Podcast
Questions and Answers
Which of the following are the main operations for a dictionary?
Which of the following are the main operations for a dictionary?
Binary search trees and heaps are the same concept.
Binary search trees and heaps are the same concept.
False (B)
What is the worst-case time complexity for the get() operation in a dictionary implemented with a linked list?
What is the worst-case time complexity for the get() operation in a dictionary implemented with a linked list?
O(n)
A dictionary is a mapping of keys to ______ where each key has at most one value.
A dictionary is a mapping of keys to ______ where each key has at most one value.
Signup and view all the answers
Match the following dictionary operations with the descriptions:
Match the following dictionary operations with the descriptions:
Signup and view all the answers
What is the time complexity of the put() method when using an array implementation of a dictionary?
What is the time complexity of the put() method when using an array implementation of a dictionary?
Signup and view all the answers
Using hashing for dictionary implementations achieves O(1) worst-case time complexity for all operations.
Using hashing for dictionary implementations achieves O(1) worst-case time complexity for all operations.
Signup and view all the answers
What type of tree will be used to implement a dictionary in the following sections of the document?
What type of tree will be used to implement a dictionary in the following sections of the document?
Signup and view all the answers
Which of the following is NOT a condition for a non-empty tree to be considered a binary search tree?
Which of the following is NOT a condition for a non-empty tree to be considered a binary search tree?
Signup and view all the answers
In a binary search tree, if the search key is smaller than the root key, the search continues in the right subtree.
In a binary search tree, if the search key is smaller than the root key, the search continues in the right subtree.
Signup and view all the answers
What is the worst-case time complexity for searching, inserting, or removing an element in a binary search tree, where h is the height of the tree?
What is the worst-case time complexity for searching, inserting, or removing an element in a binary search tree, where h is the height of the tree?
Signup and view all the answers
In the levelorder traversal method for a binary search tree, a queue is used to visit nodes level by level and the root node is enqueued ______.
In the levelorder traversal method for a binary search tree, a queue is used to visit nodes level by level and the root node is enqueued ______.
Signup and view all the answers
When removing a node with two children from a binary search tree, what is used to replace the node?
When removing a node with two children from a binary search tree, what is used to replace the node?
Signup and view all the answers
If a node in a binary search tree has no left subtree, when it is removed, it is replaced by its right subtree.
If a node in a binary search tree has no left subtree, when it is removed, it is replaced by its right subtree.
Signup and view all the answers
What data structure is primarily used in level order traversal of a binary search tree?
What data structure is primarily used in level order traversal of a binary search tree?
Signup and view all the answers
Match the following descriptions to the corresponding binary search tree operation:
Match the following descriptions to the corresponding binary search tree operation:
Signup and view all the answers
Study Notes
Dictionaries and Binary Search Trees
- Dictionaries are abstract data types with various applications, including translations, storing key-value pairs, and mapping words between languages.
- Dictionaries in computer science store at most one value for each key.
- Key methods for dictionaries include:
-
put(key: K, value: V): Adds a key-value pair. -
get(key: K): Retrieves the value associated with a key. -
remove(key: K): Removes a key-value pair. -
contains(key: K): Checks if a key exists in the dictionary. -
isEmpty: Checks if the dictionary is empty.
-
Implementation with Linked Nodes
- Dictionaries can be implemented using linked nodes, similar to queues or stacks.
- Each node stores a key, value, and a pointer to the next node.
-
get(key)andcontains(key)methods: In worst-case, checking every node takes O(n) time. -
remove(key)method: Worst-case running time is O(n). -
put(key, value)method: Worst-case running time is O(n) due to scanning all nodes.
Implementation with Arrays
- Dictionaries can be implemented using arrays.
- Each array entry stores a key-value pair.
-
get(key)andcontains(key)methods: In the worst case, checking each entry takes O(n) time. -
remove(key)method: Worst-case running time is O(n), requiring array entry swaps. -
put(key, value)method: Worst-case running time is O(n), requiring scanning all entries.
Conclusion
- Simple implementations of dictionaries using linked nodes or arrays have O(n) worst-case time complexity for most operations.
- Hashing techniques can be used to achieve better, amortized O(1) time complexity.
Binary Search Trees (BSTs)
- BSTs are tree-based data structures.
-
Definition: A binary search tree is either empty or has a root node with keys greater than all keys in the left subtree and smaller than all keys in the right subtree. This is an inductive definition implying the left and right subtrees must be binary search trees themselves. -
Searching: The general idea is to compare the target key with the root key. If the target key is smaller, proceed to the left subtree recursively; otherwise, proceed to the right subtree recursively.- Worst-case time complexity for searching is O(h), which represents the height of the tree.
-
Insertion: Similar recursive approach to searching to determine location for new key -value pair; insert new node as leaf node.- Worst-case time complexity for insertion is O(h).
-
Removal: Removing a key potentially involves a complex recursive approach to maintain the BST structure properties.- In the case of removing the maximum, look at possible right subtrees.
- If the right subtree is empty then the maximum is the current node.
- Find the largest element in the left subtree, swap with the key to be deleted and then recursively remove the largest element to maintain BST structure.
- Worst-case time complexity is O(h).
Traversal
-
Levelorder: Enqueue the root in queue, dequeue and add keys and enqueue children nodes and so on. -
Preorder: Visit root, recursively traverse left subtree then recursively traverse right subtree. -
Inorder: Recursively traverse left subtree, visit root, recursively traverse right subtree. -
Postorder: Recursively traverse left subtree, recursively traverse right subtree, then visit root.
Running Time Summary
- Time complexity depends on the height of the tree (h).
- Best case: O(1) if element is found immediately
- Worst Case: O(n) if the tree is skewed (linked list)
- Average Case: O(log n) for balanced trees
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Related Documents
Description
Explore the concept of dictionaries as abstract data types, focusing on their implementation and key methods. Learn about linked nodes and how they support operations like adding, retrieving, and removing key-value pairs. Test your understanding of these fundamental data structures in computer science.
