COS 126

Conditionals, Loops, Arrays		 Programming Assignment

The goal of this assignment is to write five short Java programs to gain practice with loops, conditionals, and arrays.

  1. Bits. Write a program Bits.java that takes an integer command-line argument N and uses a while loop to compute the number of times you need to divide N by 2 until it is strictly less than 1. Print out the error message "Illegal input" if N is negative. 
    % java Bits 0                     % java Bits 8
0                                 4

% java Bits 1                     % java Bits 16
1                                 5

% java Bits 2                     % java Bits 1000
2                                 10

% java Bits 4                     % java Bits -23
3                                 Illegal input

    Remark: This computes the number of bits in the binary representation of N, which also equals 1 + floor(log2 N) when N is positive. This quantity arises in information theory and the analysis of algorithms.


  2. Checkerboard. Write a program Checkerboard.java that takes an integer command-line argument N, and uses two nested for loops to print an N-by-N "checkerboard" pattern like the one below: a total of N2 asterisks, where each row has 2N characters (alternating between asterisks and spaces). 
    % java Checkerboard 4             % java Checkerboard 5
* * * *                           * * * * * 
 * * * *                           * * * * *
* * * *                           * * * * * 
 * * * *                           * * * * *
                                  * * * * *


  3. Probability of having at least one child of each gender. A couple beginning a family decides to keep having children until they have at least one of either sex.

    1. BoyAndGirl. Write a program BoyAndGirl.java that simulates repeatedly having a child until there is at least one of each sex. Output how many children it took to achieve this goal. Assume there is equal probability of having either a boy or a girl. Use a while loop to compute the number of children the couple has until getting at least one of each gender. 
      % java BoyAndGirl
Congratulations!  You have 3 children.

% java BoyAndGirl
Congratulations!  You have 6 children.

% java BoyAndGirl
Congratulations!  You have 2 children.

    2. BoysAndGirls. Write a program BoysAndGirls.java that takes an integer command-line argument T. In each of T independent experiments, simulate a couple having children until they have at least one of each gender. Use the results of the T experiments to estimate the average number of children the couple will have. Record and output the frequency counts for 2, 3, and 4 children, and also one count for 5 and above. Finally, output the most common number of children in a family. (If there is a tie, print only the first most common number of children.) As before, assume that the probability of having a boy or a girl is 1/2. 
      java BoysAndGirls 2
Average: 6.0 children to get at least one of each sex.
Number of families with 2 children: 0
Number of families with 3 children: 0
Number of families with 4 children: 0
Number of families with 5 or more children: 2
Most common number of children is 5 or more.

% java BoysAndGirls 10
Average: 3.5 children to get at least one of each sex.
Number of families with 2 children: 2
Number of families with 3 children: 3
Number of families with 4 children: 3
Number of families with 5 or more children: 2
Most common number of children is 3.

% java BoysAndGirls 100
Average: 3.19 children to get at least one of each sex.
Number of families with 2 children: 44
Number of families with 3 children: 24
Number of families with 4 children: 16
Number of families with 5 or more children: 16
Most common number of children is 2.

    As T increases, we expect the average number of children per family to converge. Use BoysAndGirls to formulate a hypothesis as to what this average is. Run BoysAndGirls with T = 1, 10, 100, 100000 and 1000000 to watch it converge to a sufficiently accurate estimate.


  4. Dice and the Gaussian distribution. Write a program TenDice.java that takes an integer command-line argument N, and rolls 10 fair six-sided dice, N times. Use an array to tabulate the number of times each possible total (between 10 and 60) occurs. Then print out a text histogram of the results, as illustrated below. 
    % java TenDice 1000
10: 
11: 
12: 
13: 
14: 
15: 
16: 
17: 
18: *
19: ****
20: 
21: ***
22: ******
23: ********
24: ****************
25: *************
26: **********
27: *********************************
28: ****************************************
29: *********************************
30: ***************************************************
31: *****************************************************************
32: ********************************************************
33: **************************************************************************************
34: ***********************************************************
35: *********************************************************************
36: ***********************************************************************************
37: **************************************************************
38: *****************************************************************
39: ***************************************
40: *****************************************************
41: ************************************
42: ****************************
43: ************************
44: ************************
45: *********
46: ***********
47: *******
48: ***
49: **
50: 
51: 
52: *
53: 
54: 
55: 
56: 
57: 
58: 
59: 
60:
    Remark: a classic result from probability theory (central limit theorem) asserts that the shape of the resulting histogram is well-approximated by the ubiquitous bell curve (Gaussian distribution).


Submission. Submit the files Bits.java, Checkerboard.java, BoyAndGirl.java, BoysAndGirls.java, and TenDice.java. Finally, submit a readme.txt file and answer the questions.