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Consider sorting the following array of integers in ascending order using an inplace Quicksort algorithm that uses the last element as the pivot.
\begin{array}{|l|l|l|l|l|}
\hline 60 & 70 & 80 & 90 & 100 \\
\hline
\end{array}

The minimum number of swaps performed during this Quicksort is $\_\_\_\_\_\_\_\_$.
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As array elements are already sorted so in quicksort partitioning there is no any swap required

(taking first or last element as pivot doesn't matter)
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To determine the minimum number of swaps performed during the Quicksort algorithm, we first need to partition the array using the last element (100) as the pivot. Then, we move all elements smaller than the pivot to the left of it and all elements greater than the pivot to the right of it.

Given the array:

\[ \text{[60, 70, 80, 90, 100]} \]

Using the last element (100) as the pivot, after partitioning, the array may look like this:

\[ \text{[60, 70, 80, 90, 100]} \]

Since the pivot element (100) is already at its correct position in the sorted array, there are no swaps needed for this partitioning step.

Next, we recursively apply the same process to the left and right subarrays. For the left subarray \([60, 70, 80, 90]\), the pivot is 90, and after partitioning, the array may remain the same as the pivot is already at its correct position.

For the right subarray, there is only one element (100), which is already sorted.

Therefore, no swaps are needed in this case.
So, the minimum number of swaps performed during this Quicksort is 0.

2 Comments

If the element is at right position then it is swapped with itself as Quick sort algorithm is having swap function in its algorithm. So that swap should be considered or not ?

I just want to clarify my thought whether it is True or not
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The question is true but we have to follow the actual value swaps. swap(a,a) is generally not counted. The primary reason is that if the question asks how many calls to the swap function then this thing can be considered.
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wrong it will be 0
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