lab8-kgashok.py

Table of Contents

Lab 8: Sorting

Sort the given list using selection sort and insertion sort.

[TOC]

Select vs Insert vs Merge vs Quick

  • In selectsort, the position of the update is pre-determined, starting from the end of the list. We then go select the maximum value among the unsorted elements of the list, and swap it with the element in the pre-determined location.

  • In insertsort, given a key, a copy of a pre-determined element in the list, we insert it at the appropriate location after comparing it with the unsorted elements of the list.

  • In mergesort, a divide-and-conquer partitioning algorithm (which more often requires extra memory), the input array is divided in two halves, calls itself recursively for the two halves and then merges the two sorted halves. The merge() function is used for merging two halves.

  • In quicksort, also a divide-and-conquer partitioning algorithm (lends itself to be efficiently implemented in-place without extra memory), the choice of the pivot element determines how the elements get partitioned, and calls itself recursively for the two partitions.

Solution Key

def selectsort(L):
    # start filling from the end of the list
    for slot in range(len(L)-1, 0, -1):
        positionOfMax = 0
        # find the position of the maximum value
        for location in range(1, slot + 1):
            if L[location] > L[positionOfMax]:
                positionOfMax = location

        # swap the slot with the maximum value
        temp             = L[slot]
        L[slot]          = L[positionOfMax]
        L[positionOfMax] = temp
        print(L)

    return L


def insertsort(L):

  # scan every element to determined where it must be inserted
  # Location 0 constitutes a "sorted" list already. So begin from 1
  for index in range(1, len(L)):
    key = L[index]
    # start with the immediate previous element
    j = index - 1

    # determine which 'j' it should be at
    # meanwhile, keep shifting elements to the right
    while j >= 0 and (L[j] > key):
      L[j + 1] = L[j]
      j = j - 1
      print(L)
    # end of inner while loop

    # update the list with the current element in consideration
    L[j + 1] = key
  # end of outer for loop
  return L

alist = [54,26,93,17,77,31,44,55,20]
selectsort(alist)
print(alist)
alist = [54,26,93,17,77,31,44,55,20]
insertsort(alist)
print(alist)

English-like sorting code

def selectsort(alist):
    for i in range(len(alist)):
        sublist = alist[i:]
        smallest = min(sublist)
        index_of_smallest = alist.index(smallest, i)
        #swap
        temp = alist[index_of_smallest]
        alist[index_of_smallest] = alist[i]
        alist[i] = temp
    return alist

def insertsort(alist):
    for i in range(len(alist)):
        sublist = alist[:i]
        key = alist.pop() # element to insert
        for j in range(len(sublist)):
            if key < alist[j]:
                alist.insert(j, key)
                break
        else:
            # insert it at the top of the sublist
            alist.insert(i, key)
    return alist

index-based insert sort

First see the video and then code! http://j.mp/insertSortVideo

def ins_sort(k):
    for i in range(1,len(k)):
        j = i
        while j > 0 and k[j] < k[j-1]:
	        # swapping values and it is expensive
            k[j], k[j-1] = k[j-1], k[j]
            j = j - 1
    return k

Pythonic versions

def selectsort(alist):
    for i in range(len(alist)):
        smallest, idx = min(
            (v, i) for i, v in enumerate(alist[i:]))
        alist[i], alist[idx+i] = alist[idx+i], alist[i]
    return alist

import bisect
def insert_sort(alist):
    for i in range(len(alist)):
        key = alist.pop()
        bisect.insort(alist, key, hi=i)
    return alist

Related Material

  • http://interactivepython.org/runestone/static/pythonds/SortSearch/TheInsertionSort.html

  • http://interactivepython.org/runestone/static/pythonds/SortSearch/TheSelectionSort.html

  • http://bit.ly/insertVisualizer - insertSort in the visualizer

3-problem series for learning/teaching insertsort

  • Part 1- https://www.hackerrank.com/challenges/insertionsort1

  • Part 2 - https://www.hackerrank.com/challenges/insertionsort2

  • Part 3 - https://www.hackerrank.com/challenges/correctness-invariant (fix the bug)

Recursive SelectionSort

Credits: https://code.activestate.com/recipes/576917-functional-selection-sort/#c1

def selection_sortr(L):
    if not L: return [] # terminal case
    # select the minimum value and the index where it is located
    idx, v = min(enumerate(L), key=lambda e: e[1])
    #v, idx = min((v, i) for i, v in enumerate(L))

    print(v, L[:idx], L[idx+1:])
    return [v] + selection_sortr(L[:idx] + L[idx+1:])

Output

>> selection_sortr([1,56, 99, -1, 22, 99])
-1 [1, 56, 99] [22, 99]
1 [] [56, 99, 22, 99]
22 [56, 99] [99]
56 [] [99, 99]
99 [] [99]
99 [] []
=> [-1, 1, 22, 56, 99, 99]

Visualize a slight variant of this code at https://tinyurl.com/x697cwwj

Recursive InsertionSort

import bisect
def insertion_sortr(L, nsorted=1):
    if nsorted >= len(L): return L  # terminal case
    key = L.pop() # pre-determined location
    print(key, L)
    # insert key in sublist of 'nsorted' elements
    bisect.insort(L, key, hi=nsorted)
    return insertion_sortr(L, nsorted + 1)

