The time complexity of the dynamic programming approach for the longest common substring problem is _______.
- O(n log n)
- O(n)
- O(n^2)
- O(nm)
The time complexity of the dynamic programming approach for the longest common substring problem is O(nm), where 'n' and 'm' are the lengths of the input strings. The algorithm uses a table of size n x m to store intermediate results, leading to a quadratic time complexity.
Dijkstra's algorithm relies on the use of a _______ to keep track of the shortest distances to each node.
- Hash Table
- Linked List
- Priority Queue
- Stack
Dijkstra's algorithm relies on the use of a priority queue to keep track of the shortest distances to each node efficiently. The priority queue ensures that nodes are processed in order of increasing distance, optimizing the exploration of the graph and helping in finding the shortest paths.
Imagine you need to implement a program that simulates a tic-tac-toe game board. How would you use arrays to represent the game board efficiently?
- Implement separate arrays for each row, column, and diagonal.
- Use a 1D array and perform arithmetic calculations for efficient indexing.
- Use a 2D array to represent the grid of the tic-tac-toe board.
- Utilize a linked list for efficient representation.
To efficiently represent a tic-tac-toe game board, a 2D array is commonly used. Each element of the array corresponds to a cell on the board, providing a straightforward and efficient way to simulate the grid.
What is the primary purpose of using a hash table?
- Efficient data retrieval by mapping keys to values using a hash function.
- Performing matrix operations.
- Sorting elements in ascending order.
- Storing elements in a linked list.
The primary purpose of using a hash table is to achieve efficient data retrieval by mapping keys to values using a hash function. This allows for constant-time average-case complexity for basic operations like insertion, deletion, and search.
The space complexity of radix sort is _______ compared to other sorting algorithms like merge sort and quick sort.
- O(1)
- O(n log n)
- O(n)
- O(n^2)
The space complexity of radix sort is O(1), indicating that it has a constant space requirement, making it more memory-efficient compared to other sorting algorithms like merge sort and quicksort.
Prim's algorithm typically performs better on graphs with _______ edges, while Kruskal's algorithm is more efficient on graphs with _______ edges.
- Acyclic, Cyclic
- Cyclic, Acyclic
- Dense, Sparse
- Sparse, Dense
Prim's algorithm typically performs better on graphs with sparse edges, where only a small number of edges exist. In contrast, Kruskal's algorithm is more efficient on graphs with dense edges, where a large number of edges are present. This is because the priority queue operations in Prim's algorithm are generally faster on sparse graphs.
In binary search, the array must be _______ to ensure correct results.
- Reversed
- Shuffled
- Sorted
- Unsorted
In binary search, the array must be sorted to ensure correct results. Binary search relies on the property of a sorted array to efficiently eliminate half of the remaining elements in each step.
In certain applications such as plagiarism detection, the longest common substring problem helps identify _______ between documents.
- Connections
- Differences
- Relationships
- Similarities
In certain applications like plagiarism detection, the longest common substring problem helps identify similarities between documents. By finding the longest common substring, one can detect shared sequences of words or characters, aiding in identifying potential instances of plagiarism.
Discuss the significance of the optimal substructure property in dynamic programming solutions for the Knapsack Problem.
- It ensures that the problem can be divided into smaller, overlapping subproblems, making it suitable for dynamic programming.
- It ensures that the solution to a larger problem can be constructed from optimal solutions of its overlapping subproblems.
- It implies that the problem does not have overlapping subproblems.
- It indicates that the Knapsack Problem has an efficient greedy solution.
The optimal substructure property in dynamic programming for the Knapsack Problem ensures that the solution to the overall problem can be constructed from optimal solutions to its overlapping subproblems, making it suitable for dynamic programming approaches.
In which pattern matching algorithm is a prefix table or failure function used to optimize the search process?
- Boyer-Moore Algorithm
- Brute Force Algorithm
- Knuth-Morris-Pratt Algorithm
- Rabin-Karp Algorithm
The Knuth-Morris-Pratt Algorithm uses a prefix table or failure function to optimize the search process. This allows the algorithm to skip unnecessary comparisons by taking advantage of the information about the pattern's own structure.
How does the Rabin-Karp algorithm handle potential spurious matches?
- It adjusts the length of the search window dynamically to avoid spurious matches.
- It ignores potential spurious matches and relies on a post-processing step to filter them out.
- It rehashes the entire text for each potential match to verify its accuracy.
- It uses a rolling hash function to efficiently update the hash value of the current window.
The Rabin-Karp algorithm handles potential spurious matches by using a rolling hash function. This allows it to efficiently update the hash value of the current window in constant time, reducing the likelihood of false positives.
How can you handle deletions efficiently in a hash table while maintaining performance?
- Deleting the element and shifting all subsequent elements one position to the left.
- Marking the deleted elements as "deleted" and skipping them during searches.
- Relocating all elements in the table to fill the gap left by the deleted element.
- Simply removing the element from the hash table and leaving the space empty.
Efficient deletion in a hash table involves marking the deleted elements as "deleted" and skipping them during searches. This approach prevents disruptions in the hash table's structure and maintains performance by avoiding unnecessary shifting or relocating of elements.