What is the primary feature of the class P in computational complexity theory?
A Requires random access memory
B Solvable in polynomial time
C Solvable in exponential time
D Solvable in logarithmic time
Class P consists of problems that can be solved in polynomial time, meaning there is an efficient algorithm to solve them. These problems are considered tractable and can be solved in reasonable time as input size increases.
What does the NP class represent in computational complexity?
A Problems that have no solution
B Problems solvable in polynomial time
C Problems solvable with random algorithms
D Problems for which solutions can be verified in polynomial time
NP (Non-deterministic Polynomial time) includes problems where a solution, if given, can be verified in polynomial time. Finding the solution may be hard, but checking it can be done efficiently.
What is a key difference between NP and NP-Complete problems?
A NP-Complete problems are as hard as any problem in NP
B NP problems have no solution
C NP-Complete problems can be solved faster
D NP-Complete problems are easier to solve
NP-Complete problems are the hardest problems in NP. Any NP problem can be reduced to an NP-Complete problem in polynomial time. If an NP-Complete problem can be solved in polynomial time, all NP problems can be solved in polynomial time.
What is the main goal of data compression algorithms?
A To increase data size
B To encode data in binary
C To reduce memory usage
D To generate random data
Data compression algorithms aim to reduce the size of data by encoding it more efficiently. This reduces the amount of storage required and can speed up transmission times over networks, especially for large files.
Which of the following is an example of a lossless data compression algorithm?
A PNG
B MP3
C JPEG
D MPEG
PNG (Portable Network Graphics) is a lossless image compression algorithm, meaning it compresses images without losing any data. Lossless algorithms allow the original data to be perfectly reconstructed from the compressed version.
Which of the following is true about PSPACE problems?
A Solvable in polynomial time
B Solvable by brute force
C Solvable with polynomial space
D Requires exponential time
PSPACE is a complexity class consisting of problems that can be solved using polynomial space. These problems may require exponential time but are constrained to use only polynomial amounts of memory during computation.
What is the space complexity of a problem in the class PSPACE?
A Exponential
B Polynomial
C Constant
D Logarithmic
Problems in the PSPACE class can be solved with polynomial space. This means that although the time complexity could be large, the space required for computation remains bounded by a polynomial function of the input size.
What is the purpose of the Huffman coding algorithm?
A Data compression
B Encrypting data
C Data validation
D Sorting data
Huffman coding is a lossless data compression algorithm that assigns shorter codes to more frequent characters and longer codes to less frequent ones, thereby reducing the overall size of the data.
Which of the following problems is NP-Hard?
A Matrix multiplication
B Searching in a sorted array
C Traveling Salesman Problem
D Sorting
The Traveling Salesman Problem (TSP) is NP-Hard, meaning it is at least as hard as the hardest problems in NP. It involves finding the shortest route that visits each city once and returns to the origin.
What is the worst-case time complexity of the Merge Sort algorithm?
A O(n log n)
B O(nĀ²)
C O(n)
D O(log n)
Merge Sort has a time complexity of O(n log n) in the worst case. It recursively splits the array into two halves, sorts each half, and then merges the sorted halves. This ensures consistent performance for large datasets.
What is the main challenge in solving NP-Hard problems?
A The problem requires no algorithm
B The problem can be solved in linear time
C The problem cannot be solved
D The solution requires exponential time
NP-Hard problems are computationally difficult because no known polynomial-time algorithm exists for solving them. In many cases, solving these problems requires exponential time, making them impractical to solve for large instances.
Which of the following is a characteristic of a lossless compression algorithm?
A Produces irrecoverable data loss
B Produces lossy output
C Reduces file size by eliminating redundant data
D Does not require decompression
Lossless compression algorithms reduce file sizes by eliminating redundant data without losing any information. The original data can be perfectly reconstructed from the compressed version, making it ideal for text or certain types of image compression.
Which of the following is a compression algorithm used for video files?
A MP3
B JPEG
C Binary Search
D MPEG
MPEG (Moving Picture Experts Group) is a compression algorithm used for video and audio files. It is widely used in media streaming and digital video storage due to its efficiency in compressing large video files.
What does the class NP-Complete refer to?
A Problems that are both in NP and as hard as any problem in NP
B Problems that cannot be solved
C Problems solvable in polynomial time
D Problems that are easily solvable
NP-Complete problems are the hardest problems in NP. If an efficient algorithm is found for one NP-Complete problem, it would provide efficient solutions for all problems in NP, which is one of the biggest open questions in computer science.
What is the main idea behind the greedy algorithm?
A Always pick the most expensive option
B Use dynamic programming for efficiency
C Make local optimal choices to find a global optimum
D Randomly select solutions
The greedy algorithm makes the locally optimal choice at each step, aiming to find a global optimum. While it works for certain problems like the Knapsack problem, it does not guarantee an optimal solution for all problems.