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Questions and Answers
What is the first step when inserting a new key in a binary search tree (BST)?
What is the first step when inserting a new key in a binary search tree (BST)?
- Insert the new node at the root node.
- Start searching from the root until a leaf node is found. (correct)
- Always add the new node as a right child.
- Start searching from the rightmost node.
When removing a node with two children from a BST, what is the appropriate action according to the algorithm?
When removing a node with two children from a BST, what is the appropriate action according to the algorithm?
- Link the child directly to the surrounding nodes.
- Remove the node and shift the remaining nodes to the left.
- Copy the contents of the inorder successor to the node being removed. (correct)
- Delete the node and replace it with the maximum value in the left subtree.
Which case scenario describes a situation where a node to be removed has no children?
Which case scenario describes a situation where a node to be removed has no children?
- Transfer the children to an external queue.
- The parent's link should be set to NULL. (correct)
- A new child must be added.
- The node can be replanted.
What indicates the next node in an inorder traversal of a binary search tree?
What indicates the next node in an inorder traversal of a binary search tree?
In the context of deletion in a BST, what must be ensured when removing a node with one child?
In the context of deletion in a BST, what must be ensured when removing a node with one child?
Which of the following statements about binary search trees (BST) is true?
Which of the following statements about binary search trees (BST) is true?
What does the 'TREE-MINIMUM' function return in the context of BST?
What does the 'TREE-MINIMUM' function return in the context of BST?
Which traversal method is used to find the successor in a binary search tree?
Which traversal method is used to find the successor in a binary search tree?
What is the expected time complexity for lookup, insertion, or deletion operations in a balanced binary search tree?
What is the expected time complexity for lookup, insertion, or deletion operations in a balanced binary search tree?
Which traversal method processes the nodes in the order of parent node first, then left child, and finally right child?
Which traversal method processes the nodes in the order of parent node first, then left child, and finally right child?
In a binary search tree, where would you insert a new node with a value less than the root's key?
In a binary search tree, where would you insert a new node with a value less than the root's key?
What should be done when deleting a node from a BST that has two children?
What should be done when deleting a node from a BST that has two children?
What property of a binary search tree ensures that each subtree must also be a binary search tree?
What property of a binary search tree ensures that each subtree must also be a binary search tree?
Which of the following statements about the height of a binary search tree is true?
Which of the following statements about the height of a binary search tree is true?
During postorder traversal of a binary search tree, which node is visited last?
During postorder traversal of a binary search tree, which node is visited last?
What is a key characteristic of a binary search tree that differentiates it from a regular binary tree?
What is a key characteristic of a binary search tree that differentiates it from a regular binary tree?
If a binary search tree has a height of O(n), what is likely true about its structure?
If a binary search tree has a height of O(n), what is likely true about its structure?
Which function accurately represents the process of deleting a node in a binary search tree?
Which function accurately represents the process of deleting a node in a binary search tree?
What is the primary purpose of the TREE-DELETE-WITHOUT-PARENT function in a BST?
What is the primary purpose of the TREE-DELETE-WITHOUT-PARENT function in a BST?
Which sequence of nodes is traversed first in an inorder traversal of a BST?
Which sequence of nodes is traversed first in an inorder traversal of a BST?
After deleting a node with two children from a BST, what is usually the next step?
After deleting a node with two children from a BST, what is usually the next step?
What is the output of a preorder traversal of the sequence 15, 18, 6, 7, 17, 3, 4, 13, 9, 20?
What is the output of a preorder traversal of the sequence 15, 18, 6, 7, 17, 3, 4, 13, 9, 20?
When traversing a BST in postorder, which node is visited last?
When traversing a BST in postorder, which node is visited last?
After deleting node 4 from the given BST, what key will replace it if node 4 has a right child?
After deleting node 4 from the given BST, what key will replace it if node 4 has a right child?
Which traversal method first processes the root node?
Which traversal method first processes the root node?
What is a key characteristic of a binary search tree (BST)?
What is a key characteristic of a binary search tree (BST)?
What will be the inorder traversal of a BST after sequentially deleting nodes 4, 7, and 15 from it?
What will be the inorder traversal of a BST after sequentially deleting nodes 4, 7, and 15 from it?
What represents the minimum key during deletion in a BST?
What represents the minimum key during deletion in a BST?
If a BST node has no children, what occurs during its deletion?
If a BST node has no children, what occurs during its deletion?
When finding the inorder predecessor of a node in a BST, what must be looked at?
When finding the inorder predecessor of a node in a BST, what must be looked at?
In a BST, which traversal method yields nodes in sorted order?
In a BST, which traversal method yields nodes in sorted order?
In the procedural algorithm for deleting a node, which condition is checked first?
In the procedural algorithm for deleting a node, which condition is checked first?
Which of the following is a characteristic of a postorder traversal?
Which of the following is a characteristic of a postorder traversal?
