How does Dijkstra's algorithm guarantee the shortest path in a graph with non-negative edge weights?
- Always selects the smallest tentative distance
- Considers random paths
- Prioritizes longest paths
- Utilizes heuristics for optimization
Dijkstra's algorithm guarantees the shortest path by always selecting the smallest tentative distance, ensuring that the chosen path at each step is the most optimal. It relies on a greedy approach and the non-negativity of edge weights to consistently find the shortest paths. Heuristics, random paths, or prioritizing longest paths are not part of Dijkstra's algorithm logic.
How is the next number in the Fibonacci sequence generated from the previous two numbers?
- Addition of the two preceding numbers.
- Division of the two preceding numbers.
- Multiplication of the two preceding numbers.
- Subtraction of the two preceding numbers.
The next number in the Fibonacci sequence is generated by adding the two preceding numbers. For example, if the last two numbers are 'a' and 'b', then the next number is 'a + b'. This recurrence relation defines the Fibonacci sequence.
How does the performance of regular expression matching change with the complexity of the pattern and input text?
- Performance degrades exponentially with the complexity of the pattern and input text.
- Performance improves as both pattern and input text become more complex.
- Performance is independent of the pattern complexity but depends on the input text complexity.
- Performance remains constant regardless of the complexity of the pattern and input text.
The performance of regular expression matching typically degrades exponentially with the complexity of both the pattern and input text. More complex patterns and longer input texts can lead to significantly increased processing time.
You're tasked with detecting cycles in a directed graph. Explain how you would use DFS to accomplish this task efficiently.
- Keep track of the current path in the graph
- Maintain a count of visited nodes
- Mark visited nodes during DFS traversal
- Perform topological sorting using DFS
To detect cycles in a directed graph using DFS, you can mark the visited nodes during traversal. If you encounter a node that is already marked as visited, a cycle is detected. This approach efficiently identifies cycles without the need for additional data structures.
How does regular expression matching help in text processing?
- By allowing the identification of complex patterns and facilitating search, extraction, and manipulation of textual data.
- By rearranging characters randomly to enhance creativity in text.
- It primarily focuses on character counting and basic string operations.
- Regular expression matching has no significant role in text processing.
Regular expression matching aids in text processing by enabling the identification of complex patterns within the text. This functionality is crucial for tasks such as search operations, data extraction, and manipulation of textual data based on specified patterns.
Suppose you are tasked with optimizing the delivery routes for a logistics company operating in a region with multiple warehouses and customer locations. Explain how Dijkstra's algorithm could assist in this scenario.
- Consider only the distance between warehouses and customers
- Include additional constraints like delivery time windows
- Optimize for the shortest distance between warehouses
- Prioritize routes with the fewest road intersections
Dijkstra's algorithm can be used to optimize delivery routes by incorporating constraints such as delivery time windows. It calculates the shortest path between locations, ensuring timely deliveries and potentially minimizing overall transportation costs for the logistics company.
How does the suffix tree data structure contribute to solving the longest common substring problem efficiently?
- Suffix tree allows for efficient pattern matching and finding common substrings by storing all suffixes of a string in a compressed tree structure.
- Suffix tree enables quick sorting of substrings based on their lengths.
- Suffix tree performs a linear scan of the input strings to find common characters.
- Suffix tree uses a greedy algorithm to find the longest common substring.
The suffix tree data structure contributes to solving the longest common substring problem efficiently by storing all suffixes of a string in a compressed tree structure. This allows for fast pattern matching and identification of common substrings.
An AVL tree is a self-balancing binary search tree where the _______ factor of each node is at most _______.
- Balancing, 1
- Degree, 2
- Depth, 1
- Height, 0
An AVL tree is a self-balancing binary search tree where the height factor (also known as the balance factor) of each node is at most 1. The balance factor is the difference between the height of the left and right subtrees.
Which of the following sorting algorithms is similar to selection sort in terms of repeatedly finding the minimum element from the unsorted portion and placing it at the beginning?
- Bubble Sort
- Insertion Sort
- Merge Sort
- Quick Sort
The sorting algorithm similar to selection sort, in terms of repeatedly finding the minimum element from the unsorted portion and placing it at the beginning, is Insertion Sort. Both algorithms involve building the sorted portion of the array incrementally.
What are some common algorithms used for string compression?
- Binary Search, Linear Search, Hashing, Sorting
- Breadth-First Search, Depth-First Search, Dijkstra's Algorithm, Prim's Algorithm
- QuickSort, MergeSort, BubbleSort, SelectionSort
- Run-Length Encoding, Huffman Coding, Burrows-Wheeler Transform, Arithmetic Coding
Common algorithms for string compression include Run-Length Encoding, Huffman Coding, Burrows-Wheeler Transform, and Arithmetic Coding. These algorithms efficiently represent repeated patterns or characters in a compressed form, reducing the overall size of the string.