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# Python Program for QuickSort

Just unlikely merge Sort, QuickSort is a divide and conquer algorithm. It picks an element as a pivot and partitions the given array around the picked pivot.

There are many different versions of quickSort that pick pivot in different ways.

1. Always pick the first element as a pivot
2. Always pick the last element as a pivot
3. Pick a random element as a pivot
4. Pick median as a pivot

Here we will be picking the last element as a pivot. The key process in quickSort is partition(). Target of partitions is, given an array and an element ‘x’ of array as a pivot, put x at its correct position in a sorted array and put all smaller elements (smaller than x) before x, and put all greater elements (greater than x) after x. All this should be done in linear time.

### Python Recursive QuickSortfunction

`// low  --> Starting index,// high  --> Ending indexquickSort(arr[], low, high) {  // Till starting index is lesser than ending index  if (low < high) {    // pi is partitioning index,    // arr[p] is now at right place    pi = partition(arr, low, high);    // Before pi    quickSort(arr, low, pi - 1);    // After pi    quickSort(arr, pi + 1, high);  }}`

## Python3

 `# Python program for implementation of Quicksort Sort` `# This implementation utilizes pivot as the last element in the nums list``# It has a pointer to keep track of the elements smaller than the pivot``# At the very end of partition() function, the pointer is swapped with the pivot``# to come up with a "sorted" nums relative to the pivot`  `# Function to find the partition position``def` `partition(array, low, high):` `    ``# choose the rightmost element as pivot``    ``pivot ``=` `array[high]` `    ``# pointer for greater element``    ``i ``=` `low ``-` `1` `    ``# traverse through all elements``    ``# compare each element with pivot``    ``for` `j ``in` `range``(low, high):``        ``if` `array[j] <``=` `pivot:` `            ``# If element smaller than pivot is found``            ``# swap it with the greater element pointed by i``            ``i ``=` `i ``+` `1` `            ``# Swapping element at i with element at j``            ``(array[i], array[j]) ``=` `(array[j], array[i])` `    ``# Swap the pivot element with the greater element specified by i``    ``(array[i ``+` `1``], array[high]) ``=` `(array[high], array[i ``+` `1``])` `    ``# Return the position from where partition is done``    ``return` `i ``+` `1` `# function to perform quicksort`  `def` `quickSort(array, low, high):``    ``if` `low < high:` `        ``# Find pivot element such that``        ``# element smaller than pivot are on the left``        ``# element greater than pivot are on the right``        ``pi ``=` `partition(array, low, high)` `        ``# Recursive call on the left of pivot``        ``quickSort(array, low, pi ``-` `1``)` `        ``# Recursive call on the right of pivot``        ``quickSort(array, pi ``+` `1``, high)`  `data ``=` `[``1``, ``7``, ``4``, ``1``, ``10``, ``9``, ``-``2``]``print``(``"Unsorted Array"``)``print``(data)` `size ``=` `len``(data)` `quickSort(data, ``0``, size ``-` `1``)` `print``(``'Sorted Array in Ascending Order:'``)``print``(data)`

Output
```Unsorted Array
[1, 7, 4, 1, 10, 9, -2]
Sorted Array in Ascending Order:
[-2, 1, 1, 4, 7, 9, 10]
```

Time Complexity: Worst case time complexity is O(N2) and average case time complexity is O(N log N)
Auxiliary Space: O(1)

### Python Quicksort using list comprehension

Quicksort using list comprehension is a recursive algorithm for sorting an array of elements. It works by selecting a pivot element and partitioning the array around the pivot, such that all elements less than the pivot are moved to its left and all elements greater than the pivot are moved to its right. Then, it recursively applies the same process to the left and right sub-arrays until the entire array is sorted.

Algorithm:

1.If the input array has length 0 or 1, return the array as it is already sorted.
2.Choose the first element of the array as the pivot element.
3.Create two empty lists, left and right.
4.For each element in the array except for the pivot:
a. If the element is smaller than the pivot, add it to the left list.
b. If the element is greater than or equal to the pivot, add it to the right list.
5.Recursively call quicksort on the left and right lists.
6.Concatenate the sorted left list, the pivot element, and the sorted right list.
7.Return the concatenated list.

## Python3

 `# Approach 2: Quicksort using list comprehension` `def` `quicksort(arr):``    ``if` `len``(arr) <``=` `1``:``        ``return` `arr``    ``else``:``        ``pivot ``=` `arr[``0``]``        ``left ``=` `[x ``for` `x ``in` `arr[``1``:] ``if` `x < pivot]``        ``right ``=` `[x ``for` `x ``in` `arr[``1``:] ``if` `x >``=` `pivot]``        ``return` `quicksort(left) ``+` `[pivot] ``+` `quicksort(right)` `# Example usage``arr ``=` `[``1``, ``7``, ``4``, ``1``, ``10``, ``9``, ``-``2``]``sorted_arr ``=` `quicksort(arr)``print``(``"Sorted Array in Ascending Order:"``)``print``(sorted_arr)`

Output
```Sorted Array in Ascending Order:
[-2, 1, 1, 4, 7, 9, 10]

```

Time complexity is O(n log n)

The space complexity of the algorithm is O(n)

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