Podcast Beta
Questions and Answers
What is the worst-case time complexity of Quick Sort?
Which of the following is NOT a characteristic of divide and conquer algorithms?
In the context of sorting algorithms, which one is considered in-place?
What is one reason why Merge Sort is often preferred over other sorting algorithms for large datasets?
Signup and view all the answers
Which of the following data structures is considered linear?
Signup and view all the answers
Which step is NOT part of the divide and conquer paradigm?
Signup and view all the answers
Which algorithm utilizes the property of having a worst-case time complexity of O(k+n)?
Signup and view all the answers
In recursive algorithms, what is meant by the base case?
Signup and view all the answers
What is the function used to remove an element from a stack?
Signup and view all the answers
Which attribute of a stack allows access to the most recently added element?
Signup and view all the answers
In which tree traversal method is the root node visited last?
Signup and view all the answers
Which properties are characteristic of a red-black tree?
Signup and view all the answers
What are the two functions that add and remove elements from a queue?
Signup and view all the answers
What is the binary search tree property regarding keys?
Signup and view all the answers
During the stack operation for '123+45**+', what does the stack contain immediately after the operation of '5*4'?
Signup and view all the answers
What is the purpose of a sentinel in data structures like merge sort and red-black trees?
Signup and view all the answers
Which of the following sorting algorithms is an example of a stable sorting algorithm?
Signup and view all the answers
What characterizes an in-place sorting algorithm?
Signup and view all the answers
Which of the following statements is true regarding unstable sorting algorithms?
Signup and view all the answers
What is the main purpose of the C array in the Counting-Sort algorithm?
Signup and view all the answers
In the Max-Heap structure, what must be true about the parent and child nodes?
Signup and view all the answers
What is a characteristic feature of an unstable sorting algorithm when sorting elements?
Signup and view all the answers
Which of the following sorting algorithms is classified as not in-place due to its requirement for additional memory?
Signup and view all the answers
In the context of Quick sort, what is the significance of the pivot point?
Signup and view all the answers
Study Notes
Time Complexity
- Insertion Sort - Worst case time complexity is O(n^2)
- Merge Sort - Worst case and best case time complexity is O(nlogn)
- Heap Sort - Worst case and best case time complexity is O(nlogn)
- Quick Sort - Worst case time complexity is O(n^2), best case time complexity is O(nlogn)
- Counting Sort - Time complexity is O(k+n)
- Searching Hash Table - Worst case time complexity is O(n), best case time complexity is O(1)
- BST Tree-Search - Time complexity is O(h) - where h is the height of the tree (effectively O(logn))
- BST Insert/Delete - Time complexity is O(h) - where h is the height of the tree (effectively O(logn))
- Inorder, postorder, preorder search - Time complexity is O(n)
Data Structures
-
Linear Data Structures:
- Linked List
- Arrays
- Stacks & Queues
-
Non Linear Data Structures:
- Trees
- Graphs
- Hash tables
Recursion
- When a problem breaks itself down into smaller objects.
- Calls upon itself.
- Example: Factorials
Divide and Conquer
-
Algorithms that utilize divide and conquer:
- Merge sort
- Quick sort
- Heap sort
-
Steps of divide and conquer:
- Divide - break into smaller problems
- Conquer - recursively solve the problem
- Combine - combine the solutions
Merge Sort
-
Merge(A,p,q,r) - Takes a given array and splits it into two arrays
- Left sub-array and right sub-array
- Completes them independently and combines itself back into a whole array in an ordered sequence.
- Splits into two sub-arrays (left and right), continues to break the sub-arrays array into individual "chunks" elements, compares, rearranges, and combines, until it sorts both left and right sub-array.
- Merge sort extensively utilizes sentinel nodes for efficiency.
In-Place Sorting
- Sorting algorithms that do not need extra memory to sort the elements, it sorts in the same array as the input.
- Examples: Insertion sort, quick sort
Not In-Place Sorting
- Requires additional memory - may use an extra array to store elements.
- Example: Merge sort
Stable vs Unstable Sorting
-
Stable Sorting:
- When the numbers/elements with the same value appear in the same order in the output as it did in the input.
- Important when the order of equal elements has significant meanings.
- Examples: Insertion sort, merge sort.
