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Questions and Answers
Which sorting algorithm is stable?
Which sorting algorithm is stable?
In a max-heap, A[Parent(i)] is less than or equal to A[i].
In a max-heap, A[Parent(i)] is less than or equal to A[i].
False
What is the time complexity of the best case for Quicksort?
What is the time complexity of the best case for Quicksort?
O(n log n)
A stack follows the _____ policy.
A stack follows the _____ policy.
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What are the three arrays used in Counting-Sort?
What are the three arrays used in Counting-Sort?
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Match the functions with their corresponding data structure:
Match the functions with their corresponding data structure:
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In a binary search tree, an in-order traversal visits nodes in ascending order.
In a binary search tree, an in-order traversal visits nodes in ascending order.
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What are the two main functions for manipulating elements in a Queue?
What are the two main functions for manipulating elements in a Queue?
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A red-black tree satisfies _____ properties.
A red-black tree satisfies _____ properties.
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What is the purpose of dynamic programming?
What is the purpose of dynamic programming?
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Dynamic programming incurs a time-memory trade-off.
Dynamic programming incurs a time-memory trade-off.
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What does the C table store in the context of the Longest Common Subsequence (LCS) algorithm?
What does the C table store in the context of the Longest Common Subsequence (LCS) algorithm?
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The __________ is used to represent directions for reconstructing the Longest Common Subsequence.
The __________ is used to represent directions for reconstructing the Longest Common Subsequence.
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Match the following arrows with their meanings in the LCS algorithm:
Match the following arrows with their meanings in the LCS algorithm:
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Which algorithm is used to calculate the minimum number of scalar products?
Which algorithm is used to calculate the minimum number of scalar products?
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B-Trees are unbalanced search trees designed primarily for in-memory operations.
B-Trees are unbalanced search trees designed primarily for in-memory operations.
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Name one method used for finding the longest common subsequence (LCS).
Name one method used for finding the longest common subsequence (LCS).
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Which of the following algorithms has the worst case time complexity of O(n^2)?
Which of the following algorithms has the worst case time complexity of O(n^2)?
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The dynamic programming approach saves previously solved subproblems in a __________.
The dynamic programming approach saves previously solved subproblems in a __________.
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What is indicated by a diagonal arrow in the context of the LCS algorithm?
What is indicated by a diagonal arrow in the context of the LCS algorithm?
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The time complexity of Quick Sort in the worst case is O(n log n).
The time complexity of Quick Sort in the worst case is O(n log n).
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What is in-place sorting? Provide an example of an algorithm that utilizes in-place sorting.
What is in-place sorting? Provide an example of an algorithm that utilizes in-place sorting.
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The worst case time complexity for Balanced Binary Search Trees is O(logn) and O(______).
The worst case time complexity for Balanced Binary Search Trees is O(logn) and O(______).
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Match the following algorithms with their respective sorting types:
Match the following algorithms with their respective sorting types:
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Which of the following algorithms uses the divide and conquer paradigm?
Which of the following algorithms uses the divide and conquer paradigm?
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All linear data structures are arrays.
All linear data structures are arrays.
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What is the worst case time complexity for Dijkstra's algorithm?
What is the worst case time complexity for Dijkstra's algorithm?
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Counting Sort has a worst case time complexity of O(______ + n).
Counting Sort has a worst case time complexity of O(______ + n).
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Match the following data structures with their type:
Match the following data structures with their type:
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Study Notes
Algorithm Time Complexities
- Insertion Sort: Worst case time complexity is O(n²).
- Merge Sort: Worst case time complexity is O(n log n).
- Heap Sort: Worst case time complexity is O(n log n).
- Quick Sort: Worst case time complexity is O(n²). Best case is O(n log n).
- Counting Sort: Worst case time complexity is O(k + n).
- Searching Hash Table: Worst case time complexity is O(n).
- Balanced Binary Search Tree: Worst case time complexity is O(log n).
- Unbalanced Binary Search Tree: Worst case time complexity is O(n).
- Inorder, Postorder, Preorder search: O(n).
- Cut-Rod: O(2n).
- Longest Common Subsequence: O(m + n).
- Breadth-first search: O(|V| + |E|).
- Depth-first search: O(|V| + |E|).
- Dijkstra's algorithm: O(V log V + E).
Data Structures
- Linear: Array, stack, queue, linked list
- Non-linear: Tree, graph, hash table
Divide and Conquer Algorithms
- Quicksort
- Merge sort
- Binary search
In-place Sorting
- Insertion sort
- Does not require additional space beyond the input array.
Not In-place Sorting
- Merge sort
- Requires additional space (memory) at least equal to the input, possibly more. It's often faster than in-place sorts.
Stable vs. Unstable Sorting
- Stable sorting: Maintains the original order of equal elements in the output. Example: Merge sort
- Unstable sorting: Does not guarantee the original order of equal elements in the output. Example: Quicksort.
Max-Heap Property
- A[Parent(i)] ≥ A[i]
Best Case Time Complexity for Quicksort
- Occurs when the pivot divides the array nearly in half.
Counting Sort Arrays
- Input array (A): Holds the input values.
- Output array (B): Holds the sorted output values.
- Auxiliary array (C): Used for counting the occurrences of each input value.
Stack Policy
- Last-In, First-Out (LIFO)
Queue Policy
- First-In, First-Out (FIFO)
Dynamic Programming
- Breaks down a problem into smaller overlapping subproblems.
- Saves results of subproblems to avoid redundant calculations.
- Used to solve optimization problems.
Trade-offs of Dynamic Programming
- Increased memory usage for storing results of subproblems.
- Often results in substantial time savings compared to recursive approaches.
Matrix-Chain Multiplication Algorithm
- Used for calculating the minimum number of scalar multiplications.
LCS (Longest Common Subsequence) Algorithm
- Finds the longest subsequence common to two input sequences.
- Typically uses a 2D table (B and C) to build the solution from smaller subproblems.
B-Trees
- Balanced search trees optimized for disk access.
Red-Black Tree Properties
- Every node is either 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 simple paths from the node to descendant leaves contain the same number of black nodes.
Sentinel (in Merge Sort and Red-Black Trees)
- Marker used as a boundary in arrays or other data structures to simplify processing.
Chaining in Hash Tables
- Stores elements that hash to the same slot in a linked list.
Graph Traversal Algorithms
- Depth-first search (DFS)
- Breadth-first search (BFS)
- Dijkstra's algorithm (shortest paths)
Strongly Connected Component
- A group of vertices in a graph where, for every pair of vertices, there's a directed path from one to the other.
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Description
Test your knowledge on the time complexities of various algorithms, including sorting and searching algorithms. This quiz covers both worst-case scenarios and specific data structures. Challenge yourself with questions about linear and non-linear data structures as well as divide and conquer strategies.
