$1-$Write the mathematical analysis of selection sort and write the Tilda notation for insertionSort$()$ function, and Tilda notation for comparison, Tilda notation for swap $($how many exchange$).$

$-$Assume we want to sort an array of characters, does the selection sort algorithm performance $($number of comparisons and exchanges$)$ change if the array is sorted or partially sorted, or in reverse order? $($explain$)$

#includei$=1$;$i=1$;$j--$swap$(a,j,j-1)if(a[j]$

swap$(a,j,j-1)$;

else

break;

$\}$

Describe the performance of the insertion sort algorithm:

$-$best case

$-$worst case

$-$average case