Selection sort works by repeatedly finding the minimum element from the unsorted section of an array and placing it at the beginning. It maintains two subarrays - the sorted section and the unsorted section. In each iteration, the minimum element from the unsorted section is selected and swapped with the element in the sorted section. The algorithm has a runtime of Θ(n2) and is an in-place sorting algorithm. An example is provided to illustrate the steps of selection sort on a sample array.

1. Algorithms
Selection 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
● sorts an array by repeatedly finding the minimum element (considering ascending
order) from unsorted part and putting it at the beginning .
● The algorithm maintains two subarrays in a given array.
1) The subarray which is already sorted.
2) Remaining subarray which is unsorted.
● In every iteration ,the minimum element (considering ascending order) from the
unsorted subarray is picked and moved to the sorted subarray .

4. Example
arr[] = 19, 5, 7, 12
// Find the minimum element in arr[0...3]
// and place it at beginning
5, 19, 7, 12
// Find the minimum element in arr[1...3]
// and place it at beginning of arr[1...3]
5, 7, 19, 12
// Find the minimum element in arr[2...3]
// and place it at beginning of arr[2...3]
5, 7, 12, 19

5. Algorithm .
● Let the min : 0
● Search the minimum
● Swap with value at location min
● Increment min
● Repeat until is sorted

6. Implementation .

7. C++ .
void selectionSort(int a[], int len)
{
int min, i, j ;
for(i=0; i<len-1; i++)
{
min = i ;
for(j=i+1; j<len; j++)
{
if(a[j] < a[min])
min = j ;
}
swap(&a[i], &a[min]) ;
}
}

8. JAVA .
void sort(int a[])
{
int len = a.length, min;
for (int i = 0; i < len-1; i++)
{
min = i;
for (int j=i+1; j<len; j++)
if (a[j] < a[min])
min = j;
int temp = a[min];
a[min] = a[i];
a[i] = temp;
}
}

9. Python .
def selectionSort(a):
for i in range(len(a)):
min = i
for j in range(i+1, len(a)):
if a[min] > a[j]:
min = j
a[i], a[min] = a[min], a[i]

10. Performance Runtime
● Time complexity Θ(n2
) .
● it never makes more than O(n) swaps =>
can be useful when memory write is a costly operation .

11. Execution .
Input array : [4, 6, 3, 2, 1, 9, 7]
Swap => 4, 1
First Action : [1, 6, 3, 2, 4, 9, 7]
Swap => 6, 2
Second Action : [1, 2, 3, 6, 4, 9, 7]
Swap => 6, 4
Fourth Action : [1, 2, 3, 4, 6, 9, 7]
Swap => 9, 7
Sixth Action : [1, 2, 3, 4, 6, 7, 9]
Output Array: [1, 2, 3, 4, 6, 7, 9]

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