Sorting Algorithms

Sorting Algorithms
Technical Writing(CS1305) Assignment
Shivam Singh
20148025
MNNIT
August 2015
Shivam Singh 20148025 (MNNIT) Sorting Algorithms August 2015 1 / 20

What Is A Sorting Algorithm ?

Bubble Sort
Compare each element (except the last one) with its neighbor to the
right
If they are out of order, swap them
This puts the largest element at the very end
The last element is now in the correct and ﬁnal place

Bubble Sort
right
Compare each element (except the last two) with its neighbor to the
right

Bubble Sort
right
Compare each element (except the last two) with its neighbor to the
right
Compare each element (except the last three) with its neighbor to the
right
Continue as above until you have no unsorted elements on the left

Bubble Sort
Explanation
Figure: Graphical illustration of Bubble Sort

Bubble Sort
Pseudo-Code
for i ← 0toN − 2 do
for j ← 0toN − 2 do
if A[j] ≥ A[j + 1] then
Swap(A[j],A[j+1])
end if
end for
end for

Selection Sort
Given an array of length n :

Selection Sort
Search elements 0 through n-1 and select the smallest
Swap it with the element in location 0

Selection Sort

Selection Sort
Continue in this fashion until theres nothing left to search

Selection Sort
Graphical Illustration

Selection Sort
Pseudo-Code
Min ← i
for j ← 0toN − 1 do
if A[j] ≤ A[Min] then
Min ← j
end if
end for
if i = Min then
Swap(A[i],A[Min])
end if
end for

Insertion Sort
Outer Loop
The Outer Loop i goes from 1 → N
all the elements to the left of i are sorted with respect to one another

Insertion Sort
Outer Loop
The Outer Loop i goes from 1 → N
all the elements to the left of i are sorted with respect to one another
Inner Loop
In every iteration of the Inner Loop we are :
1 Finding the elements proper place
2 Making room for the inserted element (by shifting over other elements)
3 Inserting the element

Insertion Sort
Graphical Illustration

Insertion Sort
Pseudo-Code
Temp ← A[i]
j ← i
while A[j] > Tempandj > 0 do
A[j] ← A[j − 1]
j ← j − 1
end while
A[j] ← Temp
end for

Merge Sort
A Divide and Conquer Algorithm

Merge Sort
Divide the unsorted array into 2 halves until the sub-arrays only
contain one element
Merge the sub-problem solutions together

Merge Sort
Divide the unsorted array into 2 halves until the sub-arrays only
contain one element
Merge the sub-problem solutions together
1 Compare the sub-arrays ﬁrst elements
2 Remove the smallest element and put it into the result array
3 Continue the process until all elements have been put into the result
array

Merge Sort-Explanation

Merge Sort
Pseudo-Code
Divide And Conquer
Sort(A, N)
if N ≤ 1 then
return
end if
nL ← N/2 , nR ← N − N/2
for i ← 0toMid − 1 do
Left[i] ← A[i]
end for
for i ← MidtoN − 1 do
Right[i] ← A[i]
end for
Sort(Left, nL)
Sort(Right, nR)
Merge(Left, Right, A)

Merge Sort
Pseudo-Code
Merging The SubArrays
Merge(Left, Right, A, N)
nL ← N/2 , nR ← N − N/2 , i ← j ← k ← 0
while i < nLandj < nR do
if Left[i] ≤ Right[j] then
A[k] ← Left[i]
i ← i + 1
else
A[k] ← Right[j]
j ← j + 1
end if
k ← k + 1
end while

Merge Sort
Pseudo-Code
Merging The SubArrays Cont...
while i < nL do
A[k] ← Left[i]
i ← i + 1
k ← k + 1
end while
while j < nR do
A[k] ← Right[j]
j ← j + 1
k ← k + 1
end while

Which Is The Best ?
Algorithm Time Complexity
Bubble Sort O(n2)
Selection Sort O(n2)
Insertion Sort O(n2)
Merge Sort O(n ∗ (log2n))

Which Is The Best ?
Algorithm Time Complexity
Bubble Sort O(n2)
Selection Sort O(n2)
Insertion Sort O(n2)
Merge Sort O(n ∗ (log2n))
Answer :
As we can observe from the Time Complexities, Merge Sort will be the
fastest Sorting Algorithm !

Special Mention
QuickSort
Recursive Quick Sort
QuickSort(A, Start, End)
if Start ≥ End then
return
end if
pIndex ←Partition(A, Start, End)
QuickSort(A, Start, pIndex-1)
QuickSort(A, pIndex+1, End)

Special Mention
QuickSort
Partitioning Around The Pivot
Partition(A, Start, End)
Pivot ← A[End]
PIndex ← Start
for i ← StarttoEnd − 1 do
if A[i] ≤ Pivot then
Swap(A[i],A[PIndex])
PIndex ← PIndex + 1
end if
end for
Swap(A[i],A[PIndex])
return PIndex

End
Thank you

Sorting Algorithms

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Sorting Algorithms