15-100 Sections U-V-AA / Spring 2009 / Quiz 0
15 Minutes
Pass/Fail (this quiz only!)
SHOW YOUR WORK!
1.
Mystery Code /
Arithmetic
Assuming that variables x, y, and z all hold non-negative integer values, under
what conditions in general will
the following line of code crash?
int mystery = x / y / z - x / (y / z);
2.
Sum from 0 to n
Assuming that the variable n holds a
non-negative integer value, write a code snippet that prints out the sum of the
integers from 0 to n. For example,
if n equals 3, your code should print out 6 because 0 + 1 + 2 + 3 = 6.
Note: To solve this, you may not
use loops (even if you know how!).
Instead, you should use GaussÕs
Formula: 0 + 1 + 2 + É + n
= (1/2)n2 + (1/2)n
To verify, if n equals 3, GaussÕs Formula says:
0 + 1 + 2 + 3 =
(1/2)32 + (1/2)3 = 9/2 + 3/2 = 12/2 = 6. Yep.
Hint: be sure to properly handle integer division and truncation
3.
Flag of Colombia
Write the body of a paint method for a program that displays the flag of
Colombia, using built-in colors and entirely filling the window, even when the
window is resized:
(Flag of Colombia Ð Yellow stripe on top half; blue
and red stripes on bottom half)
public void paint(Graphics page)
{
}
4.
Bonus/Optional:
a) For positive ints a, b, and c, if (a / b / c) equals (a / (b / c)), what
must be true about c? Prove this (briefly).
b) For positive ints x and y,
where y>1, under what conditions will ((x Ð 1) % y) / (y Ð 1) be non-zero?