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| Section | Objectives |
|---|---|
| Topic 1: Programming Foundations | - Programming Concepts
|
| Topic 2: Operating Systems & Architecture | - OS Fundamentals
|
| Topic 3: Computer Science Fundamentals | - Core CS Concepts
|
| Topic 4: Data & Security Basics | - Security Fundamentals
|
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NEW QUESTION # 22
Which statement describes the relationship between trees and graphs?
Answer: C
Explanation:
In discrete mathematics and computer science, atreeis a special kind ofgraph. The standard graph-theory definition is that a tree is aconnected, acyclicundirected graph. "Acyclic" means it containsno cycles, i.e., you cannot start at a vertex, follow a sequence of edges, and return to the starting vertex without repeating edges in a way that forms a loop. (Wikipedia) This property is exactly what makes option D correct.
The other options contradict the definition. If a structure has cycles, it is not a tree (though it may still be a graph). If it has unconnected nodes, it is not connected; such a structure is more like aforest(a disjoint union of trees) rather than a single tree. (Wikipedia) The idea of "levels" belongs to a particular computer-science representation called arooted tree, where one node is chosen as the root and nodes can be assigned depths
/levels based on distance from the root. But levels are not required in the abstract definition of a tree as a graph; they arise from choosing a root and orientation for convenience in algorithms like BFS/DFS, heaps, and parse trees.
So, the relationship is: every tree is a graph with extra structure-specifically, no cycles and (typically) connectivity-and the "no cycles" rule is the key distinguishing feature. (Discrete Mathematics)
NEW QUESTION # 23
What is the time complexity of a quicksort algorithm?
Answer: A
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
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