Which of the following Big O notations is appropriate for the complexity of a search algorithm?

Homework Help: Questions and Answers: Which of the following Big O notations is appropriate for the complexity of a search algorithm?

A. O(logn)
B. O(1)
C. O(n2)
D. O(n)

Answer

To determine the appropriate Big O notation for the complexity of a sorting algorithm, let’s find the most common sorting algorithms and their time complexities.

Given Options: Step by Step Answering

a) O(logn) – Logarithmic Time Complexity:

• This is typical for search algorithms that work by repeatedly dividing the data set in half, like binary search. Binary search operates on sorted data and eliminates half of the remaining elements at each step, which results in logarithmic time complexity. So, this complexity is valid for certain types of search algorithms.

b) O(1) – Constant Time Complexity:

• This occurs when the time it takes to find the element is the same regardless of the size of the input. An example would be directly accessing an element in an array by index (like an array lookup). However, for a general search algorithm (like linear or binary search), this is usually not the case. Thus, O(1) is not a common complexity for search algorithms.

c) O(n²) – Quadratic Time Complexity:

• This typically appears in algorithms involving nested loops, like some sorting algorithms (e.g., bubble sort). However, quadratic complexity is not commonly associated with search algorithms. 

d) O(n) – Linear Time Complexity:

• This is typical for a linear search algorithm, where you search through each element in the data set one by one. In the worst case, you’ll have to examine all n elements, which gives you a time complexity of O(n).

Final Answer

The appropriate Big O notations for search algorithms would typically be:

• O(logn) for algorithms like binary search, where the input data is divided repeatedly.
• O(n) for linear search, where each element is checked sequentially.

Hence, the correct answers are A. O(logn) and D. O(n), depending on the search method.

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