Department of Computer Science and Information Technology CSCI$378-$ Data Structures and Algorithms Assignment $31.$ Show in details that f$($n$)=3$ n$^2+7$ is O$($n$^2).2.$ Determine the running time of the following code in terms of Big$-$Oh notation. Show the steps in details. $3.$ Without showing the details, what is the time complexity of the following code fragment? Justify your answer. $4.$ What is the time complexity of the following algorithm if we are using the big Oh notation? When is the best case? Show your detailed work. public static void method $($int n$,$ int x$)$ f int m $=$n $/2$ ; for $($int $1-1$ ; $1<-$n ; $1++)$ for $($int j$=0$ ; $1<=$m ; j$++)$ if $($x$>0)$ for $($int k$=1$ ; k$<-$n $*$ n ; k$++)$ System, out printin $($k$)$ ; else for $(1$nt k$=1$ ; k$($k$-$n ; k$++)$ System,out.printin $($k$)$ ;