Homework Help: Questions and Answers: Which of the following Big O notations is appropriate for the complexity of a sort 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(log n):
- This time complexity is common in algorithms that reduce the problem size exponentially at each step, such as binary search.
- However, no standard sorting algorithm has a worst-case or average-case time complexity of O(log n).
b) O(1):
- O(1) implies that the algorithm runs in constant time, regardless of the size of the input.
- Sorting algorithms cannot run in O(1) because sorting requires processing the entire input.
c) O(n²):
- This is the time complexity of simple sorting algorithms like bubble sort, insertion sort, and selection sort in their worst cases.
- These algorithms iterate through the list multiple times, resulting in a quadratic time complexity of O(n²).
4. O(n):
- O(n) represents linear time complexity.
- Sorting an unsorted array in O(n) is only possible in specific cases, such as with counting sort, radix sort, or bucket sort, where certain assumptions about the data are made (e.g., the range of values is limited).
- However, general comparison-based sorting algorithms like merge sort, quick sort, or heap sort cannot achieve O(n) complexity in the average or worst case.
Final Answer
Based on the above analysis, the correct answer is:
C. O(n²)
This is correct option, because:
- O(n²) is a common and realistic complexity for many basic sorting algorithms
- It represents algorithms like bubble sort, selection sort, and insertion sort
- While some more efficient algorithms exist (like O(n log n)), O(n²) is definitely an appropriate complexity for sorting
- The other options are too efficient to be realistic for a sorting algorithm
Therefore, among the given options, C. O(n²) is the most appropriate Big O notation for a sort algorithm.
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