CS100, Spring 2000, Solutions to Prelim 1

===================================== Q1 =====================================

int n = in.readInt();
double sum = 0.0;
double squares = 0.0;
int k = 0;
double speed;
while (k != n) {
    speed = in.readDouble();
    sum = sum + speed;
    squares = squares + speed*speed;
    k = k+1;
if (n == 0) System.out.println("No molecules!");
else {
    double Vmean = sum/n;
    double Vrms = Math.sqrt(squares/n); // or Math.pow(squares/n,.5)
    System.out.println("Percent error:" + Math.abs(100*(Vrms-Vmean)/Vmean));
}

===================================== Q2 =====================================

from worst to best: semi-direct, wacko, "&&", "=="

semi-direct:                       
    if (month == 2) days = 28;       
    else if (month <= 7)             
        if (month%2 == 0) days = 30; 
        else days = 31;              
    else                             
        if (month%2 == 0) days = 31; 
        else days = 30;              

wacko: if (month == 2) days = 28; else days = (month/8+month) % 2 + 30;

"&&": if (month == 2) days = 28;
      else if (month<=7 && month%2 == 0 || month>=8 && month%2 == 1) days = 30;
      else days = 31;

"==": if (month == 2) days = 28;
      else if ((month <= 7) == (month%2 == 0)) days = 30;
      else days = 31;

===================================== Q3 =====================================

version 1:

int max;                 // max so far
int prev = in.readInt(); // previous value
int next;                // next value to process
if (prev<-10 || prev>10) System.out.println("no numbers");
else {
    next = in.readInt();
    if (prev<-10 || prev>10) System.out.println("only one number");
    else {
        max = prev+next;
        while (-10 <= prev && prev <= 10) {
            if (prev+next > max) max = prev+next;
            prev = next;
            next = in.readInt();
        }
        System.out.println("max: " + max);
    }
}

Deficiencies:
- "magic number" 10 used instead of a named constant
- has many special cases and is deeply nested
_______________________________________________________________________________

version 2:

int limit = 10;                     // valid numbers are -limit..limit
int minusInfinity = -2*limit-1;     // smaller than any legal pair sum
int max = minusInfinity;            // max so far
int prev = minusInfinity;           // previous value
int next = in.readInt();            // next value to process
// process numbers, maintaining vars above, until find number out of limits
    while (Math.abs(next) <= limit) {
        prev = next; 
        next = in.readInt();
        if (Math.abs(next) <= limit) max = Math.max(max, prev+next);
    }
 // print max pair sum (or error message, if none)
    if (max==minusInfinity) System.out.println("not enough numbers");
    else System.out.println("max: " + max);

Deficiency:
- "next in bounds" is tested twice each loop iteration
_______________________________________________________________________________

version 3:

int limit = 10;                   // valid numbers are -limit..limit
int minusInfinity = -2*limit-1 ;  // smaller than any pair sum, 
int max = minusInfinity;          // max so far
int prev = minusInfinity - limit; // previous value -- init so that if add
                                  // 0 or 1 #, still at most minusInfinity
int next = in.readInt();          // next value to process
// process numbers, maintaining vars above, until find number out of limits
    while (Math.abs(next) <= limit) {
        // update max pair sum
            max = Math.max(max, prev+next);
        // read next
            prev = next;
            next = in.readInt();
    }
// print max pair sum (or error message, if none)
    if (max <= minusInfinity) System.out.println("not enough numbers");
    else System.out.println("max: " + max);

==================================== Bonus ====================================

 B1 a) yes, 0 is a multiple of 17
 B2 d) 0 is neither positive nor negative
 B3 a) 2 is the median of 2, 2, 5
 B4 a) yes: read news with a fixed-width(=mono-spaced=non-proportional) font
 B5 c) never ok to put off to the side a comment for a group of statements 
 B6 a) Java does, but we don't allow $ as part of a variable name
 B7 b) only projects --not exercises-- are partners allowed
 B8 L) is the missing middle initial from DIS, TKY, SNA, LJB, AMH
 B9 g) Po Chen is not on CS100 staff this semester
B10 b) Tue has the least total time for office hours and tutoring