The document describes insertion sort, including an example with figures, the algorithm, implementations in Java, C++ and Python, runtime performance of Θ(n2) in the average and worst cases but Θ(n) in the best case, an example execution on sample input data, and some other notes about its properties. It is a simple sorting algorithm that works by building up a sorted sequence from left to right by inserting each element into its sorted position.

1. Algorithms
Insertion Sort
Abdelrahman M. Saleh

2. List of contents
● Introduction
● Example w/ illustrating figures
● Algorithm
● implementation (Java, C++, Python)
● Performance Runtime
○ Best, Average and worst cases.
● Execution
● Other Notes

3. Introduction
● simple sorting algorithm that works the way we sort playing cards
in our hands.
● used when number of elements is small.
● It can also be useful when input array is almost sorted,
only few elements are misplaced in complete big array.

4. Example w/ illustrating figures
Source : geeksforgeeks.org

5. Algorithm .
Loop from i = 1 to length.
Pick element arr[i]
If (i=1) then skip
Other i => insert it into sorted sequence arr[0...i-1] .

6. Implementation

7. C++ .
void insertionSort(int a[], int len)
{
int i, j, key ;
for(j=1; j<len; j++)
{
key = a[j] ;
i = j-1 ;
while(i>(-1) && a[i] > key)
{
a[i+1] = a[i] ;
i-- ;
}
a[i+1] = key ;
}
}

8. JAVA .
void sort(int a[])
{
int len = a.length;
for (int i=1; i<len; ++i)
{
int key = a[i];
int j = i-1;
while (j>=0 && a[j] > key)
{
a[j+1] = a[j];
j = j-1;
}
a[j+1] = key;
}
}

9. Python .
def insertionSort(a):
for i in range(1, len(a)):
key = a[i]
j = i-1
while j >=0 and key < a[j] :
a[j+1] = a[j]
j -= 1
a[j+1] = key

10. Performance Runtime
● Time complexity Θ(n2
) .
● Best Case : When Array is sorted Θ(n) .
● Worst Case : when array is sorted in reverse order .

11. Execution .
Input array : [9, 11, 8, 7, 6]
First Action : [9, 11, 8, 7, 6]
Move item : 11 .
Move item : 9 .
Sorted item : 8, position => 0 .
Second Action : [8, 9, 11, 7, 6] .
Move item : 11 .
Move item : 9 .
Sorted item : 7, position => 0 .
Third Action : [7, 8, 9, 11, 6]
Move item : 11 .
Move item : 9 .
Move item : 8 .
Move item : 7 .
Sorted item : 6 , position => 0 .
Output array : [6, 7, 8, 9, 11] .

12. Other Notes .
● Algorithmic Paradigm: Incremental Approach
● Sorting In Place: Yes
● Stable: Yes
● Online: Yes