sorting.py

import sys
import random

def partition3(a, l, r):
    #write your code here
    x = a[l]
    j = l 
    k = l
    for i in range(l + 1, r + 1):
        if a[i] < x:
            j += 1
            k += 1
            a[k], a[i] = a[i], a[k]
            a[k], a[j] = a[j], a[k]
        elif a[i]==x:
            k += 1
            a[k], a[i] = a[i], a[k]
    a[l], a[j] = a[j], a[l]
    return j, k   

def partition2(a, l, r):
    x = a[l]
    j = l
    for i in range(l + 1, r + 1):
        if a[i] <= x:
            j += 1
            a[i], a[j] = a[j], a[i]
    a[l], a[j] = a[j], a[l]
    return j


def randomized_quick_sort(a, l, r):
    if l >= r:
        return
    k = random.randint(l, r)
    a[l], a[k] = a[k], a[l]
    #use partition3
    m, n = partition3(a, l, r)
    randomized_quick_sort(a, l, m - 1)
    randomized_quick_sort(a, n + 1, r)


if __name__ == '__main__':
    input = sys.stdin.read()
    n, *a = list(map(int, input.split()))
    randomized_quick_sort(a, 0, n - 1)
    for x in a:
        print(x, end=' ')