Consider a scenario where you're designing a water distribution network with multiple sources and sinks. How would you adapt the Ford-Fulkerson algorithm to efficiently manage flow in this network?
- Apply the Ford-Fulkerson algorithm to maximize water flow across the network without considering the efficiency of distribution.
- Implement the Ford-Fulkerson algorithm to balance water flow efficiently among multiple sources and sinks, adjusting capacities based on demand.
- Use the Ford-Fulkerson algorithm to randomly allocate water flow to sources and sinks in the distribution network.
- Utilize the Ford-Fulkerson algorithm to prioritize water flow from one specific source to all sinks in the network.
In the water distribution network scenario, the Ford-Fulkerson algorithm is adapted to efficiently manage flow by balancing water distribution among multiple sources and sinks. Capacities are adjusted based on demand, optimizing the overall flow in the network.
Dijkstra's algorithm is used to find the shortest path from a _______ vertex to all other vertices in a weighted graph with _______ edge weights.
- Destination, Fixed
- Initial, Varying
- Source, Uniform
- Starting, Variable
Dijkstra's algorithm is used to find the shortest path from a source vertex to all other vertices in a weighted graph with uniform edge weights. It employs a greedy strategy, always selecting the vertex with the smallest known distance.
The LIS problem is significant in real-world applications such as _______.
- All of the above
- DNA Sequencing
- Image Processing
- Network Routing
The Longest Increasing Subsequence problem has significant applications in real-world scenarios such as DNA sequencing, network routing, and image processing. It is used to find the longest ordered subsequence in various contexts.
Dijkstra's algorithm is commonly employed in _______ systems to calculate the shortest route between locations.
- Database
- Operating
- Queue
- Routing
Dijkstra's algorithm is commonly employed in routing systems to calculate the shortest route between locations. It helps find the most efficient path in networks, such as road maps or computer networks.
In a graph containing cycles, _______ sorting cannot be performed as it violates the prerequisite of a directed acyclic graph (DAG).
- Depth-First
- Linear
- Radix
- Topological
In a graph containing cycles, topological sorting cannot be performed as it violates the prerequisite of a directed acyclic graph (DAG). Topological sorting relies on establishing a linear ordering of vertices, which is not possible in the presence of cycles.
Consider a scenario where you need to implement a cache to store frequently accessed database records. Explain how you would use a hash table to achieve efficient caching.
- Design a cache with a linked list for efficient record retrieval.
- Employ a hash table with keys as record identifiers and values as the corresponding database records.
- Implement a cache using a stack data structure for simplicity.
- Use a hash table with keys as the most recently accessed records for cache eviction.
To achieve efficient caching, using a hash table with keys as record identifiers and values as the corresponding database records is a suitable approach. This allows for constant-time lookups and efficient retrieval of frequently accessed records.
The Floyd-Warshall algorithm computes the shortest paths between _______ pairs of vertices in a weighted graph.
- Adjacent, Important
- All possible, All possible
- Connected, Selected
- Specific, Critical
The Floyd-Warshall algorithm computes the shortest paths between all possible pairs of vertices in a weighted graph. It uses dynamic programming to find the shortest paths and is suitable for graphs with both positive and negative edge weights.
Consider a scenario where stability in sorting is paramount, and you need to sort a list of objects with equal keys. Discuss how merge sort maintains stability and why it would be a suitable choice for this scenario.
- Merge sort does not maintain stability as it may reorder equal elements during the merging step.
- Merge sort maintains stability by preserving the relative order of equal elements during the merge step. It compares elements in a way that ensures equal elements from different subarrays retain their original order. Thus, when merging sorted subarrays, elements with equal keys remain in their original order, maintaining stability. Merge sort is a suitable choice for this scenario due to its stable sorting behavior and efficient performance.
- Merge sort maintains stability by randomly shuffling equal elements during the merge step.
- Merge sort maintains stability by using a hashing function to determine the order of equal elements during merging.
Merge sort's stability stems from its merge step, where it ensures that equal elements from different subarrays maintain their original order. This makes merge sort an ideal choice for scenarios where stability is paramount, such as when sorting objects with equal keys, as it guarantees that the relative order of equal elements is preserved.
When is the Rabin-Karp algorithm particularly useful compared to other pattern matching algorithms?
- Effective when dealing with large texts and patterns.
- Efficient for short patterns or patterns with fixed lengths.
- Preferable for patterns containing repetitive characters.
- Suitable for scenarios where preprocessing is not feasible.
The Rabin-Karp algorithm is particularly useful when dealing with large texts and patterns. Its efficiency lies in its ability to hash the pattern and compare the hash values, making it effective for scenarios where preprocessing is feasible and the pattern length is not fixed.
What type of data structure is a binary tree?
- Circular Data Structure
- Linear Data Structure
- Non-linear Data Structure
- Sequential Data Structure
A binary tree is a non-linear data structure. Unlike linear structures (e.g., arrays, linked lists), a binary tree represents a hierarchical structure where each node has at most two children, forming branches.