/*** 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 log_{2}N
, where log_{2}N 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.

- Download the program and run it
- Practice the guessing game until you can solve it in 10 tries each time
- Change the game to choose a number between 1 and 1 million, and change
the loop

to allow an appropriate number of guesses. - Change the program so that it asks the user whether they want to guess
between 1 and 100,

or between 1 and 1000, or between 1 and 1000000. The program must then automatically

choose the appropriate maximum number of guesses.

Use if... commands to decide the maximum number of guesses to allow.

**at the beginning, the HIGHEST possibility is 500, and LOWEST is 0**- calculate the MIDDLE value between LOWEST and HIGHEST - guess this
- if the response is "Right", then you can quit
- if the response is "too small", then change LOWEST to equal your GUESS+1
- if the response is "too big", then change HIGHEST to be your GUESS-1
- repeat - e.g. go back to
calculate MIDDLE and guess again

guaranteed to eventually find an answer.

Since there is a clear algorithm, we can program the COMPUTER to do the guessing automatically.

That means we can think of a secret number, and then let the COMPUTER try to guess

our number.

- Write a program that makes the computer try to guess our secret number