Suppose company X has created 3 new variants of quicksort but, because they are unsure which is asymptotically best, they have hired you to analyze their runtimes. Compute the asymptotic runtimes of the variants and use this to justify which is best:• Variant 1: Partitioning the array still takes Θ(n) time but the array will always be divided into a n x and (x−1)n x portion (where x is some constant value > 1).• Variant 2: Partitioning the array now takes Θ(n 1.1 ) time but the array will always be divided perfectly in half.• Variant 3: Partitioning the array now only takes Θ(√ n) time but all of the numbers except the pivot will be partitioned into a single array. Reminder: log n ∈ o(n c ) for all c > 0

Consider the following statements: struct nametype{string first; string last; }; struct coursetype{string name; int callnum; int credits; char grade; }; struct studenttype{nametype name; double gpa; coursetype course; }; studenttype student; studenttype classlist[100]; coursetype course; nametype name; mark the following statements as valid or invalid. if a statement is invalid, explain why.a.) student.course.callnum = "csc230"; b.) cin > > student.name; c.) classlist[0] = name; d.) classlist[1].gpa = 3.45; e.) name = classlist[15].name; f.) student.name = name; g.) cout < < classlist[10] < < endl; h.) for (int j = 0; j < 100; j++)classlist[j].name = name; i.) classlist.course.credits = 3; j.) course = studenttype.course;