Binary Trees and Heaps Quiz
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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</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.</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.</p> Signup and view all the answers

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

    <p>Chaining</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.</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.</p> Signup and view all the answers

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

    <p>Sequential search</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.</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.</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.</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.</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.</p> Signup and view all the answers

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

    <p>Queue management</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.</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.</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.</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.</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.</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.</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.</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.</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.</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.</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.</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.</p> Signup and view all the answers

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

    <p>Preorder traversal</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.</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</p> Signup and view all the answers

    Which statement is accurate regarding tree traversals?

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

    Which sorting algorithm is most suitable for partially sorted datasets?

    <p>Insertion Sort</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.</p> Signup and view all the answers

    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.

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    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!

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