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def bubbleSort(arr):
    n = len(arr)
 
    # Traverse through all array elements
    for i in range(n):
 
        # Last i elements are already in place
        for j in range(0, n-i-1):
 
            # traverse the array from 0 to n-i-1

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#This 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): 

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# To heapify subtree rooted at index i.
# n is size of heap
def heapify(arr, n, i):
    largest = i   # Initialize largest as root
    l = 2 * i + 1    # left = 2*i + 1
    r = 2 * i + 2    # right = 2*i + 2

    # See if left child of root exists and is
    # greater than root
    if l < n and arr[i] < arr[l]:

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def merge_sort(arr):
    if len(arr) >1:
        mid = len(arr)//2 #Finding the mid of the array
        L = arr[:mid] # Dividing the array elements
        R = arr[mid:] # into 2 halves

        mergeSort(L) # Sorting the first half
        mergeSort(R) # Sorting the second half

        i = j = k = 0

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def selection_sort(arr: []):
    # Traverse through all array elements
    for i in range(len(arr)):

        # Find the minimum element in remaining
        # unsorted array
        min_idx = i
        for j in range(i+1, len(arr)):
            if arr[min_idx] > arr[j]:
                min_idx = j

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def insertion_sort(arr: []):

        # Traverse through 1 to len(arr)
    for i in range(1, len(arr)):

        key = arr[i]
        
        # Move elements of arr[0..i-1], that are
        # greater than key, to one position ahead
        # of their current position