View of /trunk/rochester_problib/setDiscrete4Functions/ur_dis_4_13.pg

    1 ##DESCRIPTION
    2 ##Question 10, Section 2.2 of Discrete Math by Kenneth Rosen
    3 ##ENDDESCRIPTION
    4 
    5 DOCUMENT();        # This should be the first executable line in the problem.
    6 
    7 loadMacros(
    8 "PG.pl",
    9 "PGbasicmacros.pl",
   10 "PGchoicemacros.pl",
   11 "PGanswermacros.pl",
   12 "PGauxiliaryFunctions.pl"
   13 );
   14 
   15 TEXT(&beginproblem);
   16 
   17 BEGIN_TEXT
   18 You are the head of a division of a big Silicon Valley company and have assigned one
   19 of your engineers, Jim, the job of devising an algorithm to sort through an English
   20 text of \(n\) words and convert it into an Esperanto document.$PAR Jim comes up with an algorithm which takes \(2n^2+2^n\) bit operations to handle an
   21 input text with n words. $PAR Suppose the computers in your business can handle one bit operation every nanosecond
   22 (\(1\) nanosecond \(= 10^{-9}\) seconds).$PAR How many nanoseconds would it take Jim's algorithm to convert a text with \(10\) words
   23 on these computers?\{ans_rule(15)\}$PAR How many DAYS would it take Jim's algorithm to convert a text with \(50\) words on these
   24 computers?( Do not round your answers for WeBWorK.) \{ans_rule(15)\}$PAR
   25 END_TEXT
   26 ANS( num_cmp( 1224 ) );
   27 ANS( num_cmp( (2*50**2+2**50)/1000000000/60/60/24 ));
   28 
   29 $multiple = new_multiple_choice();
   30 
   31 $multiple -> qa(
   32 "For an input text of \(100\) words, the statement that best describes the performance
   33 of Jim's algorithm is:",
   34 "His algorithm would take more than \(40\) trillion years to run."
   35 );
   36 
   37 $multiple -> extra(
   38 "His algorithm would take between \(4\) and \(40\) years to run.",
   39 "His algorithm would take between \(4000\) and \(40,000\) years to run.",
   40 "His algorithm would take between \(40\) million and \(40\) billion years to run.",
   41 "His algorithm would take between \(40\) thousand and \(40\) million years to run.",
   42 "His algorithm would take between \(40\) billion and \(40\) trillion years to run.",
   43 "His algorithm would take between \(40\) and \(400\) years to run."
   44 );
   45 
   46 BEGIN_TEXT
   47 (Recall a million is \(10^6\), a billion is \(10^9\) and a trillion is \(10^{12}\).)$PAR
   48 \{$multiple -> print_q\}
   49 \{$multiple -> print_a\}
   50 END_TEXT
   51 
   52 ANS( checkbox_cmp( $multiple->correct_ans ));
   53 
   54 ENDDOCUMENT();        # This should be the last executable line in the problem.;