What is the time complexity of radix sort?
- O(d * (n + b))
- O(log n)
- O(n log n)
- O(n^2)
The time complexity of radix sort is O(d * (n + b)), where 'd' is the number of digits in the input numbers, 'n' is the number of elements, and 'b' is the base of the numeric representation.
How does the stability of Insertion Sort make it suitable for certain applications?
- Ignores equal elements
- Maintains the relative order of equal elements
- Randomly shuffles equal elements
- Sorts equal elements based on a random key
The stability of Insertion Sort ensures that the relative order of equal elements is maintained. This property is crucial in applications where maintaining the original order of equivalent elements is necessary, such as sorting a database by multiple criteria without disturbing the existing order of records.
How does topological sorting differ from other sorting algorithms like bubble sort or merge sort?
- Topological sorting has a time complexity of O(n^2), whereas bubble sort and merge sort have better time complexities of O(n^2) and O(n log n) respectively.
- Topological sorting is a comparison-based sorting algorithm, similar to bubble sort and merge sort.
- Topological sorting is an in-place sorting algorithm, whereas bubble sort and merge sort require additional space for sorting.
- Topological sorting is specifically designed for directed acyclic graphs (DAGs) and maintains the order of dependencies, while bubble sort and merge sort are general-purpose sorting algorithms for arrays.
Topological sorting is specialized for directed acyclic graphs (DAGs), ensuring a valid sequence of dependencies, unlike general-purpose sorting algorithms such as bubble sort and merge sort.
To handle negative edge weights, one might consider using _______ to modify Dijkstra's algorithm.
- AVL Trees
- Bellman-Ford Algorithm
- Depth-First Search
- Merge Sort
To handle negative edge weights, one might consider using the Bellman-Ford Algorithm to modify Dijkstra's algorithm. The Bellman-Ford Algorithm can handle graphs with negative weight edges, unlike Dijkstra's algorithm, making it suitable for such scenarios.
Consider a software project where multiple modules depend on each other for compilation. Explain how topological sorting can help determine the order in which these modules should be compiled.
- Ensures compilation from the most complex module to the least complex.
- Organizes modules based on their sizes.
- Randomly selects modules for compilation.
- Resolves compilation dependencies by sorting modules in an order that avoids circular dependencies.
Topological sorting is used to resolve dependencies in a directed acyclic graph (DAG). In the context of a software project, it ensures that modules are compiled in an order that avoids circular dependencies, allowing each module to be compiled only after its dependencies have been compiled.
How does a hash table handle collisions?
- By ignoring collisions and overwriting existing values.
- By rearranging the elements in the table.
- By resizing the hash table to accommodate more elements.
- By using techniques such as chaining or open addressing to resolve conflicts.
Hash tables handle collisions by employing techniques such as chaining or open addressing. Chaining involves maintaining a linked list at each bucket to store colliding elements, while open addressing involves finding the next available slot in the table.
Multidimensional arrays are arrays of _______ arrays.
- Heterogeneous
- Homogeneous
- Linear
- Non-linear
Multidimensional arrays are arrays of homogeneous arrays, meaning that each element in the outer array points to another array of the same data type.
Reversing a linked list recursively involves changing the _______ of each node.
- Data
- Next pointer
- Previous pointer
- Value
Reversing a linked list recursively involves changing the previous pointer of each node. In each recursive call, the next pointer of each node is redirected to its previous node, gradually reversing the entire list.
In the context of strings, what does the term "edit" refer to in the Edit Distance algorithm?
- All of the above.
- Deleting characters from a string.
- Inserting characters into a string.
- Modifying characters in a string.
In the context of strings and the Edit Distance algorithm, the term "edit" refers to all three operations: deleting characters, inserting characters, and modifying characters in a string. These operations are used to transform one string into another.
Which shortest path algorithm is suitable for finding the shortest path from a single source vertex to all other vertices in a weighted graph with non-negative edge weights?
- Bellman-Ford Algorithm
- Dijkstra's Algorithm
- Floyd-Warshall Algorithm
- Prim's Algorithm
Dijkstra's Algorithm is suitable for finding the shortest path from a single source vertex to all other vertices in a weighted graph with non-negative edge weights. It uses a greedy approach, iteratively selecting the vertex with the smallest known distance to the source.