In the following pseudocode the only basic step is to print one $.$ Show that the RT of this code is O$($n$^2).$ for i $=0$ to n$-1$: j :$=0$ while j $<$ i: print one $*$ j :$=$ j $+1$

Question $2.$

In an array A of n different numbers two numbers A$[$i$]$ and A$[$j$]$ form an inversion if i $<$ j$,$ but A$[$i$]>$ A$[$j$],$ i$.$e$.$ the bigger comes before the smaller. $($For example $15$ and $3$ form an inversion in $8,15,1,10,3$ since the $15$ comes before $3).($a$)$ How many inversions are there in $2,5,1,10,3?($b$)$ Design a brute$-$force algo for counting the inversions, the running time should be O$($n$2),$ if the array contains n different numbers. $($c$)$ Design a divide$-$and$-$conquer algo for counting the inversions, here the running time should be O$($nlogn$)$ if the size of the array is n$.$for the last part we can notice inversions while performing mergesort.$)$ you can suppose that the size of the array is a power of $2.$