The space complexity of Manacher's Algorithm is _______ compared to other algorithms for finding the Longest Palindromic Substring.
- Dependent
- Equal
- Greater
- Lesser
The space complexity of Manacher's Algorithm is comparatively lower than that of other algorithms for finding the Longest Palindromic Substring. It utilizes an array to store information about palindromes, leading to efficient memory usage.
In the Bounded Knapsack Problem, each item can be selected at most _______ times, while in the Unbounded Knapsack Problem, there is no restriction on the number of times an item can be selected.
- Infinite
- Limited
- One
- Zero
In the Bounded Knapsack Problem, each item can be selected at most a limited number of times, while in the Unbounded Knapsack Problem, there is no restriction on the number of times an item can be selected, allowing for an infinite number of selections.
Imagine you are working on a plagiarism detection system for academic documents. How could you employ the Edit Distance algorithm to compare textual similarities between documents?
- Apply the Edit Distance algorithm to randomly select portions of documents and compare them for plagiarism.
- Implement the Edit Distance algorithm to compare document lengths and suggest similarities based on similar document sizes.
- Use the Edit Distance algorithm to count the total number of words in each document and compare them for textual similarities.
- Utilize the Edit Distance algorithm to measure the similarity between documents by calculating the minimum number of operations (insertions, deletions, substitutions) required to transform one document into the other.
In a plagiarism detection system, the Edit Distance algorithm measures the similarity between documents by calculating the minimum number of operations (insertions, deletions, substitutions) required to transform one document into the other. This provides a quantitative measure of textual similarity for plagiarism analysis.
Circular queues help in reducing _______ wastage that occurs in linear queues.
- Memory
- Processor
- Space
- Time
Circular queues help in reducing space wastage that occurs in linear queues. In linear queues, as elements are dequeued, the space at the front becomes unusable. Circular queues address this issue by wrapping around when reaching the end of the array, effectively utilizing the available space more efficiently.
Consider a scenario where you need to dynamically update the minimum spanning tree of a graph due to frequent changes in edge weights. Which algorithm, Prim's or Kruskal's, would be easier to adapt to these changes, and why?
- Bellman-Ford
- Dijkstra's
- Kruskal's
- Prim's
Prim's algorithm would be easier to adapt to dynamic changes in edge weights. This is because Prim's algorithm builds the minimum spanning tree incrementally, allowing for straightforward updates when edge weights change. Kruskal's algorithm, on the other hand, involves sorting edges, making dynamic updates less straightforward.
What is the main difference between Prim's and Kruskal's algorithms?
- Kruskal's algorithm always selects the edge with the maximum weight.
- Kruskal's algorithm starts with an arbitrary vertex and grows the minimum spanning tree from there.
- Prim's algorithm builds the minimum spanning tree one vertex at a time, while Kruskal's algorithm builds it one edge at a time.
- Prim's algorithm uses a greedy approach and always selects the vertex with the minimum key value.
The main difference between Prim's and Kruskal's algorithms is in their approach to building the minimum spanning tree. Prim's algorithm grows the tree one vertex at a time, always selecting the vertex with the minimum key value, while Kruskal's algorithm grows the tree one edge at a time by selecting the smallest available edge.
Consider a scenario where you have a graph representing a network of cities connected by roads with tolls. Discuss the modifications needed to adapt Dijkstra's algorithm to find the shortest path while considering both distance and toll costs.
- Add toll costs to the edge weights
- Exclude edges with tolls from the graph
- Ignore toll costs and focus only on the distance
- Prioritize routes with the fewest toll booths
To adapt Dijkstra's algorithm for toll costs, you should add toll costs to the edge weights. This modification ensures that the algorithm considers both distance and toll costs when finding the shortest path, providing a more accurate representation of the actual travel expenses.
When encountering cycles in a graph, BFS _______ revisits already visited nodes.
- Always
- Never
- Occasionally
- Sometimes
When encountering cycles in a graph, BFS never revisits already visited nodes. BFS uses a queue to explore nodes, and once a node is visited, it is marked as such. Since BFS explores nodes level by level, it does not revisit nodes, ensuring that cycles do not lead to infinite loops.
In a social network analysis application, you need to find the shortest path between two users. Would DFS be an appropriate choice? Why or why not?
- Both DFS and BFS
- It depends on the specific network type
- No
- Yes
No, DFS is not an appropriate choice for finding the shortest path in a social network. DFS may find a path, but it may not be the shortest, as DFS explores one path deeply before backtracking. BFS, on the other hand, systematically explores all possible paths and ensures the shortest one is found.
In which scenarios is DFS typically preferred over BFS?
- When memory usage is a critical factor and the solution is deep in the search tree.
- When the graph is dense and there are many levels of hierarchy.
- When the graph is sparse and the solution is likely to be found at a lower depth.
- When the solution is close to the root of the search tree.
DFS is typically preferred over BFS when memory usage is a critical factor, and the solution is deep in the search tree. This is because DFS explores as far as possible along each branch before backtracking, which might reduce memory requirements compared to BFS.