Q$4.($a$)$ The function listed below implements a sorting algorithm called selection sort. Explain how the algorithm works, with reference to the program. Demonstrate the operation of the algorithm on the array $[684529].$ typedef int Key; void selection$\_$sort$($Key $*$array$,$ int n$)\{$ int i$,$ j$,$ min, minindex, temp; for$($i $=0$; i $<$ n$-1$; i$++)\{$ min $=$ array$[$i$]$; minindex $=$ i; for$($j $=$ i $+1$; j $<$ n; j$++)\{$ if $($array$[$j$]<$ min$)\{$ min $=$ array$[$j$]$; minindex $=$ j; $\}\}$ temp $=$ array$[$i$]$; array$[$i$]=$ min; array$[$minindex$]=$ temp; $\}\}(55\%)($b$)$ Assuming that we define the complexity of the algorithm to be equal to the number of comparisons made in sorting N elements, derive an equation which expresses the worst$-$case $($i$.$e$.$ highest$)$ complexity as a function of N$.$ Compare this value with the best$-$case $($i$.$e$.$ lowest$)$ complexity of the algorithm.