Advanced Sorting Algorithms: Master Merge Sort and Quick Sort

Question 1

In the divide-and-conquer approach to problem-solving, what is the initial step?

Accepted Answer

Breaking the problem into smaller subproblems

Answer

Solving the problem directly without decomposition

Answer

Ignoring the problem and moving on

Answer

Simplifying the problem using a heuristic

Question 2

What is the average-case time complexity of the quick sort algorithm?

Accepted Answer

O(n log n)

Answer

O(n)

Answer

O(n^2)

Answer

O(n log n^2)

Question 3

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

Accepted Answer

O(n^2)

Answer

O(n log n)

Answer

O(log n)

Question 4

Which of the following is the base case for merge sort when the array is being divided?

Accepted Answer

When there is only one element in the array.

Answer

When there are two elements in the array.

Answer

When the array is empty.

Answer

When the array is sorted.

Question 5

What is the time complexity of merge sort in the average case when the array has n elements?

Accepted Answer

O(n log n)

Answer

O(n^2)

Answer

O(log n)

Answer

O(n)

Question 6

Which of the following is an advantage of merge sort over quick sort?

Accepted Answer

Guaranteed O(n log n) time complexity.

Answer

In-place sorting.

Answer

Recursive nature.

Answer

Divide-and-conquer approach.

Question 7

What is the purpose of the "partition" function in quick sort?

Accepted Answer

To divide the array into two subarrays based on a pivot.

Answer

To sort the entire array.

Answer

To find the smallest element in the array.

Answer

To merge two sorted subarrays.

Question 8

Which of the following algorithms is most suitable for sorting a large array that is mostly sorted?

Accepted Answer

Merge sort

Answer

Quick sort

Answer

Bubble sort

Answer

Insertion sort

Question 9

Both Merge Sort and Quick Sort employ which strategy?

Accepted Answer

Divide-and-conquer

Answer

Selection

Answer

Insertion

Answer

Bubble

Question 10

In Merge Sort, which phase combines the sorted sub-arrays?

Accepted Answer

Merge

Answer

Divide

Answer

Sort

Answer

Conquer

Question 11

Which of the following is NOT a potential drawback of Quick Sort?

Accepted Answer

Guaranteed O(n log n) time complexity

Answer

Reduced efficiency on nearly sorted arrays

Answer

Increased stack usage

Answer

Recursion overhead

Question 12

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

Accepted Answer

O(n log n)

Answer

O(n^2)

Answer

O(n)

Answer

O(log n)

Question 13

In Quick Sort, which approach is commonly used to select the pivot element?

Accepted Answer

Median-of-three

Answer

First element

Answer

Last element

Answer

Middle element

Question 14

In terms of stability, what is the difference between Merge Sort and Quick Sort?

Accepted Answer

Merge Sort is stable, while Quick Sort is not

Answer

Quick Sort is stable, while Merge Sort is not

Answer

Both Merge Sort and Quick Sort are stable

Answer

Neither Merge Sort nor Quick Sort are stable

Question 15

Which of the following is a practical application of Merge Sort?

Accepted Answer

Sorting large datasets efficiently

Answer

Finding the median of an array

Answer

Generating random numbers

Answer

Searching for a particular element

Question 16

Which of the following is the base case for the merge sort algorithm?

Accepted Answer

The array has only one element

Answer

The array is empty

Answer

The array is sorted

Answer

The array is fully reversed

Question 17

What is the purpose of the pivot element in the quick sort algorithm?

Accepted Answer

To divide the array into two subarrays

Answer

To determine the sorted position of the element

Answer

To maintain the stability of the sorted results

Answer

To improve the time complexity of the algorithm

Question 18

What is the purpose of the recursion in the quick sort algorithm?

Accepted Answer

To divide the array into smaller subarrays

Answer

To maintain the stability of the sorted results

Answer

To handle duplicate elements efficiently

Answer

To improve the time complexity of the algorithm

Question 19

What is the key idea behind the divide-and-conquer approach used in merge sort and quick sort?

