Sample answers, CS1110 Prelim 3, Spring 2008 David Gries djg17
1
Q1. /** = “this rhino or one of its ancestors has
name n. */
public boolean hasName(String n) {
if (String.equals(n)) return true;
return
(father == null ? false : father.hasName(n)) ||
(mother == null ? false : mother.hasName(n));
}
}
Q2. (a) Output: the message “Exception!!”
(b) public class BadNumberException
extends Exception {
/** Constructor: instance with empty
string for a detail message */
public BadNumberException()
{ super(); }
/** Constructor: instance with detail
message d*/
public BadNumberException (String d)
{ super(d); }
}
(c) /** = greatest common divisor of x and y.
Throw a BadNumberException if x<=0 or
y<=0. */
public static int GCD(int x, int y) throws
BadNumberException {
if (x <= 0 || y <= 0) {
throw new BadNumberException(
“x and y have to be positive integers”);
}
int b= x; int c= y;
/* inv: gcd(x, y) = gcd(b, c), b > 0, and c > 0 */
while (b != c) {
if (b < c) c= c – b;
else b= b – c;
}
return b;
}
Q3. (a) // inv: each row 0..k-1 of sq sums to sum.
for (int k= 0; k < sq.length; k = k + 1) {
// Return false if row k does not sum to sum.
int rowsum= 0;
for (int j= 0; j < sq.length; j= j + 1) {
rowsum= rowsum + sq[k][j];
}
if (rowsum != sum)
return false;
}
/* post: each row 0..sq.length-1 sums to sum */
return true;
(b) /* inv: rows 0..k-1 and cols 0..k-1 sum to sum
*/
for (int k= 0; k < sq.length; k= k+1) {
int colsum= 0; // will be sum of col k
int rowsum= 0; // will be sum of row k
for (int j= 0; j < sq.length; j= j + 1) {
colsum= colsum + sq[j][k];
rowsum= rowsum + sq[k][j];
}
if (colsum != sum || rowsum != sum) {
return false;
}
}
return true;
Q4. (a) Code in a construct can reference any of the
names declared in that construct as well as names that
appear in enclosing constructs (unless a name is
declared twice, in which case the closer one prevails).
(b) Within an object: this refers to the object itself,
while super refers to the object but only the
partitions for the superclass and above. Also,
“this(…);” can be used to call another constructor in
this object and “super(…);” can be used to call a
constructor in the superclass partition of the object.
(c) To override a method is to redeclare an inherited
method in a class. this.m(...) or m(…)
Q5. (a)
/** = an integer j that satisfies
b[p..j] <= x < b[j+1..q-1]
Precondition: b[p..q-1] is sorted */
public static int bsearch(int[] b, int x, int p, int q)
(b) int j= p-1;
int k= q;
// invariant: b[p..j] <= x < b[k..q-1]
while (j+1 != k) {
int e= (j+k)/2;
if (b[e] <= x) j= e;
else k= e;
}
return j;