3. • Sorting is an operation that segregates items into groups
according to specified criterion.
• Arranging items of the same kind, class or nature in some
ordered sequence.
• A = { 3 1 6 2 1 3 4 5 9 0 } A = { 0 1 1 2 3 3 4 5 6 9 }
• Sorting is a fundamental application for any domain
• Sorting help done to make searching faster
Sorting: Introduction
3
4. Examples:
• Words in a dictionary are sorted
• Files in a directory are often listed in sorted order.
• The index of a book is sorted
• Sorting Books in Library
• Sorting Individuals by Height (Feet and Inches)
• Sorting Movies in Blockbuster (Alphabetical)
• Sorting Numbers (Sequential)
• etc
Sorting: Introduction
4
5. • Imagine finding the phone number of your friend in
your mobile phone, but the phone book is not sorted.
• Need
– Efficient and quick data access
– Efficient data manipulation
Sorting: Introduction
5
6. • A sorting algorithm is an algorithm that puts elements of a list
in a certain order.
– The most used orders
lexicographical order.
• Types
– Bubble Sort
– Selection Sort
– Insertion Sort
– Quick Sort
– Merge Sort
– etc.,
are numerical order and
–
Sorting Algorithm
6
7. Selection Sort
• Selection sort is a simple sorting algorithm. It selects the
smallest element from an unsorted list in each iteration and
places that element at the beginning of the unsorted list.
7
8. Selection Sort
8
Algorithm
Step 1: Start with the 1st element, scan the entire list to find its
smallest element and exchange it with the 1st element.
Step 2: Start with the 2nd element, scan the remaining list to find
the smallest among the last (N-1) elements and exchange it with
the 2nd element.
Step 3: Continue this until the entire list is sorted.
10. 10
Selection Sort: Implementation
def selectionsort(t): #Method I:
for i in range(len(t)):
min_index=i
for j in range(i+1,len(t)):
if t[j] < t[min_index]:
min_index=j
t[min_index],t[i]=t[i],t[min_index]
print("List elements after",i+1,"phase is",t)
def selectionsort(t): #Method II:
for i in range(len(t)):
smallest=min(t[i:])
index_of_smallest=t.index(smallest,i)
t[i],t[index_of_smallest]=t[index_of_smallest],t[i]
print("List elements after",i+1,"phase is",t)
t=list(map(int,input("Enter the List elements separated by
space:").split(" ")))
print("List before sorting is",t)
selectionsort(t)
print("List after sorting is",t)
11. Selection Sort: Implementation
11
Output:
Enter the List elements separated by space:6 2 19 3 2
List before sorting is [6, 2, 19, 3, 2]
List elements after 1 phase is [2, 6, 19, 3, 2]
List elements after 2 phase is [2, 2, 19, 3, 6]
List elements after 3 phase is [2, 2, 3, 19, 6]
List elements after 4 phase is [2, 2, 3, 6, 19]
List elements after 5 phase is [2, 2, 3, 6, 19]
List after sorting is [2, 2, 3, 6, 19]
12. • Sorting a list by inserting element at appropriate position.
• An example of an insertion sort occurs in everyday life while
playing cards.
– To sort the cards in your hand you extract a card, shift the
remaining cards, and then insert the extracted card in the
correct place.
– This process is repeated until all the cards are in the correct
sequence.
Insertion Sort
12
13. To insert 12, we need to
make room for it by moving
first 36 and then 24.
Insertion Sort
13
17. Algorithm
Step 1: In every pass, an element is compared with all its previous
elements.
Step 2: If at some point it is found that the element can be inserted
at a position then space is created by shifting other elements one
position to the right and insert the element at the suitable
position.
Step 3: The steps are repeated for all elements in the array.
Insertion Sort
17
19. Insertion Sort: Implementation
19
def insertionsort(t):
for i in range(1,len(t)):
key=t[i]
j=i-1
while j>=0 and t[j]>key:
t[j+1]=t[j]
j=j-1
t[j+1]=key
print("List elements after",i,"phase is",t)
t=list(map(int,input("Enter the List elements separated by
space:").split(" ")))
print("List before sorting is",t)
insertionsort(t)
print("List after sorting is",t)
20. Insertion Sort: Implementation
20
Output:
Enter the List elements separated by space:6 2 19 4 2
List before sorting is [6, 2, 19, 4, 2]
List elements after 1 phase is [2, 6, 19, 4, 2]
List elements after 2 phase is [2, 6, 19, 4, 2]
List elements after 3 phase is [2, 4, 6, 19, 2]
List elements after 4 phase is [2, 2, 4, 6, 19]
List after sorting is [2, 2, 4, 6, 19]
21. Bubble Sort
• Bubble Sort is the simplest sorting algorithm that works by
repeatedly swapping the adjacent elements if they are in
wrong order.
