algorithm

Sort the following 24 functions from asymptotically smallest to asymptotically largest, indi- cating ties if there are any. Do as much as you can, you will receive partial credit if you do not sort all of them. You will also need to turn in proofs that justify your answers to receive full credit! All logarithms are base 2 unless otherwise stated n1 +( 1/ log n) 2n ea (log n)(n/2) log(200) n1.5 - (n - 2)4.5 .i logi log"(n/2) (log n)log'n llog log(n!) (log n)logn log2 n 2+1 2log log 2" log 17n (1+)200h n(log n)2 (log log n)/(log n) n n1/ log log r log log n 7n To simplify notation, write f(n) g(n) to mean f(n) 0(g(n), f(n) g(n) to mean f(n) 6(g(n)), and f(n) g(n) to mean f(n) %(n)). For example, the functions n2, n, (), n3 could be sorted either as n3 (5) n> n or as n> n; (n) n Sort the following 24 functions from asymptotically smallest to asymptotically largest, indi- cating ties if there are any. Do as much as you can, you will receive partial credit if you do not sort all of them. You will also need to turn in proofs that justify your answers to receive full credit! All logarithms are base 2 unless otherwise stated n1 +( 1/ log n) 2n ea (log n)(n/2) log(200) n1.5 - (n - 2)4.5 .i logi log"(n/2) (log n)log'n llog log(n!) (log n)logn log2 n 2+1 2log log 2" log 17n (1+)200h n(log n)2 (log log n)/(log n) n n1/ log log r log log n 7n To simplify notation, write f(n) g(n) to mean f(n) 0(g(n), f(n) g(n) to mean f(n) 6(g(n)), and f(n) g(n) to mean f(n) %(n)). For example, the functions n2, n, (), n3 could be sorted either as n3 (5) n> n or as n> n; (n) n