Podcast
Questions and Answers
Which of the following algorithms has a worst-case time complexity of O(n^2)?
Which of the following algorithms has a worst-case time complexity of O(n^2)?
Merge Sort is an example of an in-place sorting algorithm.
Merge Sort is an example of an in-place sorting algorithm.
False
Name one linear data structure.
Name one linear data structure.
array
The worst-case time complexity of Quick Sort is O(____).
The worst-case time complexity of Quick Sort is O(____).
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Match the following algorithms with their time complexities:
Match the following algorithms with their time complexities:
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Which of the following algorithms utilize the divide and conquer paradigm?
Which of the following algorithms utilize the divide and conquer paradigm?
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An unbalanced binary search tree has a worst-case time complexity of O(log n).
An unbalanced binary search tree has a worst-case time complexity of O(log n).
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Provide an example of a stable sorting algorithm.
Provide an example of a stable sorting algorithm.
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Which of the following is NOT a reason for using dynamic programming?
Which of the following is NOT a reason for using 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 type of algorithm is used to calculate the minimum number of scalar products?
What type of algorithm is used to calculate the minimum number of scalar products?
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The ___ table is used to store the lengths of various subproblems in the LCS algorithm.
The ___ table is used to store the lengths of various subproblems in the LCS algorithm.
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What is true about a stable sorting algorithm?
What is true about a stable sorting algorithm?
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Match the following arrow directions with their meanings in LCS:
Match the following arrow directions with their meanings in LCS:
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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].
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What is stored in the B table of the LCS?
What is stored in the B table of the LCS?
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B-trees are designed for use primarily in main memory applications.
B-trees are designed for use primarily in main memory applications.
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What are the names of the two functions used to add and remove elements from a stack?
What are the names of the two functions used to add and remove elements from a stack?
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What is the output of the LCS algorithm?
What is the output of the LCS algorithm?
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The best case time complexity for Quicksort occurs when the pivot divides the array _ into half.
The best case time complexity for Quicksort occurs when the pivot divides the array _ into half.
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Match the following traversal types with their output order:
Match the following traversal types with their output order:
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What policy does a queue use?
What policy does a queue use?
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Chaining is a method used to resolve collisions in hash tables.
Chaining is a method used to resolve collisions in hash tables.
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List the three arrays used in Counting-Sort and their purposes.
List the three arrays used in Counting-Sort and their purposes.
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Study Notes
Algorithm Time Complexities
- Insertion Sort: Worst case time complexity is O(n^2).
- 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(n^2). Best case time complexity is O(n log n).
- Counting Sort: Worst case time complexity is O(k + n), where k is the range of input values.
- Searching Hash Table: Worst case time complexity is O(n).
Data Structures
Linear Data Structures
- Array
- Stack
- Queue
- Linked List
Non-linear Data Structures
- Tree
- Graph
- Hash Table
Sorting Algorithms
Stable vs. Unslable Sorting
- Stable sorting: Maintains the relative order of elements with equal values. Examples include Merge Sort.
- Unstable sorting: Does not maintain the relative order of equal elements. Examples include Quick Sort.
Divide and Conquer Algorithms
- Quicksort
- Merge Sort
- Binary Search
Binary Search Tree Property
- If a node y is in the left subtree of node x, then y's key is less than or equal to x's key.
- If a node y is in the right subtree of node x, then y's key is greater than or equal to x's key.
Tree Attributes
- Root
- Parent
- Child
- Leaf
- Edge
- Key
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, then 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
- A sentinel is a special value used as a boundary condition for algorithms like merge sort.
Chaining (Hash Tables)
- A technique to handle collisions in hash tables by placing elements with the same hash value in a linked list.
Dynamic Programming
- Breaks down a problem into smaller overlapping subproblems to optimize resource utilization.
- Uses a table to store the solutions to these subproblems to avoid redundant computations.
- Used for optimization problems.
Graph Traversal Algorithms
- Depth-First Search (DFS)
- Breadth-First Search (BFS)
Strongly Connected Components (SCC)
- A strongly connected component in a graph is a maximal set of vertices such that for any two vertices u and v in the component, there is a path from u to v and a path from v to u.
Minimum Spanning Tree (MST) Algorithms
- Prim's Algorithm
- Kruskal's Algorithm
Dijkstra's Algorithm
- Finds the shortest paths from a single source vertex to all other vertices in a graph with non-negative edge weights.
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Description
This quiz covers fundamental concepts related to data structures, sorting algorithms, and their time complexities. Explore insertion sort, merge sort, quicksort, and various data structures like arrays, trees, and hash tables. Test your understanding of stability in sorting and the divide and conquer strategy.
