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## How to implement Iterative QuickSort Algorithm?

##### its about How to implement Iterative QuickSort Algorithm

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Following is a typical recursive implementation of Quick Sort that uses last element as pivot.

# A typical recursive Python

# implementation of QuickSort

# Function takes last element as pivot,

# places the pivot element at its correct

# position in sorted array, and places all

# smaller (smaller than pivot) to left of

# pivot and all greater elements to right

# of pivot

def partition(arr, low, high):

i = (low - 1)         # index of smaller element

pivot = arr[high]     # pivot

for j in range(low, high):

# If current element is smaller

# than or equal to pivot

if arr[j] <= pivot:

# increment index of

# smaller element

i += 1

arr[i], arr[j] = arr[j], arr[i]

arr[i + 1], arr[high] = arr[high], arr[i + 1]

return (i + 1)

# The main function that implements QuickSort

# arr[] --> Array to be sorted,

# low --> Starting index,

# high --> Ending index

# Function to do Quick sort

def quickSort(arr, low, high):

if low < high:

# pi is partitioning index, arr[p] is now

# at right place

pi = partition(arr, low, high)

# Separately sort elements before

# partition and after partition

quickSort(arr, low, pi-1)

quickSort(arr, pi + 1, high)

# Driver Code

if __name__ == '__main__' :

arr = [4, 2, 6, 9, 2]

n = len(arr)

# Calling quickSort function

quickSort(arr, 0, n - 1)

for i in range(n):

print(arr[i], end = " ")

The above implementation can be optimized in many ways

1) The above implementation uses last index as pivot. This causes worst-case behavior on already sorted arrays, which is a commonly occurring case. The problem can be solved by choosing either a random index for the pivot, or choosing the middle index of the partition or choosing the median of the first, middle and last element of the partition for the pivot. (See this for details)

2) To reduce the recursion depth, recur first for the smaller half of the array, and use a tail call to recurse into the other.

3) Insertion sort works better for small subarrays. Insertion sort can be used for invocations on such small arrays (i.e. where the length is less than a threshold t determined experimentally). For example, this library implementation of qsort uses insertion sort below size 7.

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