• It is also known as exchange sort.
21
22. Algorithm
• Compare adjacent elements and exchange them if they are out of
order
Step I: Comparing the first two elements, the second and third
elements, and so on, will move the largest (or smallest)
elements to the end of the array
Step II: Repeating this process will eventually sort the array
into ascending (or descending) order
• Bubble up - After each pass the largest element is bubbled to its
position.
Bubble Sort
22
24. Bubble Sort: Implementation
24
def bubblesort(t):
n=len(t)
for i in range(n):
for j in range(0,n-i-1):
if t[j] > t[j+1]:
t[j],t[j+1]=t[j+1],t[j] #Swap
print("List elements after",i+1,"phase is",t)
t=list(map(int,input("Enter the List elements separated by
space:").split(" ")))
print("List before sorting is",t)
bubblesort(t)
print("List after sorting is",t)
25. Bubble Sort: Implementation
25
Output:
Enter the List elements separated by space:12 2 3 11 1 10
List before sorting is [12, 2, 3, 11, 1, 10]
List elements after 1 phase is [2, 3, 11, 1, 10, 12]
List elements after 2 phase is [2, 3, 1, 10, 11, 12]
List elements after 3 phase is [2, 1, 3, 10, 11, 12]
List elements after 4 phase is [1, 2, 3, 10, 11, 12]
List elements after 5 phase is [1, 2, 3, 10, 11, 12]
List elements after 6 phase is [1, 2, 3, 10, 11, 12]
List after sorting is [1, 2, 3, 10, 11, 12]
26. • Sort a sequence of n elements into non-decreasing order. This
algorithm is an example of divide and conquer approach.
– Divide: Divide the n-element sequence to be sorted into two
subsequences of n/2 elements each
– Conquer: Sort the two subsequences recursively using merge sort.
– Combine:
answer.
26
Merge Sort
sub
problem 2
of size n/2
sub
problem 1
of size n/2
a solution to
sub problem 1
a solution to
the original
problem
a solution to
sub problem 2
Merge the two sorted subsequences to produce the sorted
a problem
of size n
28. Algorithm
• Split list into about equal halves and make copies of eac2h8 half in lists
B and C
• Sort arrays B and C recursively
• Merge sorted arrays B and C as follows:
• Repeat the following until no elements remain in one of the list:
• compare the first elements in the remaining unprocessed
portions of the list
• copy the smaller of the two into original list, while incrementing
the index indicating the unprocessed portion of that list
• Once all elements in one of the lists are processed, copy the
remaining unprocessed elements from the other list into original
Merge Sort
29. 3 27 38 43 10 82
R 9
L
0 1 2 3 0 1 2
i j
A
0 1 2 3 4 5
k
Initially, i=0,
j=0, k=0
L[i]<
6
= R[j]
A[k]=L[i]
++i, ++k
3 27 38 43 10 82
R 9
L
i j
3
0
A
1 2 3 4 5
k
L[i]>R[j]
A[k]=R[j]
++j,6++k
3 27 38 43 9 82
10
j
L R
i
3 9
0
A
1 2 3 4 5
k
L[i]>R[j]
A[k]=R[j]
++j,6++k
Merge Sort: Merge Operation
29
30. k
L[i]<=R[j]
A[k]=L[i]
++i, ++k
3 27 38 43 9 10 82
j
L R
i
3 9 10
0
A
1 2 3 4 5 6
L[i]<=R[j]
A[k]=L[i]
++i, ++k
3 27 38 43 9 10 82
j
L R
i
0
A
1 2 3 4
5
3 9 6 10 27
k
3 27 38 43 9 10
k
R 82
j
L
0
A
1
i
2 3 4
5
3 9 6 10 27 38
L[i]<=R[j]
A[k]=L[i]
++i, ++k
Merge Sort: Merge Operation
30
31. k
3 27 38 43 9 10 82
j
L R
i
3 9 10 27 38 43
0
A
1 2 3 4 5
L[i]>R[j]
A[k]=R[j]
++j, +6+k
k
3 27 38 43 9 10 82
R
i j
0 1 2 3 4
5
3 9 6 10 27 38 43 82
L[i]>R[j]
A[k]=R[j]
++j, ++k
All Elements Sorted
Merge Sort: Merge Operation
31
L
A
32. Merge Sort
32
def mergesort(alist):
print("Splitting", alist)
if len(alist)>1:
mid=len(alist)//2
lefthalf=alist[:mid]
righthalf=alist[mid:]
mergesort(lefthalf)
mergesort(righthalf)
i,j,k=0,0,0
while (i<len(lefthalf)) and (j<len(righthalf)):
if lefthalf[i]<righthalf[j]:
alist[k]=lefthalf[i]
i=i+1
else:
alist[k]=righthalf[j]
j=j+1
k=k+1
33. List – Merge Sort
33
while i<len(lefthalf):
alist[k]=lefthalf[i]
i=i+1
k=k+1
while j<len(righthalf):
alist[k]=righthalf[j]
j=j+1
k=k+1
print("Merging", alist)
t=list(map(int,input("Enter the List elements separated by
space:").split(" ")))
print("List before sorting is",t)
mergesort(t)
print("List after sorting is",t)
34. 34
List – Merge Sort
Output:
Enter the List elements separated by space:6 9 2 4 2
List before sorting is ['6', '9', '2', '4', '2']
Splitting ['6', '9', '2', '4', '2']
Splitting ['6', '9']
Splitting ['6']
Splitting ['9']
Merging ['6', '9']
Splitting ['2', '4', '2']
Splitting ['2']
Splitting ['4', '2']
Splitting ['4']
Splitting ['2']
Merging ['2', '4']
Merging ['2', '2', '4']
Merging ['2', '2', '4', '6', '9']
List after sorting is ['2', '2', '4', '6', '9']
35. 35
• Searching is the process of finding a desired element in set of
items. The desired element is called "target".