Flashcards
Maximum Node
Maximum Node
The node with the largest key value in a Binary Search Tree (BST).
Minimum Node
Minimum Node
The node with the smallest key value in a BST.
Successor (BST)
Successor (BST)
The node immediately after a given node in an inorder traversal of a BST.
Predecessor (BST)
Predecessor (BST)
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Tree Insertion
Tree Insertion
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Tree Deletion (0 children)
Tree Deletion (0 children)
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Tree Deletion (1 child)
Tree Deletion (1 child)
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Tree Deletion (2 children)
Tree Deletion (2 children)
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BST
BST
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Inorder Traversal
Inorder Traversal
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Preorder Traversal
Preorder Traversal
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Postorder Traversal
Postorder Traversal
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Tree-Delete-Without-Parent
Tree-Delete-Without-Parent
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Delete Node
Delete Node
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Inorder Successor
Inorder Successor
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TREE-MINIMUM
TREE-MINIMUM
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Node Deletion
Node Deletion
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Key Value
Key Value
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Tree Traversal
Tree Traversal
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Binary Search Tree (BST) Structure
Binary Search Tree (BST) Structure
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Deleting in BST
Deleting in BST
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Creating a BST
Creating a BST
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BST-deletion algorithms
BST-deletion algorithms
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Binary Search Tree (BST)
Binary Search Tree (BST)
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BST Properties
BST Properties
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BST Lookup Time
BST Lookup Time
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BST Worst Case Height
BST Worst Case Height
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Preorder Traversal
Preorder Traversal
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Inorder Traversal
Inorder Traversal
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Postorder Traversal
Postorder Traversal
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BST Node Structure
BST Node Structure
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BST Search Time Complexity
BST Search Time Complexity
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BST Insertion
BST Insertion
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Study Notes
Binary Search Tree (BST)
- BSTs, sometimes called ordered or sorted binary trees, store keys in sorted order.
- Properties:
- The left subtree of a node contains only nodes with keys less than the node's key.
- The right subtree of a node contains only nodes with keys greater than the node's key.
- The left and right subtrees each must also be a binary search tree.
- There must be no duplicate nodes.
- Operations (lookup, addition, deletion) can be executed efficiently.
- Operations traverse the tree from root to leaf, making comparisons to keys, and deciding whether to continue searching in left or right subtrees.
- On average, each comparison allows operations to skip about half of the tree, making the time proportional to the logarithm of the number of items stored.
- Average height of a BST with n nodes is O(log n).
- Worst case height of a BST with n nodes is O(n).
- A tree node has:
data
: Data elementleft
: Pointer to left noderight
: Pointer to right noderoot
: Pointer to root node (initially NULL)
newnode(int element)
creates a new node in the tree.
Traversals
- Preorder: (parent, left, right)
- Inorder: (left, parent, right)
- Postorder: (left, right, parent)
- Example Preorder traversal: 60, 41, 16, 25, 53, 46, 42, 55, 74 …
- Example Inorder traversal: 16, 25, 41, 42, 46, 53, 55, 60 …
- Example Postorder traversal: 25, 16, 42, 46, 55, 53, 41, 62…
Searching
TREE-SEARCH(x, k)
:- If x is nil or k equals x.key, return x.
- If k < x.key, return
TREE-SEARCH(x.left, k)
. - Otherwise, return
TREE-SEARCH(x.right, k)
.
ITERATIVE-TREE-SEARCH(x, k)
:- While x is not nil and k is not equal to x.key:
- If k < x.key, x = x.left.
- Otherwise, x = x.right.
- Return x.
- While x is not nil and k is not equal to x.key:
- Running time (both iterative and recursive) is O(h), where h is the height of the tree.
Minimum and Maximum
TREE-MINIMUM(x)
:- While x.left is not nil, x = x.left.
- Return x.
TREE-MAXIMUM(x)
:- While x.right is not nil, x = x.right.
- Return x.
Successor and Predecessor
- Successor: next node in inorder traversal.
- Predecessor: previous node in inorder traversal.
Insertion
- New key is inserted at a leaf node.
- Search from root to leaf to find insertion point.
- Add the new node as a child of the leaf node.
- Duplicate keys are not allowed.
- If a key already exists, return the existing node.
Deletion
- Search for the node to remove.
- Execute the removal algorithm.
- Case 1: No children: Set parent's corresponding link to nil and dispose of the node.
- Case 2: One child: Link the single child directly to the parent of the removed node.
- Case 3: Two children: Find the inorder successor (minimum in the right subtree), copy its contents to the node being removed, and delete the inorder successor from the right subtree.
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Description
This quiz explores the fundamentals of Binary Search Trees (BSTs), including their properties, operations, and efficiency. Learn how BSTs organize data and the implications for searching, adding, and deleting nodes. Test your understanding of these essential data structures in computer science.