/*** Guess a Secret Number *************************************
Luke is making a game for his little sister, to keep her busy.
The program chooses a number between 1 and 500, and the user must
try to guess the number. They are permitted to guess 10 times.
****************************************************************/
public class GuessNumber
{
public GuessNumber()
{ int secret = (int)(Math.random()*500+1);
for(int c = 1; c <= 10; c=c+1)
{
int guess = Integer.parseInt( input("Your guess?") );
if(guess < secret)
{ output("too small"); }
if(guess > secret)
{ output("too big"); }
if(guess == secret)
{ output("RIGHT! That took " + c + " guesses.");
System.exit(0);
}
}
}
public static void main(String[] args)
{ new GuessNumber(); }
public String input(String prompt)
{ return javax.swing.JOptionPane.showInputDialog(null,prompt); }
public void output(String message)
{ javax.swing.JOptionPane.showMessageDialog(null,message); }
}
|
It seems like 10 guesses would not be enough to guess a number chosen
from 500 choices. But the divide-and-conquer
strategy, it is possible to win this game every time. You must guess
250 as the first guess. Then the program tells you
whether the secret number is higher or lower. This cuts the number
of possibilities in half. Then you need to guess the
middle number of the ones that are
left.
| Guess: 250 too small Guess: 375 too big Guess: 315 too small Guess: 345 too small Guess: 360 too big Guess: 352 too small Guess: 356 too small Guess: 358 too big Guess: 357 RIGHT! That took 9 guesses |
At every guess, it cuts the number of remaining possibilities in half,
like this:
500
250
125
63
32
16
8
4
2
1
We see this takes 10 steps, so 10 guesses should be enough if we use the
divide-and-conquer strategy.
If we use a divide and conquer algorithm
that cuts the problem in half over and over again, it is much faster than
an exhaustive algorithm that
simply counts through all the possibilities - e.g. guess 1, then 2, then
3, etc..
If we can divide the problem in half over and over again, then the number
of steps is not N (the number of items), but rather log2N
, where log2N is
defined as "the number of times you must divide a number by 2 until the
result is 1 or smaller."
A typical example of divide-and-conquer as a binary
search, which is exactly what we are doing
when we try to guess the number by guessing in the middle each time.