In the Selection Sort algorithm, the best-case scenario occurs when the array is already sorted in ascending order. In this situation, one might think that the best-case time complexity could be reduced to O(n) since the algorithm should detect the sorted state and avoid unnecessary swaps.
However, in Selection Sort, even when the array is sorted, the algorithm will still perform the same number of comparisons as in the average and worst-case scenarios. Let's go through the steps of Selection Sort in the best-case scenario:
For each iteration (i = 0 to i = n-1):
Assume the current element is the minimum (min_idx = i).
Find the minimum element in the unsorted part of the array (j = i+1 to j = n-1).
Perform the swap (if needed) to place the minimum element in its correct position.
Even when the array is sorted, Selection Sort will still compare each element with all other elements in the unsorted part to find the minimum element. This results in the same number of comparisons as in the average and worst-case scenarios.
As a result, the best-case time complexity of Selection Sort remains O(n^2), which is less efficient compared to algorithms that can achieve O(n) time complexity for the best-case scenario, such as Optimized Bubble Sort, Insertion Sort, or algorithms like Merge Sort and Quick Sort, which can achieve O(n log n) time complexity in all cases.
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Best Case Big O of Bubble vs Insertion Sort
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In the Selection Sort algorithm, the best-case scenario occurs when the array is already sorted in ascending order. In this situation, one might think that the best-case time complexity could be reduced to O(n) since the algorithm should detect the sorted state and avoid unnecessary swaps.
However, in Selection Sort, even when the array is sorted, the algorithm will still perform the same number of comparisons as in the average and worst-case scenarios. Let's go through the steps of Selection Sort in the best-case scenario:
For each iteration (i = 0 to i = n-1):
Assume the current element is the minimum (min_idx = i).
Find the minimum element in the unsorted part of the array (j = i+1 to j = n-1).
Perform the swap (if needed) to place the minimum element in its correct position.
Even when the array is sorted, Selection Sort will still compare each element with all other elements in the unsorted part to find the minimum element. This results in the same number of comparisons as in the average and worst-case scenarios.
As a result, the best-case time complexity of Selection Sort remains O(n^2), which is less efficient compared to algorithms that can achieve O(n) time complexity for the best-case scenario, such as Optimized Bubble Sort, Insertion Sort, or algorithms like Merge Sort and Quick Sort, which can achieve O(n log n) time complexity in all cases.