Binary Tree Quiz: Master Degenerate Binary Trees

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Questions and Answers

What is the key property of a binary search tree?

Value at node is smaller in the right subtree and larger in the left subtree (correct)

Each node can have at most one parent

Nodes can have 0 or more children

Nodes can have at most two children

What is the time complexity of searching in a balanced binary tree with n nodes?

$O(n)$ time

$O(\log(n))$ time (correct)

$O(1)$ time

$O(n\log(n))$ time

What is the height of a degenerate binary tree with n nodes?

Height = $O(n\log(n))$

Height = $O(1)$

Height = $O(\log(n))$

Height = $O(n)$ (correct)

What is the terminology used for a node with no child?

Leaf Signup and view all the answers

What is the terminology used for a node with no parent?

Root Signup and view all the answers

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

2 Signup and view all the answers

What is the time complexity of searching in a degenerate binary tree with n nodes?

$O(n)$ time Signup and view all the answers

What type of binary tree is useful for searches due to its $O(\log(n))$ time complexity?

Balanced binary tree Signup and view all the answers

What is the time complexity for insertion in a balanced binary search tree?

$O(\log n)$ Signup and view all the answers

When performing deletion in a binary search tree, what is the time complexity for a balanced tree?

$O(\log n)$ Signup and view all the answers

What is the purpose of tree rotations in maintaining balance in a binary search tree?

To maintain or restore the balance of the tree Signup and view all the answers

What is the purpose of a heap in data structures?

To implement priority queues Signup and view all the answers

What is the time complexity for removing the minimum element from a heap?

$O(\log n)$ Signup and view all the answers

What is the height of a heap storing $n$ keys?

$O(\log n)$ Signup and view all the answers

Which type of tree is a generalization of 2/3 trees?

B-tree Signup and view all the answers

What is the purpose of parse trees in computer science?

To represent hierarchical data Signup and view all the answers

In which traversal method is the root visited before the subtrees?

Pre-order traversal Signup and view all the answers

What is the goal of tree traversal in data structures?

To visit every node of the tree Signup and view all the answers

What algorithm is used for building a heap in data structures?

Floyd’s Method Signup and view all the answers

What is the maximum number of children a node can have in a binary tree?

2 Signup and view all the answers

What is the time complexity of searching in a degenerate binary tree with $n$ nodes?

$O(n)$ Signup and view all the answers

In a binary search tree, what property is maintained where the value at each node is smaller in the left subtree and larger in the right subtree?

Binary property Signup and view all the answers

What is the height of a degenerate binary tree with $n$ nodes?

$O(n)$ Signup and view all the answers

What is the time complexity for insertion in a balanced binary search tree?

$O(\log(n))$ Signup and view all the answers

What is the terminology used for a node with no child in a tree?

Leaf Signup and view all the answers

What is the time complexity of searching in a balanced binary tree with $n$ nodes?

$O(\log(n))$ Signup and view all the answers

What type of binary tree has a height of $O(\log(n))$ for $n$ nodes?

Balanced binary tree Signup and view all the answers

What is the time complexity of insertion in a balanced binary search tree?

O(log(n)) Signup and view all the answers

What is the terminology used for a node with no parent?

Root Signup and view all the answers

What is the height of a degenerate binary tree with n nodes?

$n$ Signup and view all the answers

What is the time complexity of searching in a degenerate binary tree with n nodes?

O(n) Signup and view all the answers

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

2 Signup and view all the answers

What is the height of a heap storing $n$ keys?

$O(log(n))$ Signup and view all the answers

What is a key property (invariant) that is maintained in a binary search tree?

Smaller values in left subtree, larger values in right subtree Signup and view all the answers

What is the goal of tree traversal in data structures?

Visit every node of a tree Signup and view all the answers

What type of binary tree is useful for searches due to its $O(log(n))$ time complexity?

Balanced binary search tree Signup and view all the answers

What is the purpose of parse trees in computer science?

Represent textual programs as tree structures Signup and view all the answers

What is the key property of a binary search tree?

Maintains ordering of elements Signup and view all the answers

In a binary search tree, what is the time complexity of searching in a degenerate binary tree with $n$ nodes?

$O(n)$ Signup and view all the answers

What is the maximum number of children a node can have in a binary tree?

Unlimited Signup and view all the answers

What is the key property of a binary search tree?

Value at each node is smaller in the left subtree and larger in the right subtree Signup and view all the answers

What is the height of a degenerate binary tree with $n$ nodes?

