Homework SourseSort the following functions from asymptotically smallest to
Sort the following functions from asymptotically smallest to asymptotically largest. That is, the function f (n) and the next function g (n) must always follow that f (n) element O (g(n)). If the two functions have asymptotic the same order, i.e., f (n) = theta (g (n)), then also indicate that. Remember lgn = log_2 n. n, lg n, Squareroot n, 3^n, Squareroot lg n, lg Squareroot n, 3^Squareroot n, Squareroot 3^n, 3 lg n, lg (3^n), 3^lg Squareroot n, 3 Squareroot lg n, Squareroot 3^lg n, Ig (Squareroot 3^n), Squareroot lg (3^n), 5^n, 5^Squareroot n, Squareroot 5^n, 5^lg n, lg (5^n), 5^lg Squareroot n, 5^Squareroot lg n, Squareroot 5^lg n, lg (Squareroot 5^n), Squareroot lg (5^n).
Solution
solution--
sorted from lowest asymptotic to largest asymptotic
lg n,lgn,lg n,n=lg(3n)lg(5n)=,n=lg(3n)=lg(3n)=lg(5n)=lg(5n),3lg n,3ln n,3ln n,3n,3n,3n,5lg n,5ln n,5ln n,5n,5n,5n
