintain the heap property.

Signup and view all the flashcards

Find-max/Find-min

Finding the maximum or minimum value in a heap.

Signup and view all the flashcards

Insertion

Adding a new element to the heap.

Signup and view all the flashcards

Deletion

Removing an element from the heap.

Signup and view all the flashcards

Extract Min-Max

Returning and deleting the largest or smallest value in a heap.

Signup and view all the flashcards

What is a tree?

A tree is a hierarchical data structure that consists of nodes connected by edges. It has a single root node and branches out to other nodes.

Signup and view all the flashcards

What is a binary tree?

A binary tree is a specific type of tree where each node can have a maximum of two children: a left child and a right child.

Signup and view all the flashcards

What is an advantage of a BST?

A binary search tree (BST) allows for efficient searching because its nodes are arranged in a way that maintains a sorted order. Values in the left subtree are smaller than the root node, and values in the right subtree are larger.

Signup and view all the flashcards

How to check if a tree is a BST?

To check if a binary tree is a BST, we need to ensure that for each node, all values in its left subtree are smaller than its own value, and all values in its right subtree are larger. We can use traversal methods to check this.

Signup and view all the flashcards

What is a heap?

A heap is a binary tree-based data structure that follows a specific ordering property based on the heap type (min-heap or max-heap). In a min-heap, the parent node is always smaller than its children, while in a max-heap, the parent node is always larger than its children.

Signup and view all the flashcards

What is the difference between a Max Heap and a Min Heap?

A Max Heap is a type of heap where the largest value is always at the root node. In a Min Heap, the smallest value is always at the root node.

Signup and view all the flashcards

What is the root node?

The root of the tree is the node at the top, which has no parent.

Signup and view all the flashcards

What are the internal nodes?

Internal nodes are any nodes that have at least one child.

Signup and view all the flashcards

How many descendants does a node have?

Descendants of a node are all the nodes that can be reached by traversing down from that node.

Signup and view all the flashcards

How many ancestors does a node have?

Ancestors of a node are all the nodes that are on the path from the node to the root.

Signup and view all the flashcards

Study Notes

Unit 7 - Trees

  • Data structures like stacks and queues are linear, stored sequentially or in linked lists.
  • Trees and binary trees are non-linear structures.
  • A tree is a nonlinear data structure consisting of nodes and edges.
  • Properties of a tree:
    • There is a designated root node.
    • Remaining nodes are partitioned into subsets (subtrees) under the root.
  • Nonterminal vertices have successors, while terminal vertices (leaves) have none.
  • N-ary trees have non-terminal vertices with at most n successors.
  • Binary trees are n-ary trees with non-terminal vertices having at most 2 successors.
  • Trees can be represented using parentheses, nesting, or indentation.

Module Objectives

  • Students should be able to discuss the characteristics of trees and binary trees.
  • Understand various tree representations.
  • Distinguish between trees and binary trees.
  • Demonstrate the conversion between trees and binary trees.
  • Discuss searching using a binary tree.
  • Implement tree and binary tree applications.

Tree Vocabulary

  • Node: A component of the tree holding data.
  • Edge/Branch: The connection between parent and child nodes (may have a weight).
  • Root: The top element of the hierarchical structure.
  • Child: A node's immediate successor (may have zero or more successors).
  • Parent: A node's predecessor (each node has exactly one parent).
  • Leaf/Terminal: A node with no children.
  • Descendant: An extension of the child relationship (a node is a descendant of its ancestor).
  • Ancestor: An extension of the parent relationship (a parent is an ancestor to its child).
  • Sibling: Child nodes with the same parent.
  • Internal Node/Non-terminal: A node with at least one child.
  • Path: The sequence of edges between a node and one of its descendants.
  • Path Length: The number of edges in a path.
  • Depth/Level: The length of the path from the root.
  • Height: The longest path length from a node to the deepest leaf.
  • Subtree: A tree made from descendants of a node.
  • Degree of a Node: Number of subtrees.
  • Degree of a Tree: Maximum degree of nodes in the tree.
  • Forest: A set of disjoint trees.

Tree Traversals

  • Depth-First Search (DFS): Explores a path completely before backtracking. Uses a stack.
  • Breadth-First Search (BFS): Explores all nearest possibilities first, before moving to more distant nodes. Uses a queue.

Binary Tree

  • A binary tree is a finite set of nodes or is empty.
  • A binary tree contains at most two disjoint binary trees as subtrees of the root node.
  • A binary tree may be empty, but a tree must have at least one node.

Types of Binary Trees

  • Rooted binary tree: Has a root node and every node has a maximum of two children.
  • Full binary tree: Nodes have either 0 or 2 children.
  • Perfect binary tree: All interior nodes have 2 children, and all leaves have same depth.
  • Complete binary tree: All levels are completely filled except possibly the last level where nodes are as far left as possible.

Balanced Binary Tree

  • A binary tree is balanced if the heights of the left and right subtrees of any node differ by at most one.
  • A balanced tree has a height of O(log n) where n represents the number of nodes.
  • Degenerate tree -- A tree that behaves like a linked list, where each node only has one child.

Tree Traversals

  • Preorder: Root → Left → Right
  • Inorder: Left → Root → Right
  • Postorder: Left → Right → Root

Expression Trees

  • Used for representing expressions in a tree-like structure.
  • Leaves represent operands; nodes contain operators.
  • Inorder traversal generates infix expressions
  • Preorder traversal generates prefix expressions
  • Postorder traversal generates postfix expressions

Binary Search Tree (BST)

  • A binary tree where nodes are arranged in order:
  • Left subtree contains values less-than-or-equal to the node.
  • Right subtree contains values greater than the node.

Heap Tree

  • A complete binary tree with an ordering property: value in any node is smaller (min-heap) or larger (max-heap) than all values in its subtrees.

  • The smallest/largest value is always at the root.

  • All levels are completely filled except perhaps the bottom level, which is full from left to right.

Heap Operations

  • Heapify: Rearranges the heap to maintain its heap property.
  • Find-max/min: Finds the maximum/minimum element.
  • Insertion: Adds a new element.
  • Deletion: Removes an element.
  • Extract Min/Max: Returns and removes the minimum/maximum element, respectively

B-Trees

  • A balanced m-way search tree used for disk-based storage.
  • Every node (except the root) contains at least M/2 and at most M-1 values.
  • All leaves are at the same depth (perfectly balanced).

Graph Traversal

  • Methods for visiting every vertex and edge exactly once.
  • Breadth-first search (BFS): Visits vertices level-by-level, starting from a source vertex.
  • Depth-first search (DFS): Visits vertices by following paths as far as possible before backtracking.

Studying That Suits You

Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

Quiz Team

Related Documents

DSA Unit 7 - Trees PDF

Description

Test your understanding of binary trees and heaps with this quiz. Questions cover time complexity, deletion operations, heap properties, and more. Perfect for students of data structures!

More Like This

Binary Trees Quiz
3 questions

Binary Trees Quiz

BetterKnownIvory avatar
BetterKnownIvory
Binary Trees and Search Trees Quiz
10 questions

Binary Search Tree Quiz: Test Your Knowledge with Our Binary Tree Quiz

LustrousNephrite3669 avatar
LustrousNephrite3669
Heaps and Binary Trees Quiz
10 questions

Heaps and Binary Trees Quiz

ColorfulSanctuary avatar
ColorfulSanctuary
Data Structures: Heaps and Linked Lists
48 questions

Data Structures: Heaps and Linked Lists

StylishSpessartine avatar
StylishSpessartine
Use Quizgecko on...
Browser
Open
Browser
Browser