$O(n)$ Signup and view all the answers

What is the time complexity of searching in a balanced binary tree with $n$ nodes?

$O( ext{log}(n))$ Signup and view all the answers

What is the time complexity for insertion in a balanced binary search tree?

$O( ext{log}(n))$ Signup and view all the answers

What type of binary tree has a height of $O( ext{log}(n))$ for $n$ nodes?

Balanced binary tree Signup and view all the answers

What is the time complexity of inserting a new value into a balanced binary search tree?

$O(\log(n))$ Signup and view all the answers

In a binary search tree, what is the time complexity of searching in a degenerate tree with $n$ nodes?

$O(n)$ Signup and view all the answers

What is the key property (invariant) maintained in a binary search tree?

Smaller values in the left subtree, larger values in the right subtree Signup and view all the answers

What is the goal of tree traversal in data structures?

Visit every node of a tree Signup and view all the answers

What is the time complexity for removing the minimum element from a heap?

$O(\log(n))$ Signup and view all the answers

Which type of tree is a generalization of 2/3 trees?

B-trees Signup and view all the answers

What is the terminology used for a node with no child in a tree?

Leaf node Signup and view all the answers

What algorithm is used for building a heap in data structures?

Floyd’s Method Signup and view all the answers

What is the primary goal of sorting?

To arrange elements in ascending or descending order Signup and view all the answers

Which sorting algorithm is the simplest?

Bubble Sort Signup and view all the answers

What is the time complexity of bubble sort in the worst case?

$O(n^2)$ Signup and view all the answers

In bubble sort, what happens if E1 is greater than E2?

They are swapped Signup and view all the answers

What is the primary advantage of merge sort over bubble sort?

Merge sort has a better time complexity Signup and view all the answers

Which sorting algorithm involves 'bubbling up' and 'counting down'?

Bubble Sort Signup and view all the answers

What is the primary disadvantage of bubble sort?

Inefficient for large datasets Signup and view all the answers

What is the time complexity of bubble sort?

O($n^2$) Signup and view all the answers

What is the time complexity of selection sort?

O($n^2$) Signup and view all the answers

In the analysis of bubble sort, how many times does the inner loop execute on average for each execution of the outer loop?

About $n/2$ times Signup and view all the answers

How many times does the outer loop execute in the selection sort algorithm?

$n-1$ times Signup and view all the answers

What is the work done in the inner loop of the selection sort algorithm?

Constant (swap two array elements) Signup and view all the answers

What is the purpose of the outer loop in the selection sort algorithm?

To iterate through the array and select the smallest element Signup and view all the answers

What is the purpose of the inner loop in the bubble sort algorithm?

To compare adjacent elements in the array Signup and view all the answers

What is the time complexity of the algorithm to remove the minimum element from a heap?

O(log$n$) Signup and view all the answers

Study Notes

Binary Search Tree Properties

A binary search tree maintains the property that the value at each node is smaller in the left subtree and larger in the right subtree.
The time complexity of searching in a balanced binary tree with n nodes is O(log(n)).
The time complexity of searching in a degenerate binary tree with n nodes is O(n).

Tree Terminology

A node with no child is called a leaf node.
A node with no parent is called the root node.

Binary Tree Properties

The maximum number of children a node can have in a binary tree is 2.
The height of a degenerate binary tree with n nodes is n-1.

Heap Properties

The time complexity for removing the minimum element from a heap is O(log(n)).
The height of a heap storing n keys is O(log(n)).
The purpose of a heap in data structures is to provide efficient sorting and priority queue operations.

Tree Traversal

The purpose of tree traversal is to visit nodes in a specific order.
The goal of tree traversal is to access or modify nodes in the tree.
The pre-order traversal method visits the root node before the subtrees.

Binary Search Tree Operations

The time complexity for insertion in a balanced binary search tree is O(log(n)).
The time complexity for deletion in a balanced binary search tree is O(log(n)).
Tree rotations are used to maintain balance in a binary search tree.

Other Data Structures

Parse trees are used in computer science to represent the syntactic structure of source code.
B-Tree is a generalization of 2/3 trees.
Heapsort is an algorithm used for building a heap in data structures.

