CS211 Prelim 1 Solutions. 11 Mar 2004
QUESTION 1.
/** b[0..N-1] is sorted in ascending order.
Return an integer k that truthifies this assertion:
b[0..k] <= x < b[k+1..N-1] */
public static int search(int[] b, int x) {
int k= -1; int h= N;
// invariant: b[0..k] <= x < b[h..N-1]
while (h != k+1) {
int e= (k+h) / 2;
// { -1 ≤ k < e < h <= N }
if (b[e] <= x) k= e;
else h= e;
}
return k;
}
QUESTION 2(a).
Prove the base and inductive cases:
Base case: Prove P(0).
Inductive case: Assume P(0), …, P(k),
for k >= 0, and prove P(k+1).
QUESTION 2(b).
A class C is made abstract so that it cannot be
instantiated.
A method is made abstract so that it must be
overridden in any subclass of C.
QUESTION 2(c).
try {
dn= Integer.parseInt(somestring);
}
catch (NumberFormatException e) {
dn= 1;
}
QUESTION 3
/** = longest common subsequence of s1 and s2 */
public static String lcs(String s1, String s2) {
if (s1.length() == 0 || s2.length() == 0)
return "";
// { s1 and s2 have at least one char each }
if (s1.charAt(0) == s2.charAt(0)) {
return s1.charAt(0) +
lcs(s1.substring(1), s2.substring(1));
}
// { first chars are different }
String first= lcs(s1, s2.substring(1));
String second= lcs(s1.substring(1), s2);
if (first.length() >= second.length())
return first;
else return second;
}
QUESTION 4(a).
public class Celebrity implements Personal {
private String name;
private int age;
// Constructor: instance with name n and age a
public Celebrity(String n, int a)
{ name = n; age = a; }
// = the name of this Celebrity
public String getName() { return name; }
// = the age of this Celebrity
public int getAge() { return age; }
}
QUESTION 4(b).
public class Actor extends Celebrity
implements Business {
private String address;
private int earnings;
// Constructor: instance with name n, age a,
// address addr, and earnings e
public Actor(String n, int a, String addr, int e)
{ super(n,a); address = addr; earnings = e; }
// = the address of this Actor
public String getAddress() { return address; }
// = the earnings of this Actor
public int getEarnings() { return earnings; }
}
QUESTION 5. The inner class. Place it right after
method iterator, and add a blank remove() function to
make it compilable. There is no need for an explicit
constructor; we use the default.
/** An iterator of the Processes in this instance */
public class ProcessIterator implements Iterator {
int posA = 0; // index of next position in userA
int posB = 0; // index of next position in userB
/** = there exists another item to enumerate */
public boolean hasNext()
{ return (posA < sizeA || posB < sizeB); }
/** = next element in the enumeration. Throw
NoSuchElementException if no more items */
public Object next() {
if (!hasNext())
throw new NoSuchElementException();
if (posB == sizeB ||
(posA < sizeA && userA[posA].priority >=
userB[posB].priority)) {
posA= posA+1;
return userA[posA-1].priority;
}
posB= posB+1;
return userB[posB-1].priority;
}
}