Question

Sort the following vector of numbers using quicksort. Use the first value in the partition as the pivot value. You should be able to determine where each of the recursive calls and swaps are.

Vector: 95, 22, 76, 51, 8, 33, 5, 82, 46, 16, 60, 2

Answer 1

The quicksort algorithm is used to sort a vector by selecting a pivot, partitioning the array, and then recursively sorting the sub-arrays. The process involves choosing the pivot and making swaps when necessary to ensure sorted sub-arrays.

Step-by-step explanation:

The question involves sorting a vector of numbers using the quicksort algorithm. Quicksort is a comparison sort, where one element, called the pivot, is chosen from the array partition. All elements smaller than the pivot are moved before it, and all greater elements are moved after it. This partitioning is the key process within the quicksort, which recursively sorts the sub-arrays on the different sides of the pivot.

To sort the given vector: 95, 22, 76, 51, 8, 33, 5, 82, 46, 16, 60, 2, we start with 95 as our first pivot. Let's break down the steps to understand the recursion and swaps:

1. Pivot = 95. Partition: 2, 22, 76, 51, 8, 33, 5, 82, 46, 16, 60 swap 95 with 60 (the last element smaller than 95 in the partition).
2. Quicksort the sub-array to the left of 60.
3. Pivot = 2. Partition: Nothing to the left. Everything is greater than 2. Swap 2 with itself.
4. Quicksort the sub-array to the right of 2, which is the entire array minus 2.
5. Continue the same process, selecting a new pivot for each sub-array and partitioning until all sub-arrays have been sorted.

Note that the recursion continues, but only swaps when necessary. By recursively partitioning and sorting the sub-arrays, the vector will be fully sorted.