• Any search is said to be successful or unsuccessful depending
upon whether the element that is being searched is found or not.
• For efficient data manipulation need fast searching.
• Static Search Structure
• Built once and searched many times
• Insertions occur before any retrieval
• Dynamic Search Structure
• Insertion, deletion and search operations can occur simultaneously
Searching: Introduction
36. 36
• Based on the type of search operation, these algorithms are
generally classified into two categories:
• Sequential Search: In this, the list or array is traversed
sequentially and every element is checked.
• For example: Linear Search.
• Interval Search: These algorithms are specifically designed for
searching in sorted data-structures. These type of searching
algorithms are much more efficient than Linear Search as they
repeatedly target the centre of the search structure and divide
the search space in half.
• For Example: Binary Search.
Searching: Algorithm
37. • This is the simplest method for searching.
• In this technique of searching, finding a particular value in a list,
that consists of checking every one of its elements, one at a time
and in sequence, until the desired one is found
• This method can be performed on a sorted or an unsorted list.
Sequential Search
37
38. Algorithm
• Step 1: Start the search from the first element and Check the key
element with each element of list x.
• Step 2: If element is found, return the index position of the key.
• Step 3: If element is not found, print element is not present.
Sequential Search
38
39. • Searching in case of unsorted list begins from the 0th element
and continues until the element or the end of the list is reached.
• Example: Find 12
35 42 12 5
12 Found!
Head
Sequential Search: Unsorted List
40. • Example: Find 13
35 42 12 5
Head
Sequential Search: Unsorted List
13 Not Found!
41. • Example: Find 13
5 12 35 42
Head
Sequential Search: Sorted List
13 Not Found!
42. 42
Sequential Search: Implementation
def linearSearch(L,ele):
for i in range(0,len(L)):
if(L[i]==ele):
return i+1
break
else:
return -1
l=input("Enter the List elements separated by
space:").split(" ")
e=input("Enter the element to search:"))
result=linearSearch(l,e)
if result>=0:
print(e,'is present in position ',result)
else:
print(e,'is not found in the list'+str(l))
Output:
Enter List elements separated by space:4 5 1 8 9
Enter the element to search:8
8 is present in position 4
43. • Binary search is an efficient algorithm for finding an item from a
sorted list of items.
divide and conquer
• This algorithm is also an example of
approach.
• The most essential thing of this method is it requires the list to be
in sorted order..
Binary Search
43
44. Binary Search
44
Algorithm
Step 1: Obtain the middle element
Step 2: If it equals searched value, return position and go to step 4
Step 3: Other wise, two cases possible.
Step 3.1: If search value < middle element, repeat the
procedure for sub list before the middle element.
Step 3.2: If search value > middle element, repeat the
procedure for sub list after the middle element.
Step 4: Stop the algorithm.
54. 54
Binary Search: Implementation
def binarysearch(t,s):
low=0
high=len(t)-1
while high >= low:
middle=(low+high)//2
if t[middle] < s:
low=middle+1
elif t[m] >s:
high=middle-1
else:
return middle
return -1
t=input("Enter the List elements separated by space:").split("
")
s=input("Enter the element to search:")
result=binarysearch(t,s)
if result >= 0:
print(s," found at position",result+1)
else:
print(s," not found in the lsit"+str(t))
Output:
Enter the List elements
separated by space: 4 5 6 7 8
Enter the element to search:
8
8 is found at position 5
