Practice code with the "Quick Sort" algorithm
The principle of Quick sort algorithm
Quick sort is an efficient sorting algorithm. Here’s how it works:
 Choose a pivot: select an element from the array (commonly the first, last, or a random element).
 Partition: rearrange the array so elements less than the pivot come before it, and elements greater come after. The pivot is now in its final position.
 Recursively sort: apply the same process to the subarrays on either side of the pivot.
 Base case: stop when subarrays have one or zero elements, as they are already sorted.
Example
Let’s go through Quick Sort stepbystep with the example array [5, 3, 7, 6, 2, 1, 8]
.
 Initial Array:
[5, 3, 7, 6, 2, 1, 8]
 Pivot:
5
(first element)
Step 1: Partitioning
 Elements less than
5
:[3, 2, 1]
 Elements equal to
5
:[5]
 Elements greater than
5
:[7, 6, 8]
The array now looks like: [3, 2, 1] [5] [7, 6, 8]
Step 2: Recursively sort subarrays
Left subarray [3, 2, 1]
:
 Pivot:
3
 Partitioning:
 Elements less than
3
:[2, 1]
 Elements equal to
3
:[3]
 Elements greater than
3
:[]
 Elements less than
The array now looks like: [2, 1] [3] []
Right subarray [7, 6, 8]
:
 Pivot:
7
 Partitioning:
 Elements less than
7
:[6]
 Elements equal to
7
:[7]
 Elements greater than
7
:[8]
 Elements less than
The array now looks like: [6] [7] [8]
Step 3: Recursively sort again
Left subarray [2, 1]
:
 Pivot:
2
 Partitioning:
 Elements less than
2
:[1]
 Elements equal to
2
:[2]
 Elements greater than
2
:[]
 Elements less than
The array now looks like: [1] [2] []
[6] [7] [8]
is already sorted.
Step 4: Combine sorted arrays
 Left part:
[1, 2, 3]
 Middle part:
[5]
 Right part:
[6, 7, 8]
Final sorted array: [1, 2, 3, 5, 6, 7, 8]
The naive simple version
This version of quicksort correctly implements the core idea but differs from the “classic” quicksort in a few ways:
 Classic quicksort sorts the array in place, without using additional lists (
smaller_elements
andlarger_elements
). It rearranges elements within the original array to partition around the pivot.
The real version
A closer version of quick sort would look like this:
Alternatives
 Pivot selection: while choosing the first or last element as the pivot is a valid approach, it’s not the only one. The medianofthree method, which selects the median of the first, middle, and last elements, is often used to improve performance and reduce the chance of encountering worstcase scenarios.
 Twopointer technique: classic quicksort does indeed use a twopointer technique. One pointer starts at the beginning and the other at the end, moving towards each other to partition the array. This method can improve efficiency by reducing the number of swaps needed.
Complexity
The time complexity of quicksort can vary depending on how the pivot is chosen and the input array’s characteristics:

Best case: O(n log n): this occurs when the pivot is chosen in such a way that it divides the array into two nearly equal halves each time.

Average case: O(n log n): in most practical scenarios, quicksort performs close to its best case due to its efficient partitioning and divideandconquer approach.

Worst case: O(n²): this happens when the pivot is chosen poorly, resulting in highly unbalanced partitions. An example is when the smallest or largest element is always chosen as the pivot, leading to unbalanced recursion.
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