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Analyzing the Complexity of Algorithms

Description: This quiz is designed to assess your understanding of the concepts related to analyzing the complexity of algorithms. It covers topics such as time complexity, space complexity, and asymptotic analysis.
Number of Questions: 14
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Tags: algorithms complexity analysis time complexity space complexity asymptotic analysis
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Which of the following is not a common way to measure the time complexity of an algorithm?

  1. Big O notation

  2. Big Omega notation

  3. Big Theta notation

  4. Little o notation


Correct Option: D
Explanation:

Little o notation is not commonly used to measure the time complexity of an algorithm. It is used to describe the asymptotic behavior of a function as its input approaches a specific value.

What is the time complexity of an algorithm that performs a linear search on an array of size n?

  1. O(n)

  2. O(n log n)

  3. O(n²)

  4. O(1)


Correct Option: A
Explanation:

A linear search algorithm takes O(n) time because it needs to examine each element of the array in the worst case.

Which of the following algorithms has the best time complexity for sorting an array of size n?

  1. Bubble Sort

  2. Selection Sort

  3. Insertion Sort

  4. Merge Sort


Correct Option: D
Explanation:

Merge Sort has the best time complexity for sorting an array of size n, which is O(n log n). It uses the divide-and-conquer approach to sort the array efficiently.

What is the space complexity of an algorithm that stores the entire input array in memory while processing it?

  1. O(n)

  2. O(n log n)

  3. O(n²)

  4. O(1)


Correct Option: A
Explanation:

The space complexity of an algorithm that stores the entire input array in memory is O(n) because it requires n units of space to store each element of the array.

Which of the following sorting algorithms has the worst-case time complexity of O(n²)?

  1. Bubble Sort

  2. Selection Sort

  3. Insertion Sort

  4. Merge Sort


Correct Option: A
Explanation:

Bubble Sort has the worst-case time complexity of O(n²) because it compares each element of the array with every other element, resulting in a total of n * (n - 1) / 2 comparisons.

What is the time complexity of an algorithm that performs a binary search on a sorted array of size n?

  1. O(n)

  2. O(n log n)

  3. O(n²)

  4. O(1)


Correct Option: B
Explanation:

Binary search has a time complexity of O(n log n) because it repeatedly divides the search space in half, reducing the number of elements to be searched by a factor of 2 in each iteration.

Which of the following algorithms has the best space complexity for finding the minimum value in an array of size n?

  1. Linear Search

  2. Selection Sort

  3. Insertion Sort

  4. Merge Sort


Correct Option: A
Explanation:

Linear search has the best space complexity for finding the minimum value in an array of size n because it only requires O(1) space to store the current minimum value.

What is the time complexity of an algorithm that performs a depth-first search on a graph with V vertices and E edges?

  1. O(V)

  2. O(V + E)

  3. O(V²)

  4. O(E²)


Correct Option: B
Explanation:

The time complexity of depth-first search on a graph is O(V + E) because it visits each vertex and edge once in the worst case.

Which of the following algorithms has the worst-case space complexity of O(n²)?

  1. Bubble Sort

  2. Selection Sort

  3. Insertion Sort

  4. Merge Sort


Correct Option: A
Explanation:

Bubble Sort has the worst-case space complexity of O(n²) because it creates a temporary array of size n to store the sorted elements.

What is the time complexity of an algorithm that performs a breadth-first search on a graph with V vertices and E edges?

  1. O(V)

  2. O(V + E)

  3. O(V²)

  4. O(E²)


Correct Option: B
Explanation:

The time complexity of breadth-first search on a graph is O(V + E) because it visits each vertex and edge once in the worst case.

Which of the following algorithms has the best time complexity for finding the maximum value in an array of size n?

  1. Linear Search

  2. Selection Sort

  3. Insertion Sort

  4. Merge Sort


Correct Option: A
Explanation:

Linear search has the best time complexity for finding the maximum value in an array of size n because it only requires O(1) space to store the current maximum value.

What is the space complexity of an algorithm that stores the path from the root node to the target node in a binary search tree while searching for a specific value?

  1. O(n)

  2. O(n log n)

  3. O(n²)

  4. O(1)


Correct Option: A
Explanation:

The space complexity of storing the path from the root node to the target node in a binary search tree is O(n) because the worst-case scenario is when the target node is located at the deepest level of the tree.

Which of the following algorithms has the best time complexity for finding the median of an array of size n?

  1. Bubble Sort

  2. Selection Sort

  3. Insertion Sort

  4. Quick Select


Correct Option: D
Explanation:

Quick Select has the best time complexity for finding the median of an array of size n because it uses a randomized selection algorithm that has an expected time complexity of O(n).

What is the time complexity of an algorithm that performs a topological sort on a directed acyclic graph (DAG) with V vertices and E edges?

  1. O(V)

  2. O(V + E)

  3. O(V²)

  4. O(E²)


Correct Option: B
Explanation:

The time complexity of topological sort on a DAG is O(V + E) because it visits each vertex and edge once in the worst case.

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