07 sorting algorithms

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Introduction to Python Programming

(7) Sorting Algorithms

S. Thater and A. Friedrich

Saarland University

Winter Semester 2011/2012

S. Thater and A. Friedrich ( Saarland University) Introduction to Python Programming Winter Semester 2011/2012 1 / 15
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Sorting Algorithms

Agenda:

Insertion Sort

Selection Sort

Bubblesort

MergesortQuicksort

Goals:

Understand the above sorting algorithms.

Get an idea that there are differences in efficiency.Get used to recursion.

We wont talk about complexity theory in this lecture.

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Swapping two items of a list

How can we swap two items of a list?

1 a = [5, 3]

2

3

Today, we always assume that our list is called a.

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Selection Sort

Selection Sort

Until list is empty:

Find the smallest element of the remaining list.

Append it to a new list.

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Selection Sort: Code

1 def selection_sort(a):

2 """ sorting algorithm, creates a NEW list """

3 b = []

4 # Why is the list a copied here?

5 a = a[:]

6 while len(a) > 0:

7 # Find minimum of the list8 minimum = 0

9 for i in range(1, len(a)):

10 if a[i] < a[minimum]:

11 minimum = i

12 # Remove the minimum from the list13 # and append it to the new list

14 b.append(a.pop(minimum))

15 return b

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Selection Sort - in place

Selection Sort

For each ifrom 0 to N2:

Find the smallest element of the remaining list.

If this element is smaller than a[i], exchange it with a[i].

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Selection Sort (in place): Code

1 def selection_sort_in_place(a):2 """ sorting algorithm, works in-place"""

3 # point to element at position i


5 # Find the smallest element in the

6 # rest of the list

7 minimum = i

8 for j in range(i+1, len(a)):

9 if a[j] < a[minimum]:

10 minimum = j

11 # exchange elements

12 temp = a[i]13 a[i] = a[minimum]

14 a[minimum] = temp

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Insertion Sort

Insertion SortLook at one element after the other and insert it into the list at

the correct position.

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Insertion Sort - in-place

Insertion Sort

Look at one element after the other and insert it into the part of

the list already dealt with at the correct position.

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Insertion Sort: Code

1 def insertion_sort_in_place(a):2 """ sorting algorithm, works in-place"""

3 # go through list


5 # Remember value of a[i]

6 v = a[i]

7 j = i

8 # Go backwards in list and shift to

9 # the right if element > value to be

10 # inserted

11 while a[j-1] > v and j>=1:

12 a[j] = a[j-1]

13 j -= 1

14 # insert the value at its correct position

15 a[j] = v

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Bubble Sort

Bubble SortGo through the list again and again

and exchange neighboring

elements (if necessary).

Stop if no changes have been

made while going through the listonce.

Implementation: Your task. Try notto just copy it from the web. :)

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Recursion: Base Case

1 def factorial(x):2 # base case

3 if (x


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Recursion: Base Case

Base cases for sorting algorithms:

empty lists are sorted.

lists with only one element are sorted.

All other lists may still need sorting.

1 if len(a)


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Mergesort: Divide & Conquer

Dividelists & sort them

recursively.

Mergesorted lists.

on board

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Quicksort: Divide & Conquer

Dividelists using a pivotelement from the list:

(a) items < pivot

(b) items > pivot

Sort (a) and (b)

recursively.

Mergesorted lists:

(a) +[pivot]+ (b)

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07 sorting algorithms

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