Sorting Algorithms

The primary goal of sorting is to arrange elements in a specific order.
Bubble sort is the simplest sorting algorithm.
The time complexity of bubble sort is O(n^2) in the worst case.
The primary advantage of merge sort over bubble sort is its efficiency.
The primary disadvantage of bubble sort is its slow performance.
Selection sort involves finding the minimum element and swapping it with the first element.

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Description

Test your knowledge of tree data structures with this quiz. Explore concepts such as nodes, children, binary trees, terminology, and binary search trees. This quiz covers fundamental aspects of trees in computer science and data structures.

Tree Data Structures Quiz

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Podcast

Questions and Answers

What is the key property of a binary search tree?

What is the time complexity of searching in a balanced binary tree with n nodes?

What is the height of a degenerate binary tree with n nodes?

What is the terminology used for a node with no child?

What is the terminology used for a node with no parent?

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

What is the time complexity of searching in a degenerate binary tree with n nodes?

What type of binary tree is useful for searches due to its $O(\log(n))$ time complexity?

What is the time complexity for insertion in a balanced binary search tree?

When performing deletion in a binary search tree, what is the time complexity for a balanced tree?

What is the purpose of tree rotations in maintaining balance in a binary search tree?

What is the purpose of a heap in data structures?

What is the time complexity for removing the minimum element from a heap?

What is the height of a heap storing $n$ keys?

Which type of tree is a generalization of 2/3 trees?

What is the purpose of parse trees in computer science?

In which traversal method is the root visited before the subtrees?

What is the goal of tree traversal in data structures?

What algorithm is used for building a heap in data structures?

What is the maximum number of children a node can have in a binary tree?

What is the time complexity of searching in a degenerate binary tree with $n$ nodes?

In a binary search tree, what property is maintained where the value at each node is smaller in the left subtree and larger in the right subtree?

What is the height of a degenerate binary tree with $n$ nodes?

What is the time complexity for insertion in a balanced binary search tree?

What is the terminology used for a node with no child in a tree?

What is the time complexity of searching in a balanced binary tree with $n$ nodes?

What type of binary tree has a height of $O(\log(n))$ for $n$ nodes?

What is the time complexity of insertion in a balanced binary search tree?

What is the terminology used for a node with no parent?

What is the height of a degenerate binary tree with n nodes?

What is the time complexity of searching in a degenerate binary tree with n nodes?

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

What is the height of a heap storing $n$ keys?

What is a key property (invariant) that is maintained in a binary search tree?

What is the goal of tree traversal in data structures?

What type of binary tree is useful for searches due to its $O(log(n))$ time complexity?

What is the purpose of parse trees in computer science?

What is the key property of a binary search tree?

In a binary search tree, what is the time complexity of searching in a degenerate binary tree with $n$ nodes?

What is the maximum number of children a node can have in a binary tree?

What is the key property of a binary search tree?

What is the height of a degenerate binary tree with $n$ nodes?

What is the time complexity of searching in a balanced binary tree with $n$ nodes?

What is the time complexity for insertion in a balanced binary search tree?

What type of binary tree has a height of $O( ext{log}(n))$ for $n$ nodes?

What is the time complexity of inserting a new value into a balanced binary search tree?

In a binary search tree, what is the time complexity of searching in a degenerate tree with $n$ nodes?

What is the key property (invariant) maintained in a binary search tree?

What is the goal of tree traversal in data structures?

What is the time complexity for removing the minimum element from a heap?

Which type of tree is a generalization of 2/3 trees?

What is the terminology used for a node with no child in a tree?

What algorithm is used for building a heap in data structures?

What is the primary goal of sorting?

Which sorting algorithm is the simplest?

What is the time complexity of bubble sort in the worst case?

In bubble sort, what happens if E1 is greater than E2?

What is the primary advantage of merge sort over bubble sort?

Which sorting algorithm involves 'bubbling up' and 'counting down'?

What is the primary disadvantage of bubble sort?

What is the time complexity of bubble sort?

What is the time complexity of selection sort?

In the analysis of bubble sort, how many times does the inner loop execute on average for each execution of the outer loop?

How many times does the outer loop execute in the selection sort algorithm?

What is the work done in the inner loop of the selection sort algorithm?

What is the purpose of the outer loop in the selection sort algorithm?

What is the purpose of the inner loop in the bubble sort algorithm?

What is the time complexity of the algorithm to remove the minimum element from a heap?

Study Notes

Binary Search Tree Properties

Tree Terminology

Binary Tree Properties

Heap Properties

Tree Traversal

Binary Search Tree Operations

Other Data Structures