Accepted Answer

Breaking down the problem into smaller subproblems, solving them, and combining the results

Answer

Sorting the elements incrementally by comparing adjacent elements

Answer

Reversing the order of the elements in the array

Answer

Shuffling the elements in the array randomly

Question 20

What is the time complexity of merge sort?

Accepted Answer

O(n log n)

Answer

O(n^2)

Answer

O(n)

Answer

O(log n)

Question 21

In merge sort, the merge step involves:

Accepted Answer

Combining two sorted subarrays into one sorted array

Answer

Dividing the array into two subarrays

Answer

Recursively sorting subarrays

Answer

Selecting the pivot element

Question 22

Which of the following is NOT a potential application of merge sort?

Accepted Answer

Sorting very small arrays

Answer

External sorting

Answer

Sorting linked lists

Answer

Implementing a priority queue

Question 23

In quick sort, the process of rearranging elements around a pivot is known as:

Accepted Answer

Partitioning

Answer

Dividing

Answer

Merging

Answer

Conquering

Question 24

For an array of size n, what is the time complexity of merge sort?

Accepted Answer

O(n log n)

Answer

O(n)

Answer

O(n^2)

Question 25

Which of the following describes the recursive property of quick sort?

Accepted Answer

The array is divided into two subarrays, and each subarray is sorted independently.

Answer

The middle element is chosen as the pivot, and the array is partitioned around it.

Answer

The array is sorted until it is empty.

Question 26

In quick sort, what is the significance of the pivot element?

Accepted Answer

It divides the array into two subarrays of approximately equal size.

Answer

It is the smallest element in the array.

Answer

It has no impact on the sorting process.

Question 27

What is the purpose of the sentinel node in merge sort?

Accepted Answer

It simplifies the merging of sorted subarrays.

Answer

It serves as a placeholder at the end of the array.

Answer

It allows the algorithm to handle empty subarrays.

Question 28

What is the space complexity of quick sort for an array of size n?

Accepted Answer

O(1)

Answer

O(n)

Answer

O(log n)

Question 29

Which optimization is commonly applied to merge sort?

Accepted Answer

Bottom-up approach

Answer

Using a heap instead of merging subarrays

Answer

Multiple cores for parallel processing

Question 30

What is the worst-case performance of quick sort?

Accepted Answer

O(n^2)

Answer

O(n)

Answer

O(n log n)

Question 31

Which of the following is a practical application of merge sort?

Accepted Answer

External sorting of large datasets

Answer

Sorting linked lists

Answer

Frequency counting

Question 32

In merge sort, the process of repeatedly dividing the list into smaller parts until they become individual elements is known as:

Accepted Answer

Splitting

Answer

Merging

Answer

Sorting

Answer

Comparing

Question 33

Which of the following time complexities represents merge sort's average and best-case performance?

Accepted Answer

O(n log n)

Answer

O(log n)

Answer

O(n^2)

Answer

O(n)

Question 34

In quick sort, the element selected as a benchmark to partition the list is referred to as the:

Accepted Answer

Pivot

Answer

Median

Answer

Middle element

Answer

Minimum element

Question 35

Comparing merge sort and quick sort, which algorithm has a more consistent time complexity, meaning its performance is less affected by the input data?

Accepted Answer

Merge sort

Answer

Quick sort

Answer

Both have similar consistency

Answer

Neither has consistent time complexity

Question 36

Which of the following techniques is employed in quick sort to enhance its average-case performance?

Accepted Answer

Randomized pivoting

Answer

Tail recursion optimization

Answer

Sentinel value usage

Answer

In-place sorting

Question 37

In the context of quick sort, what is the purpose of the partitioning step?

