Identify whether the given problems are Decision Problems, Counting Problems, or Search Problems. Write your answer in front of each problem.

  • Does a given binary string have an even number of zeros?

    This is a Decision Problem because the question asks whether a specific condition (in this case, having an even number of zeros in a binary string) is true or false. Decision problems are problems where the solution is a simple “yes” or “no” answer. In this case, the goal is to check the binary string and determine whether the number of zeros in it is even, providing a binary outcome.

  • Flipping a coin results in heads or tails. If a coin is flipped 20 times, how many different sequences of heads and tails are possible?

    This is a Counting Problem because it asks for the total number of different possible outcomes (sequences) of flipping a coin 20 times. In counting problems, the goal is to determine how many possible combinations, arrangements, or selections can be made given certain constraints or choices. Since each coin flip has 2 possible outcomes (heads or tails), and the coin is flipped 20 times, the total number of possible sequences is calculated by raising 2 to the power of 20.

  • Does a certain Java program say “yes” to an empty input?

    This is a Decision Problem because the question is asking whether a condition holds true for the given input (whether the Java program will output “yes” when the input is empty). Decision problems typically involve determining if a certain state or condition exists, and the solution is always a binary answer—true or false, yes or no.

  • How many ways can the letters of the word TRIANGLE be arranged?

    This is a Counting Problem because it requires calculating the number of distinct ways the letters in the word “TRIANGLE” can be arranged. Counting problems often involve permutations and combinations where you are determining the number of possible arrangements of objects or elements in different scenarios. Since the letters in “TRIANGLE” are all unique, the solution involves finding the number of permutations of the 8 letters, which is 8!8!, or 40,320.

  • The N-queens problem, where the goal is to place eight queens on a chessboard such that no queen attacks any other.

    This is a Search Problem because the task is to search for a valid configuration of the 8 queens on the chessboard that satisfies the constraints. Search problems involve finding a solution from a set of possible solutions that satisfy specific conditions or constraints. In this case, the solution requires finding an arrangement where no two queens share the same row, column, or diagonal.

Related Questions:

  1. What is the major difference between solving simple problems and complex problems?
  2. Why do software designers prefer to use IPO charts?
  3. What are the methods used to design a solution?
  4. Which computational thinking technique breaks down a problem into smaller parts?
  5. Identify three computing problems from other subjects you are studying.
  6. Why do we need to think computationally?
  7. Telephone numbers usually have 9 digits. The first two digits represent the area code and remain constant. The last 7 digits represent the number and cannot begin with 0. How many different telephone numbers are possible with a given area code?
  8. There are 4 different roads from city A to city B and 2 different roads from city B to city C. Draw a map of the given situation and determine how many possible routes exist from city A to city C passing through city B.
  9. Compare and contrast the star and ring network topologies.
  10. Why is mesh topology considered the most reliable but also the most expensive to implement?
  11. What is the role of the Application Layer in the OSI model?
  12. Describe the evolution of computer generations from the first generation to the fourth generation, highlighting the key technological developments and their impact on computing.
  13. Discuss the importance of categorizing and understanding different types of systems, both natural and artificial, and provide examples of each type.
  14. Explain the characteristics and potential challenges associated with fifth-generation computers that aim to understand natural languages and possess thinking capabilities. What are the implications of such advancements in computing on society?
  15. Explain the fundamental components of network communication, and how do they work together to facilitate data transfer?
  16. Describe the roles of common communication devices like hubs, switches, routers, and gateways in data communication. How do they contribute to the functionality of a network?
  17. Discuss the advantages and limitations of different network topologies including bus, star, ring, and mesh. When should each topology be used in a network design?
  18. What is the OSI model, and how does it help in understanding the process of data communication? Explain each of the seven layers and their functions.
  19. Explain the evolution of the Internet from its origins to the modern-day global network. What major technological advancements contributed to its growth?
  20. Discuss the advantages and disadvantages of the Internet, considering factors like global connectivity, information access, privacy concerns, and digital addiction.