Challenging Algorithms and Sorting Concepts

What is the time complexity of the worst-case scenario for Quick Sort?

• O(log n)

• O(n)

• O(n log n)

• O(n^2)

Explain the difference between stable and unstable sorting algorithms.

• Unstable sorting algorithms can only sort numbers.

• Stable sorting algorithms are faster than unstable ones.

• Stable sorting algorithms preserve the order of equal elements; unstable sorting algorithms do not.

• Stable sorting algorithms can sort only strings.

What is the primary advantage of using Merge Sort over Quick Sort?

• Merge Sort is stable.

• Merge Sort requires less comparison operations.

• Merge Sort is faster for small datasets.

• Quick Sort is more memory efficient.

Define Big O notation and provide an example of its use.

• O(n^2) suggests that the algorithm's time complexity decreases with larger inputs.

• O(1) indicates constant time complexity regardless of input size.

• O(log n) means the algorithm's performance is unaffected by input size.

• An example of Big O notation is O(n), which indicates that the time complexity of an algorithm grows linearly with the size of the input n.

How does Shell Sort improve upon Insertion Sort?

• Shell Sort uses a single gap to compare elements, similar to Insertion Sort.

• Shell Sort requires more memory than Insertion Sort.

• Shell Sort allows for larger gaps between elements, reducing the number of inversions and improving efficiency over Insertion Sort.

• Shell Sort is slower than Insertion Sort for small datasets.

What is the average-case time complexity of Heap Sort?

• O(n)

• O(log n)

• O(n^2)

• O(n log n)

Describe the concept of 'divide and conquer' in algorithm design.

• Divide and conquer is an algorithm design paradigm that divides a problem into smaller subproblems, solves them independently, and combines their solutions.

• Divide and conquer is an approach that only works for linear problems.

• Divide and conquer is a method that combines all subproblems into one large problem.

• Divide and conquer focuses on solving problems sequentially without breaking them down.

What are the key factors to consider when analyzing the performance of an algorithm?

• Time complexity, space complexity, scalability, efficiency, input size, and data structure.

• Cost of development, marketing strategy, user feedback

• User interface design, documentation quality, community support

• Algorithm's popularity, implementation language, developer experience

Explain the significance of the Master Theorem in analyzing recursive algorithms.

• The Master Theorem is significant because it allows for efficient analysis of the time complexity of recursive algorithms.

• The Master Theorem provides a way to analyze iterative algorithms exclusively.

• The Master Theorem is only applicable to non-recursive algorithms.

• The Master Theorem is significant for its role in sorting algorithms only.

What is the worst-case time complexity of Bubble Sort and why is it inefficient?

• O(n^2)

• O(log n)

• O(n log n)

• O(n)