The dynamic programming approach for LCS utilizes a _______ to efficiently store and retrieve previously computed subproblems.
- List
- Queue
- Stack
- Table
The dynamic programming approach for finding the Longest Common Subsequence (LCS) utilizes a table to efficiently store and retrieve previously computed subproblems. This table is often a 2D array where each cell represents the length of the LCS for corresponding substrings.
Explain how the Manacher's algorithm can be adapted to solve the longest common substring problem efficiently.
- Apply Manacher's algorithm only to the first string in the set.
- Apply Manacher's algorithm separately to each string and compare the results.
- Manacher's algorithm is not applicable to the longest common substring problem.
- Utilize Manacher's algorithm on the concatenated strings with a special character between them.
Manacher's algorithm can be adapted for the longest common substring problem by concatenating the input strings with a special character between them and then applying the algorithm. This approach efficiently finds the longest common substring across multiple strings.
A* search ensures optimality under certain conditions, such as having an _______ heuristic and no _______.
- Admissible
- Inadmissible
- Informed
- Uninformed
A* ensures optimality when the heuristic used is admissible, meaning it never overestimates the true cost to reach the goal. Additionally, the algorithm should have no cycles with negative cost to guarantee optimality. This combination ensures that A* explores the most promising paths first, leading to the optimal solution.
agine you are designing a navigation app for a city with one-way streets and varying traffic conditions. Discuss how you would utilize Dijkstra's algorithm to provide users with the most efficient route.
- Consider traffic conditions and adjust edge weights
- Determine the shortest path based on distance only
- Ignore one-way streets and focus on overall distance
- Optimize for fastest travel time based on current traffic
In this scenario, Dijkstra's algorithm should consider traffic conditions by adjusting edge weights accordingly. It ensures the algorithm provides the most efficient route by factoring in not just distance but also the current state of traffic on each road segment.
How does Bellman-Ford algorithm handle negative weight cycles in a graph?
- Adjusts the weights of edges in the negative cycle to make them positive
- Continues the process, treating the graph as if there are no negative cycles
- Ignores them
- Terminates and outputs a negative cycle detected
Bellman-Ford algorithm detects negative weight cycles by observing that if there is a relaxation operation in the graph after performing V-1 iterations, then there is a negative weight cycle. It terminates and outputs the detection of a negative cycle in the graph.
Lossy compression in string compression sacrifices _______ in favor of _______.
- Compression Efficiency, Decompression Speed
- Compression Ratio, Data Integrity
- Data Integrity, Compression Efficiency
- Decompression Speed, Compression Ratio
Lossy compression in string compression sacrifices Data Integrity (the fidelity of the original data) in favor of achieving a higher Compression Ratio. This means that some information is discarded or approximated during compression, leading to a smaller compressed size but a loss of accuracy in the reconstructed data.
Imagine you are designing a recommendation system for an e-commerce platform. How could you utilize the Longest Increasing Subsequence problem to enhance the user experience?
- Apply the Longest Increasing Subsequence to sort products based on popularity.
- Identify user preferences by finding the Longest Increasing Subsequence in their purchase history.
- Use the Longest Increasing Subsequence to optimize the delivery route for recommended items.
- Utilize the Longest Increasing Subsequence to categorize products efficiently.
In the context of a recommendation system, utilizing the Longest Increasing Subsequence can help identify user preferences by analyzing their purchase history. The longest increasing subsequence represents the products that the user tends to buy in a sequence, aiding in personalized recommendations.
Consider a scenario where you have to detect if there is a cycle in a graph. Would BFS or DFS be more efficient for this task? Provide reasoning for your answer.
- Both BFS and DFS
- Breadth-First Search (BFS)
- Depth-First Search (DFS)
- Neither BFS nor DFS
DFS is more efficient for detecting cycles in a graph. DFS explores as far as possible along each branch before backtracking, making it well-suited to identify cycles. If a back edge is encountered during the traversal, it indicates the presence of a cycle. BFS, being level-based, may also detect cycles but is not as efficient as DFS in this specific task.
Imagine you are designing a navigation system for a delivery service. Explain how you would utilize the A* search algorithm to find the most efficient routes for delivery trucks.
- Incorporate heuristics based on distance and traffic conditions
- Randomly choose paths for diversity
- Rely solely on historical data for route planning
- Use only real-time data for decision-making
In this scenario, A* search can be utilized by incorporating heuristics based on factors such as distance and traffic conditions. This approach allows the algorithm to intelligently navigate through the road network and find the most efficient routes for delivery trucks.
What data structure does a queue resemble in real-world scenarios?
- Line
- List
- Stack
- Tree
A queue resembles a real-world line where elements are arranged in a linear order. It follows the First-In-First-Out (FIFO) principle, similar to people standing in a line, where the person who arrives first is served first.