-
Unstable Sorting:
- Output values are not preserved as it would be in stable sorting, so the input order is different than the output order for elements that are the same.
- Faster because it's not necessarily ensuring the elements that are the same are in the same order, faster > accuracy.
- Examples: Heap sort and quick sort.
Max-Heapify
-
Max-Heapify(A,i) - Takes an input array and creates sub arrays (left and right)
- Each element of the array goes down the left or right sub array and is placed in order by index to sort them and satisfy the property of a max heap.
- You check if the left child is less than or equal to the value of the parent.
Max Heap Property
- The parent must be greater than or equal to the child.
- A[Parent(i)] >= A[i]
- Min heap is the reverse.
Partition (Quick Sort)
- Partition(A,p,r) Takes a given array, splits it into two arrays, and places it back together with similar elements, similar to merge sort.
Quick Sort Best Case Time Complexity
- Achieved when the pivot point ensures the split is practically equal, resulting in a time complexity of O(nlogn).
Counting Sort Arrays
- A is contains the input array.
- B is the output array.
- C is the extra storage array used for counting occurrences of elements in the input array.
Stacks
- Uses a Last In First Out policy (LIFO).
Queues
- Uses a First In First Out policy (FIFO).
Evaluate Stack Operation
-
123+45**+
- Push 1 to the stack.
- Push 2 to stack.
- Push 3 to stack.
- Encounter a plus sign, so we pop the previous two elements.
- Do addition - 2+3=5 and push 5 to the stack (stack is now 1,5).
- Push 4.
- Push 5 (stack is now 1,5,4,5).
- Encounter a '*' - pop the previous two elements (4 and 5) and multiply.
- Push 20 to the stack (stack is now 1,5,20).
- Encounter a '*' - pop 20 and 5 and multiply.
- Push 100 to the stack.
- Encounter a '+' - pop the previous two elements (100,1).
- Add 100 and 1, and push 101 to the stack.
Stack Operations
- Push - adds to the stack.
- Pop - removes from the stack.
Stack Attribute
- Top - keeps track of the most recent element pushed into the stack.
Queue Operations
- Enqueue - add to the queue.
- Dequeue - remove from the queue.
Queue Attributes
- Head - keeps track of the index of the first element in the queue.
- Tail - keeps track of the index of the next location a new element can be inserted.
Doubly Linked List
- Contains a pointer to the previous and next node in the list.
List-Insert and List-Delete
- List-Insert - Inserts an element into the list.
- List-Delete - Deletes an element from the list.
Tree Structure Attributes
- Key: Unique identifier for each node.
- Parent: Node directly above a given node.
- Left: Pointer to the left child node.
- Right: Pointer to the right child node.
- Edge: Connection between nodes.
- Siblings: Nodes at the same level with the same parent.
- Nodes: Each element of the tree structure.
- Leaves: Nodes with no children.
- Root: Topmost node in the tree.
Binary Search Tree Property
- The key of the left child of any node is less than or equal to the key of its parent.
- The key of the right child of any node is greater than or equal to the key of its parent.
Binary Search Tree Traversal
- Inorder traversal: 25, 30, 35, 40, 45, 50, 60
- Preorder traversal: 40, 30, 25, 35, 50, 45, 60
- Postorder traversal: 25, 35, 30, 45, 60, 50, 40
Tree Height and Depth
- Height: 2
- Depth: 2
Iterative-Tree-Search
- Performs a search through the tree in an iterative (loop) manner.
Inserting a Node into a Tree
- Follows the binary search tree property.
Transplating a Node in a Tree
- Used for deleting nodes in a tree.
Red-Black Tree Properties
- Every node has a color (red or black).
- The root is black.
- Every leaf (NIL) is black.
- If a node is red, both its children are black.
- For each node, all paths from the node to descendant leaves contain the same number of black nodes.
Sentinel
- A marker or boundary in a data structure.
- Used for clarity and efficiency in Merge Sort and Red-Black Tree algorithms.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Related Documents
Description
Test your knowledge on data structures and their time complexities with this quiz. You'll explore various sorting algorithms, their performance, and characteristics of linear and non-linear data structures. Challenge yourself and solidify your understanding of fundamental concepts in computer science.
