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Which sorting algorithm will take least time when all elements of input array are identical? Consider typical implementations of sorting algorithms.
- a)Insertion Sort
- b)Heap Sort
- c)Merge Sort
- d)Selection Sort
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
Which sorting algorithm will take least time when all elements of inpu...
The insertion sort will take θ(n) time when input array is already sorted.
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Which sorting algorithm will take least time when all elements of inpu...
Insertion Sort is the sorting algorithm that will take the least time when all elements of the input array are identical. Here's why:
Explanation:
- Insertion Sort:
- In Insertion Sort, the algorithm checks each element in the array and moves it to its correct position by comparing it with elements on its left side.
- When all elements are identical, there is no need to move any elements around as they are already in the correct order.
- This results in the best-case time complexity of O(n) for Insertion Sort when all elements are the same, making it the most efficient choice in this scenario.
- Heap Sort, Merge Sort, and Selection Sort:
- Heap Sort, Merge Sort, and Selection Sort have worst-case time complexities of O(n log n), O(n log n), and O(n^2) respectively, regardless of the input array being identical or not.
- These algorithms involve more comparisons and movements of elements, which are unnecessary when all elements are the same.
Therefore, in the case where all elements of the input array are identical, Insertion Sort is the most efficient sorting algorithm due to its linear time complexity.
Explanation:
- Insertion Sort:
- In Insertion Sort, the algorithm checks each element in the array and moves it to its correct position by comparing it with elements on its left side.
- When all elements are identical, there is no need to move any elements around as they are already in the correct order.
- This results in the best-case time complexity of O(n) for Insertion Sort when all elements are the same, making it the most efficient choice in this scenario.
- Heap Sort, Merge Sort, and Selection Sort:
- Heap Sort, Merge Sort, and Selection Sort have worst-case time complexities of O(n log n), O(n log n), and O(n^2) respectively, regardless of the input array being identical or not.
- These algorithms involve more comparisons and movements of elements, which are unnecessary when all elements are the same.
Therefore, in the case where all elements of the input array are identical, Insertion Sort is the most efficient sorting algorithm due to its linear time complexity.
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