15-100 Sections U-V-AA / Spring 2009
Midterm Exam #1 (Written Portion)
Exam Date:  Tue 3-Mar-2009

16 Questions + 2 Bonus Questions / 50 Minutes
All questions are equally weighted (5 points each / 80 points total)

Note: Unicode ‘A’ is 65, ‘a’ is 97, and ‘0’ is 48.

Part I: What will the following code snippets print?

1. System.out.println(1 + 5 % 2 * 3);
System.out.println(99 / 98 / 97 + 96 / 95);

2. double d = 1.93431235412324;
int i = 3/(int)d + (int)(3/d);
d = Math.pow(Math.ceil(d),1+Math.floor(d));
System.out.println(d + "," + i);

3. char c = 'b';
int i = 'b';
String s = "A" + c + i;
System.out.println(c + "," + i + "," + s);

4. String s = "\\a\tb\nc\te";
System.out.println(s + s.length());

5. String s = "abcdef", t = s + s;
for (int i=t.length()-2; i>0; i/=3)
System.out.print(t.charAt(i));

6. String[] a = { "abc", "def", "ccc" };
for (int i=0; i<3; i++)
for (int j=i+1; j<3; j++) {
System.out.println(i + "," + j);
if (a[i].charAt(j) == a[j].charAt(i))
System.out.println(a[i].charAt(j));
}

7. Scanner scanner = new Scanner("1234252 + 6728 == 1240980");
scanner.useDelimiter("2");
while (scanner.hasNextInt())
System.out.println(scanner.next());
System.out.println("---");
do
System.out.println(scanner.next());
while (scanner.hasNextInt());

8. int i=8, j= 12;
while (true) {
if ((i % 3) == (j % 4))
break;
else if ((i % 4) > (j % 3)) {
j--;
continue;
}
System.out.println(i + "," + j);
j--;
i++;
}
System.out.println(i + "," + j);

// Hint: This code prints out exactly 3 lines.

9. String s = "abbc", t = s+s+s;
int i = 0;
while (t.indexOf("ca") >= 0) {
t = ((i % 2 == 0) ? t.replace("bc","c") : t.substring(3));
i++;
System.out.println(i + "," + t);
}

// Hint: This code prints out exactly 4 lines.

Part II: Write just a few lines of code (not entire methods) for each of these problems.

Assume all variables are already declared and initialized.

1. Print “empty” if the String s is empty or “null” if it is null. Print nothing otherwise.

2. Print “yes” if the String s is a palindrome (same forwards as backwards) and “no” otherwise. Empty strings are palindromes, but null strings are not. Also, "Aa" and "ab a" are not palindromes.

3. Assume these methods are already written:
public static int f(int x)
and
public static int g(int x)
Using these methods, and assuming that "a" is a non-null array of int’s, print all the values x in the array a where exactly one of f(x) or g(x) is even and the other is odd.

Part III: What will the following code snippets paint? Draw your answer inside the 100x100 window provided for you. Do not worry about being pixel-perfect. Within a few pixels is fine.

4.
page.drawRect(25,25,25,25);
page.drawRect(50,50,25,25);
for (int x=25; x<100; x+=50)
for (int y=25; y<100; y+=50)
if (x <= y) {
int dx = (x > 50) ? 0 : -10;
page.fillRect(x+dx,y,20,20);
}

5.
page.drawLine(50, 30, 50, 80);
Polygon p = new Polygon();
int[] a = { 2, 4, 6, 8, 9, 7, 5, 3 };
for (int i=0; i<a.length; i+=2)
p.addPoint(10*a[i],10*a[i+1]);
page.drawPolygon(p);

Part IV: Answer the following questions in general, and in just a few words of plain English.

For example, consider this method:
public boolean foo(int x) {
return (Math.abs(x) - x == 0);
}
This method “tests if x is non-negative”. No credit will be given for missing this generality, and stating what the code (obviously) does at a lower level, as in: “tests if the difference of the absolute value of x and x is equal to zero.”

6. In general, when does this method return “true”?

public static boolean h(int[] a, int[] b) {
int x = 0;
int m = Math.max(a.length, b.length);
for (int i=0; i<m; i++) {
if (i < a.length) x += a[i];
if (i < b.length) x -= b[i];
}
return (x == 0);
}

7. In general, assuming d is in the range (0,1), what does this method do?

public static void g(double d) {
if ((d < 0) || (d >= 1)) {
System.out.println("out of range");
return;
}
int max = 1000;
int bestX = 0, bestY = 1;
double bestDiff = -1;
for (int x=0; x<=max; x++)
for (int y=x+1; y<=max; y++) {
double guess = 1.0*x/y;
double diff = Math.abs(guess - d);
if ((bestDiff < 0) || (diff < bestDiff)) {
bestDiff = diff;
bestX = x;
bestY = y;
}
}
System.out.println(bestX + "/" + bestY);
}

8. Bonus/Optional:
The preceding problem is needlessly inefficient – it makes on the order of (max²) guesses, so it runs very slowly as max increases to, say, one million or so. Explain how to change the code so it makes on the order of (max) guesses, thus allowing us to efficiently increase max even to a billion or so.

9. Bonus/Optional: In general, what does this method do?

public static int q(int[] z) {
int a=9,b=8,c=7,d=a*b/c,e=a+b-c,f=d-e;
for (int q=z.length-1; q>=0; q--)
for (int r=Math.abs(z[q]); r>0; r/=d)
for (int s=r%e;s>0; s/=d)
f+=(s%2);
return f;
}