Master Divide-and-Conquer Algorithms: Enhance Your Problem-Solving Skills

Question 1

Which of the following is NOT a characteristic of divide-and-conquer algorithms?

Accepted Answer

Always having a time complexity of O(n^2)

Answer

Recursively breaking down the problem into smaller subproblems

Answer

Solving subproblems separately

Answer

Combining solutions of subproblems to solve the original problem

Question 2

Which algorithm below is NOT a divide-and-conquer algorithm?

Accepted Answer

Selection sort

Answer

Merge sort

Answer

Quick sort

Answer

Binary search

Question 3

What is the worst-case time complexity of quick sort?

Accepted Answer

O(n^2)

Answer

O(n)

Answer

O(n log n)

Answer

The worst-case time complexity cannot be determined.

Question 4

Which of the following is an advantage of merge sort over other divide-and-conquer sorting algorithms?

Accepted Answer

It is stable.

Answer

It runs in-place.

Answer

It has O(1) space complexity.

Answer

It is the fastest sorting algorithm.

Question 5

Which step is NOT part of the quick sort algorithm?

Accepted Answer

Calculating the median of the array

Answer

Partitioning the array based on a pivot

Answer

Recursively applying quick sort to subarrays

Answer

Combining sorted subarrays into a single sorted array

Question 6

In quick sort, the purpose of the pivot element is to:

Accepted Answer

Divide the array into approximately equal-sized subarrays

Answer

Represent the median of the array

Answer

Determine the position of the smallest element

Answer

Compare every element in the array

Question 7

Identify the crucial step in the quick sort algorithm.

Accepted Answer

Partitioning the array into two subarrays

Answer

Recursively sorting each subarray

Answer

Finding the array's median

Answer

Swapping the array's first and last elements

Question 8

Write the recurrence relation for binary search's time complexity.

Accepted Answer

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

Answer

T(n) = T(n/3) + c

Answer

T(n) = T(n/4) + c

Answer

T(n) = T(n/2) + T(n/4) + c

Question 9

Which of the following is NOT an advantage of divide-and-conquer algorithms?

Accepted Answer

Guaranteed optimal solutions

Answer

Efficiency for large problem sizes

Answer

Simplicity of implementation

Answer

Suitability for parallel computing

Question 10

Which of the following accurately defines the essence of divide-and-conquer algorithms?

Accepted Answer

They systematically decompose a problem into smaller subproblems until they reach a base case, then combine the solutions to obtain the final solution.

Answer

They employ brute force to exhaustively explore all possible solutions.

Answer

They require a stack to store the subproblems, ensuring a depth-first traversal.

Answer

They sort the problem input before applying any further operations.

Question 11

Which of the following is NOT a key step in the quick sort algorithm?

Accepted Answer

Finding the maximum element in the array

Answer

Partitioning the array into two subarrays based on a pivot element

Answer

Recursively sorting the subarrays

Answer

Combining the sorted subarrays

Question 12

The purpose of a recurrence relation in the analysis of divide-and-conquer algorithms is to:

Accepted Answer

Represent the relationship between the input size and the time complexity of the algorithm

Answer

Determine the maximum depth of recursion

Answer

Calculate the space complexity of the algorithm

Answer

Prove the correctness of the algorithm

Question 13

Which of the following is a practical application of the binary search algorithm?

Accepted Answer

Searching for a specific element in a sorted array

Answer

Sorting an unsorted array

Answer

Finding the minimum element in an array

Answer

Merging two unsorted arrays

Question 14

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

Accepted Answer

O(1)

Answer

O(n)

Answer

O(n log n)

Answer

O(n^2)

Question 15

The base case for the recurrence relation that describes the time complexity of merge sort is:

Accepted Answer

When the array has only one element

Answer

When the array is empty

Answer

When the array is sorted

Answer

When the array has an even number of elements

Question 16

A key advantage of using a divide-and-conquer approach to problem-solving is that it:

Accepted Answer

Decomposes complex problems into smaller, more manageable subproblems

Answer

Guarantees an optimal solution to the problem

Answer

Reduces the space complexity of the algorithm

Answer

Eliminates the need for recursion

Question 17

The expected time complexity of binary search on a sorted array of size 'n' is:

Accepted Answer

O(log n)

Answer

O(1)

Answer

O(n)

Answer

O(n^2)

Question 18

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

Accepted Answer

When the array has one element

Answer

When the array is sorted

Answer

When the array has an odd number of elements

Answer

When the array has a duplicate element

Question 19

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

Accepted Answer

O(n^2)

Answer

O(n)

Answer

O(n log n)

Answer

O(2^n)

Question 20

Which of the following recurrence relations represents the time complexity of the binary search algorithm?

Accepted Answer

T(n) = T(n/2) + 1

Answer

T(n) = T(n/3) + 1

Answer

T(n) = T(2n) + 1

Answer

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

Question 21

Which of the following is NOT a characteristic of divide-and-conquer algorithms?

Accepted Answer

Having a time complexity of O(n)

Answer

Dividing the problem into smaller subproblems

Answer

Solving the subproblems recursively

Answer

Combining the solutions of the subproblems

Question 22

Which of the following is NOT a characteristic of divide-and-conquer algorithms?

