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| Section | Weight | Objectives |
|---|---|---|
| Topic 1: Discrete Mathematics & Logic | 25% | - Boolean algebra and digital logic - Propositional and predicate logic - Set theory, relations, functions - Proof techniques and mathematical induction |
| Topic 2: Algorithms & Complexity | 25% | - Algorithm design and analysis - Recursion and iterative structures - Sorting and searching algorithms - Big O notation, time and space complexity |
| Topic 3: Software Engineering & Programming Basics | 15% | - Testing and debugging fundamentals - Basic syntax and control structures - Programming paradigms - Software development lifecycle |
| Topic 4: Computer Architecture & Organization | 15% | - CPU, memory, I/O systems - Memory hierarchy and performance - Instruction sets and execution cycles - Von Neumann architecture |
| Topic 5: Data Structures | 20% | - Data storage and retrieval principles - Primitive and composite data types - Trees, graphs, hash tables - Arrays, linked lists, stacks, queues |
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NEW QUESTION # 70
Which principle can be used to implement an algorithm to calculate factorial or Fibonacci sequence?
Answer: D
Explanation:
Factorial and Fibonacci are classic examples used to teachrecursion, a technique where a function solves a problem by calling itself on smaller subproblems. The key requirement for recursion is (1) abase casethat stops further calls and (2) arecursive casethat reduces the problem size. For factorial, the definition is (n! = n
\times (n-1)!) with base case (0! = 1) (or (1! = 1)). For Fibonacci, (F(n) = F(n-1) + F(n-2)) with base cases (F (0)=0) and (F(1)=1). These mathematical definitions map directly into recursive code, which is why textbooks frequently introduce recursion using these sequences.
While factorial and Fibonacci can also be computed iteratively, the question asks for the principle that can be used to implement such algorithms, and recursion is the canonical textbook answer. Recursion also connects to important CS topics: call stacks, activation records, and divide-and-conquer problem solving.
Option A ("procedural programming") and option D ("object-oriented programming") are broader paradigms rather than the specific technique used in the classic implementations. Option B ("iterative programming") is a valid alternative approach, but the standard instructional principle highlighted for these particular examples is recursion. Textbooks also note that naive recursive Fibonacci is inefficient (exponential time) unless optimized with memoization or converted to an iterative or dynamic programming approach.
NEW QUESTION # 71
What is the time complexity of a quicksort algorithm?
Answer: D
Explanation:
Quicksort is a divide-and-conquer sorting algorithm. It works by selecting a pivot element, partitioning the array into two subarrays (elements less than the pivot and elements greater than the pivot), and then recursively sorting those subarrays. In the average case, the partition step splits the array into roughly equal halves, so the recurrence is commonly written as (T(n) = T(n/2) + T(n/2) + O(n)), where (O(n)) is the cost of partitioning. This solves to (O(n \log n)), which is why quicksort is widely taught as an efficient general- purpose sorting method.
However, textbooks also emphasize that quicksort has a worst-case time complexity of (O(n