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13 Questions

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Binary Trees Overview

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Questions and Answers

What is the main advantage of heaps compared to Binary Search Trees (BSTs)?

Predictable structure and easy insertion and deletion (correct)

Easier traversal of elements

Higher performance in searching

Greater flexibility in data types

Which operation is fundamentally improved by employing heap properties?

Finding the minimum element

Searching for an element

Sorting an array (correct)

Merging two heaps

How can you determine the index of the left child of a node in a heap represented as an array?

2i + 1 (correct)

(i + 1) / 2

i - 1

What is the purpose of the heapify operation?

To build a heap from an unsorted array Signup and view all the answers

What is the time complexity of extracting the maximum element from a MaxHeap?

O(log n) Signup and view all the answers

What is the definition of the degree of a node in a tree?

The number of children nodes of that node Signup and view all the answers

Which traversal order is used to print the leaves of a binary tree first?

Postorder Signup and view all the answers

What is the correct time complexity for searching for an element in a balanced Binary Search Tree (BST)?

O(log n) Signup and view all the answers

In a binary tree, what is the height of an empty tree defined as?

-1 Signup and view all the answers

Which of these statements about heaps is NOT true?

Heaps are ordered structures Signup and view all the answers

What operation is crucial for insertion in a pointer-based implementation of a Binary Search Tree?

Recursively comparing the key to find correct position Signup and view all the answers

Which type of tree is used for Huffman coding?

Binary tree Signup and view all the answers

When deleting a node with two children in a Binary Search Tree, what is the recommended approach?

Replace it with its inorder successor or predecessor Signup and view all the answers

Study Notes

Binary Trees

A binary tree is a tree where each node can have a maximum of two children.
The height of an empty binary tree is -1.
The degree of a node is the number of its children.
Binary trees are not used for storing relational data.
Huffman coding uses a binary tree.
Decision trees are used for machine learning.
Finding the height of a general tree can be done through iterative or recursive traversal.
Counting the nodes in a general tree can be done using any traversal method.
"Left, Root, Right" traversal order is called inorder.
Deleting a node involves replacing it with its inorder successor or predecessor.
Postorder traversal prints the leaves first.
Binary tree node components include data and left/right child pointers.
Inserting an element into a binary tree has a time complexity of O(n).
In a binary search tree (BST), the left subtree contains nodes with smaller keys than the root and the right subtree contains nodes with larger keys than the root.
Database indexing is a real-world BST application.
Searching in a balanced BST has a time complexity of O(log n).
Inorder traversal produces a sorted sequence of elements in a BST.

Heaps

Heaps are unordered.
BSTs are ordered.
Heaps are complete binary trees.
Heaps always have a complete structure, unlike BSTs which can be unbalanced.
Percolate up is used to restore the heap property after an insertion.
Extracting the maximum element from a MaxHeap has a time complexity of O(log n).
In MinHeaps, the root has the smallest value, and all leaf nodes have larger values.
The parent of a node (i) in a heap array is calculated as (i - 1) / 2.
Sorting an array can use heap properties for optimization.
A heap can be represented as a complete binary tree.
The minimum number of nodes in a heap of height h is 2^(h-1) .
Heaps provide predictable structure and easy insertion/deletion compared to BSTs.
Heapify builds a heap from an array.
Removing the largest element from a MaxHeap involves removing the root and reheapifying.
Inserting a new element is more efficient in a heap compared to an array.
The heap property ensures the smallest element is at the root of a MinHeap.
A heap in an array uses compact storage without pointers.
Building a heap from an unsorted array has a time complexity of O(n).

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Description

This quiz covers the fundamental concepts of binary trees, including their structure, traversal methods, and applications in areas like Huffman coding and machine learning. Test your understanding of key definitions and operations related to binary trees.