(e) f(n)-5P0.+37 (a) I(n)-2n logs(2n +17n+1) 2. 30 points) Do the sane ns in problem #1. but this time you don't have to be rigorous (that is to say it). you don't have to prove the algorithmic complexity, you can just claim (b) go(n)n logs (n log2(n))3n1.01 (c) ge(n) 2log2(n)3+7n d) ga(n)-log2(5 +n) (e) g,(n) = (3n + 17) logs(2n3 + n) + 4n () gr(n)5 +72m+8 (h) ga(n)2++1 3,) (20 points) For each of the following algorithms: find the approximate running times, find a simple comparison function g(n) so that the running time is in (g(n), and prove that the running time function of the given algorithm is i jyour chosen theia set. (a) FUNCTON ,(n) RET JRN(s) (b) FUNCT ON fa(n) RETURN(s) (c) FUNCTON fa(n) FOR i In/5] TO n DO FOR j i TO n DO RETURN(s) (d) FUNCTON fa(n) FOR i n TO 2n2 DO RETURN(s) (e) FUNCT:ON fs(n) FOR J 5 TO i DO FOR k /10 i DO RETURN(s) (e) f(n)-5P0.+37 (a) I(n)-2n logs(2n +17n+1) 2. 30 points) Do the sane ns in problem #1. but this time you don't have to be rigorous (that is to say it). you don't have to prove the algorithmic complexity, you can just claim (b) go(n)n logs (n log2(n))3n1.01 (c) ge(n) 2log2(n)3+7n d) ga(n)-log2(5 +n) (e) g,(n) = (3n + 17) logs(2n3 + n) + 4n () gr(n)5 +72m+8 (h) ga(n)2++1 3,) (20 points) For each of the following algorithms: find the approximate running times, find a simple comparison function g(n) so that the running time is in (g(n), and prove that the running time function of the given algorithm is i jyour chosen theia set. (a) FUNCTON ,(n) RET JRN(s) (b) FUNCT ON fa(n) RETURN(s) (c) FUNCTON fa(n) FOR i In/5] TO n DO FOR j i TO n DO RETURN(s) (d) FUNCTON fa(n) FOR i n TO 2n2 DO RETURN(s) (e) FUNCT:ON fs(n) FOR J 5 TO i DO FOR k /10 i DO RETURN(s)