Accepted Answer

They modify the original input.

Answer

They divide the problem into smaller subproblems.

Answer

They conquer the subproblems recursively.

Answer

They combine the solutions to the subproblems to solve the original problem.

Question 23

What is the time complexity of the merge sort algorithm?

Accepted Answer

O(n log n)

Answer

O(n)

Answer

O(n^2)

Answer

O(log n)

Question 24

What is a key difference between the merge sort and quick sort algorithms?

Accepted Answer

Merge sort is stable while quick sort is not.

Answer

Quick sort is stable while merge sort is not.

Answer

Merge sort is in-place while quick sort is not.

Answer

They have the same time complexity.

Question 25

What is the worst-case time complexity of the binary search algorithm?

Accepted Answer

O(log n)

Answer

O(1)

Answer

O(n)

Answer

O(n^2)

Question 26

Which of the following recurrence relations represents the time complexity of merge sort?

Accepted Answer

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

Answer

T(n) = T(n/2) + T(n/4) + ... + T(1) + O(n)

Answer

T(n) = nT(n-1) + O(1)

Answer

T(n) = 2T(n-1) + O(n^2)

Question 27

How is the pivot element chosen in the quick sort algorithm?

Accepted Answer

The middle element of the list or a random element of the list

Answer

The first element of the list.

Answer

The last element of the list.

Answer

The element with the largest value in the list.

Question 28

What is the difference between a recursive and iterative solution to a problem?

Accepted Answer

Recursive solutions use recursion while iterative solutions use loops.

Answer

Iterative solutions use recursion while recursive solutions use loops.

Answer

They are the same thing.

Answer

Recursive solutions are always more efficient than iterative solutions.

Question 29

Which of the following is NOT a step in the merge sort algorithm?

Accepted Answer

Merge the sorted halves in arbitrary order

Answer

Divide the array into two halves

Answer

Recursively sort each half

Answer

Ensure that the final array is sorted in ascending order

Question 30

What is the time complexity of merge sort for an array of size n?

Accepted Answer

O(n log n)

Answer

O(n)

Answer

O(n^2)

Answer

O(log n)

Question 31

What is the base case for the binary search algorithm?

Accepted Answer

When the start and end indices cross.

Answer

When the array is empty.

Answer

When the target value is found.

Answer

When the array size is 1.

Question 32

Which of the following problems is NOT suitable for a divide-and-conquer approach?

Accepted Answer

Finding the shortest path in a graph

Answer

Sorting an array

Answer

Searching a sorted array

Answer

Computing the Fibonacci sequence

Question 33

Which of the following is the time complexity of merge sort?

Accepted Answer

O(n log n)

Answer

O(n)

Answer

O(n^2)

Answer

O(log n)

Question 34

Which of the following is NOT a step in the quick sort algorithm?

Accepted Answer

Merge the sorted subarrays.

Answer

Choose a pivot element.

Answer

Partition the array into two subarrays.

Answer

Sort the subarrays recursively.

Question 35

What is the worst-case performance of binary search?

Accepted Answer

O(log n)

Answer

O(1)

Answer

O(n)

Answer

O(n^2)

Question 36

What is the key difference between merge sort and quick sort?

Accepted Answer

Merge sort is stable, while quick sort is not

Answer

Quick sort is faster than merge sort on average

Answer

Merge sort uses more memory than quick sort

Answer

Quick sort is more difficult to implement than merge sort

Question 37

Which of the following is a key advantage of using a divide-and-conquer algorithm?

Accepted Answer

Breaks down complex problems into smaller, simpler subproblems

Answer

Solves problems of exponential complexity

Answer

Guarantees an optimal solution

Answer

Prevents the potential for stack overflow

Question 38

What is the time complexity of the merge sort algorithm?

Accepted Answer

O(n log n)

Answer

O(n^2)

Answer

O(n)

Answer

O(log n)

Question 39

Given a sorted array, what is the time complexity of binary search?

Accepted Answer

O(log n)

Answer

O(n)

Answer

O(n^2)

Answer

O(1)

Question 40

Which of the following is a key distinction between merge sort and quick sort?

Accepted Answer

Merge sort is a stable sorting algorithm, while quick sort is not

Answer

Quick sort has a guaranteed O(n log n) time complexity, while merge sort does not

Answer

Merge sort is a bottom-up algorithm, while quick sort is a top-down algorithm

Answer

Merge sort does not require additional space for merging, while quick sort does

Question 41

What is the goal of the partition step in quick sort?

Accepted Answer

To divide the array into two subarrays

Answer

To sort the entire array

Answer

To determine the median of the array

Answer

To reduce the size of the array by half

Question 42

Which of the following is a potential drawback of divide-and-conquer algorithms?

Accepted Answer

Complexity of implementation

Answer

Increased time complexity

Answer

Reduced efficiency

Answer

Reduced memory usage

Question 43

What is the time complexity of merge sort?

Accepted Answer

O(n log n)

Answer

O(n)

Answer

O(n^2)

Answer

O(n log n^2)

Question 44

Which of the following is a recursive step in the merge sort algorithm?

Accepted Answer

Merging the sorted halves

Answer

Dividing the array into two halves

Answer

Sorting the array using a base case

Answer

Finding the midpoint of the array