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Questions and Answers
What is the key property of a binary search tree?
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?
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?
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?
What is the terminology used for a node with no child?
What is the terminology used for a node with no parent?
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?
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 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 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?
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?
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 tree rotations in maintaining balance in a binary search tree?
What is the purpose of a heap in data structures?
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 time complexity for removing the minimum element from a heap?
What is the height of a heap storing $n$ keys?
What is the height of a heap storing $n$ keys?
Which type of tree is a generalization of 2/3 trees?
Which type of tree is a generalization of 2/3 trees?
What is the purpose of parse trees in computer science?
What is the purpose of parse trees in computer science?
In which traversal method is the root visited before the subtrees?
In which traversal method is the root visited before the subtrees?
What is the goal of tree traversal in data structures?
What is the goal of tree traversal in data structures?
What algorithm is used for building a heap 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 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?
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?
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 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 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 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 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 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 time complexity of insertion in a balanced binary search tree?
What is the terminology used for a node with no parent?
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 height of a degenerate binary tree with n nodes?
What is the time complexity of searching in 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?
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 the height of a heap storing $n$ keys?
What is a key property (invariant) that is maintained in a binary search tree?
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 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 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 purpose of parse trees in computer science?
What is the key property of a binary search tree?
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?
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 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 key property of a binary search tree?
What is the height of a degenerate binary tree with $n$ nodes?
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 of searching in a balanced binary tree with $n$ nodes?
What is the time complexity for insertion in a balanced binary search tree?
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 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?
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?
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 key property (invariant) maintained in a binary search tree?
What is the goal of tree traversal in data structures?
What is the goal of tree traversal in data structures?
What is the time complexity for removing the minimum element from a heap?
What is the time complexity for removing the minimum element from a heap?
Which type of tree is a generalization of 2/3 trees?
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 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 algorithm is used for building a heap in data structures?
What is the primary goal of sorting?
What is the primary goal of sorting?
Which sorting algorithm is the simplest?
Which sorting algorithm is the simplest?
What is the time complexity of bubble sort in the worst case?
What is the time complexity of bubble sort in the worst case?
In bubble sort, what happens if E1 is greater than E2?
In bubble sort, what happens if E1 is greater than E2?
What is the primary advantage of merge sort over bubble sort?
What is the primary advantage of merge sort over bubble sort?
Which sorting algorithm involves 'bubbling up' and 'counting down'?
Which sorting algorithm involves 'bubbling up' and 'counting down'?
What is the primary disadvantage of bubble sort?
What is the primary disadvantage of bubble sort?
What is the time complexity of bubble sort?
What is the time complexity of bubble sort?
What is the time complexity of selection 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?
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?
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 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 outer loop in the selection sort algorithm?
What is the purpose of the inner loop in the bubble 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?
What is the time complexity of the algorithm to remove the minimum element from a heap?
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.