Output

insertion_sortr([1, 56, 99, -1, 22, 99])
99 [1, 56, 99, -1, 22]
22 [1, 99, 56, 99, -1]
-1 [1, 22, 99, 56, 99]
99 [-1, 1, 22, 99, 56]
56 [-1, 1, 22, 99, 99]
=> [-1, 1, 22, 56, 99, 99]

Recursive QuickSort

http://mcsp.wartburg.edu/zelle/python/sigcse-workshop/mgp00064.html

def qsort(L):
  if len (L) <= 1: return L

  return qsort([n for n in L[1:] if n < L[0]]) + \
    [L[0]] + \
    qsort([n for n in L[1:] if n >= L[0]])

or

def qsort(L):
  if len(L) <= 1: return L

  def subList(pivot, op):
    return [elem for elem in L[1:] if op(elem, pivot)]

  return qsort(subList(L[0], operator.lt)) + \
    [L[0]] + \
    qsort(subList(L[0], operator.ge))

or using lambda and filter

from operator import ge as greater, lt as lesser

def qsort(L):
  if len(L) <= 1: return L
  pivot   = L[0]
  sublist = lambda op: [*filter(lambda num: op(num, pivot), L[1:])]

  return qsort(sublist(lesser))+ [pivot] + qsort(sublist(greater))

print(qsort([3,1,4,2,5]) == [1,2,3,4,5])

and the most efficient:

import random

def quicksort(s):
  len_s = len(s)
  if len_s < 2:
    return s

  pivot = s[random.randrange(0, len_s)]

  L = [x for x in s if x < pivot]
  E = [x for x in s if x == pivot]
  G = [x for x in s if x > pivot]

  return quicksort(L) + E + quicksort(G)

Improved version of lambda code (without using filter):

from operator import ge, lt

def qsort(L, first=True):
  if len(L) <= 1:
    return L

  L = L[:] if first else L
  pivot = L.pop()
  sublist = lambda op: [n for n in L if op(n, pivot)]

  return [*qsort(sublist(lt), False), pivot, *qsort(sublist(ge), False)]

Related Material

http://bit.ly/quickSortVideoCD - a video explaining QuickSort incrementally in a CyberDojo session.

Recursive MergeSort (in-place)

def mergesort(nums):
  print ("nums:", nums)
  n = len(nums)
  if n > 1:
    # split into sublists
    m = n // 2
    nums1, nums2 = nums[:m], nums[m:]
    # recursively sort each piece
    mergesort(nums1)
    mergesort(nums2)
    # merge the sorted pieces back into original list
    merge(nums1, nums2, nums)


def merge(lst1, lst2, lst3):
  i1, i2, i3 = 0, 0, 0
  n1, n2 = len(lst1), len(lst2)

  print(lst1, lst2, lst3)
  while i1<n1 and i2<n2:
    print(i1, i2, i3)
    if lst1[i1] < lst2[i2]:
      lst3[i3] = lst1[i1]
      i1 = i1 + 1
    else:
      lst3[i3] = lst2[i2]
      i2 = i2  + 1
    i3 = i3 + 1

  # avoid `extend`, as it will not do in-place
  while i1 < n1:
    lst3[i3] = lst1[i1]
    i1 = i1 + 1
    i3 = i3 + 1
  while i2 < n2:
    lst3[i3] = lst2[i2]
    i2 = i2 + 1
    i3 = i3 + 1

  print("Interim (nums):", lst3)

Unit test file

from mergesort import mergesort
import unittest
import random

class Test_mergesort(unittest.TestCase):

    def test_simple_lists(self):
        alist = [1, 4, 5, 2, 4, 3, 10, 2, -4]

        expected = sorted(alist)
        mergesort(alist)
        self.assertEqual(expected, alist)


    def generate_random_list(self):
        alist = []
        for i in range (10):
            x = [random.randrange(-100, 101, 1)] * random.randrange(0, 6)
            alist.extend(x)

        random.shuffle(alist)
        # print(sorted(alist))
        return alist

    def test_random_list(self):
        alist = self.generate_random_list()

        expected = sorted(alist)
        mergesort(alist)
        self.assertEqual(expected, alist)



if __name__ == '__main__':
    unittest.main()

Recursive QuickSort, in-place

def swap(arr,x,y):
    mem = arr[x]
    arr[x] = arr[y]
    arr[y] = mem


def qsort(ar,start,end):
    # base case
    if end-start <= 0:
        return ar
    # pivot
    pivot = ar[end]
    # init index for the next pivot
    # which is used in the next recursive qsort calls below
    ind = start
    # loop less final value (pivot)
    for i in range(start,end):
        elem = ar[i]
        if elem <= pivot:
            # move lesser elements to the left side
            swap(ar,i,ind)
            ind += 1
        else:
            # leave greater elements as-is
            pass
    swap(ar,ind,end) # swap in the pivot element
    print(ar)
    # left side contains pivot, and lesser elements
    ar = qsort(ar,start,ind-1)
    # right side contain greater elements than pivot
    ar = qsort(ar,ind+1,end)
    return ar

n = int(input())
ar = [int(x) for x in input().split()]
qsort(ar,0,n-1)

Related Material

http://bit.ly/quickSortVideo

What exactly does this accomplish?

  from threading import Timer
  l = [8, 2, 4, 6, 7, 1]
  for n in l:
      Timer(n, lambda x: print(x), [n]).start()

Read the analysis here - http://j.mp/sleepSortGeek

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