Accepted Answer

To divide the list into two sublists based on a pivot element

Answer

To find the median element

Answer

To sort the entire list

Answer

To find the maximum and minimum elements

Question 38

Which sorting algorithm employs a divide-and-conquer strategy, recursively dividing the unsorted list into halves, sorting each half, and merging them into a sorted whole?

Accepted Answer

Merge Sort

Answer

Heap Sort

Answer

Counting Sort

Answer

Insertion Sort

Question 39

The time complexity of Merge Sort for an array of size n is:

Accepted Answer

O(n log n)

Answer

O(log n)

Answer

O(n^2)

Answer

O(n)

Question 40

Which sorting algorithm selects a pivot element, partitions the list into two sublists based on the pivot, and recursively sorts the sublists?

Accepted Answer

Quick Sort

Answer

Radix Sort

Answer

Merge Sort

Answer

Bubble Sort

Question 41

A potential drawback of Quick Sort is its:

Accepted Answer

Worst-case time complexity of O(n^2)

Answer

Additional memory requirement

Answer

Difficult to implement

Answer

Not stable

Question 42

In Merge Sort, which step involves dividing the array into two halves?

Accepted Answer

Divide

Answer

Conquer

Answer

Merge

Answer

Pivot

Question 43

Which of the following accurately represents the time complexity of Merge Sort?

Accepted Answer

O(n log n)

Answer

O(n^2)

Answer

O(n)

Question 44

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

Accepted Answer

O(n^2)

Answer

O(n log n)

Answer

O(n)

Question 45

For large datasets, which sorting algorithm is more efficient?

Accepted Answer

Merge Sort

Answer

Bubble Sort

Answer

Selection Sort

Answer

Insertion Sort

Question 46

In Merge Sort, what is the purpose of the conquer step?

Accepted Answer

Merge two sorted halves into a single sorted array

Answer

Find the maximum element in the array

Answer

Split the array into smaller segments

Question 47

State the recurrence relation for the time complexity of Merge Sort:

Accepted Answer

T(n) = 2T(n/2) + c

Answer

T(n) = c

Answer

T(n) = T(n-1) + c

Answer

T(n) = nT(n/2)

Question 48

In Quick Sort, after partitioning, the elements to the left and right of the pivot are arranged such that:

Accepted Answer

Elements to the left are smaller than the pivot, while elements to the right are greater than or equal to the pivot

Answer

Elements to the left are greater than the pivot, while elements to the right are smaller than or equal to the pivot

Question 49

Which algorithm utilizes a sentinel value to simplify boundary conditions during partitioning?

Accepted Answer

Quick Sort

Answer

Merge Sort

Answer

Bubble Sort

Answer

Insertion Sort

Question 50

In Merge Sort, the primary operation in the merge step involves:

Accepted Answer

Comparing and merging elements from two sorted subarrays.

Answer

Swapping elements within a single subarray.

Answer

Recursively dividing the array into smaller subarrays.

Answer

Finding a pivot element and partitioning the array.

Question 51

If the pivot in Quick Sort is consistently chosen as the last element, what input array arrangement leads to the worst-case scenario?

Accepted Answer

The array is already sorted in ascending or descending order.

Answer

The array contains many duplicate elements.

Answer

The array has elements alternating between large and small values.

Answer

The array is randomly ordered.

Question 52

The primary advantage of using a divide-and-conquer approach in sorting algorithms like Merge Sort and Quick Sort is:

Accepted Answer

Efficiently breaking down the problem into smaller, recursively solvable subproblems.

Answer

Eliminating the need for additional memory space.

Answer

Ensuring a stable sorting order for equal elements.

Answer

Simplifying the implementation of the sorting algorithm.

Question 53

In Merge Sort, how are the sorted subarrays combined to produce the final sorted output?

Accepted Answer

By merging the sorted subarrays pairwise, comparing elements from each.

Answer

By swapping elements within each subarray based on their sorted order.

Answer

By iteratively selecting the minimum element from each subarray.

Answer

By simply concatenating the sorted subarrays together.