Solution for
Programming Exercise 5.2
THIS PAGE DISCUSSES ONE POSSIBLE SOLUTION to
the following exercise from this on-line
Java textbook.
Exercise 5.2:
A common programming task is computing statistics of a set of numbers. (A statistic
is a number that summarizes some property of a set of data.) Common statistics
include the mean (also known as the average) and the standard deviation (which tells
how spread out the data are from the mean). I have written a little class called
StatCalc that can be used to compute these statistics, as well as the sum of
the items in the dataset and the number of items in the dataset. You can read
the source code for this class in the file StatCalc.java.
If calc is a variable of type StatCalc, then the following methods
are defined:
- calc.enter(item); where item
is a number, adds the item to the dataset.
- calc.getCount() is a function that
returns the number of items that have been added to the dataset.
- calc.getSum() is a function that
returns the sum of all the items that have been added to the dataset.
- calc.getMean() is a function that
returns the average of all the items.
- calc.getStandardDeviation() is a function that
returns the standard deviation of the items.
Typically, all the data are added one after the other calling the enter()
method over and over, as the data become available. After all the data have been entered, any of the
other methods can be called to get statistical information about the data.
The methods getMean() and getStandardDeviation() should only
be called if the number of items is greater than zero.
Modify the current source code, StatCalc.java, to add
instance methods getMax() and getMin(). The getMax()
method should return the largest of all the items that have been added to the
dataset, and getMin() should return the smallest. You will need to
add two new instance variables to keep track of the largest and smallest items that
have been seen so far.
Test your new class by using it in a program to compute statistics for a set
of non-zero numbers entered by the user. Start by creating an object of type
StatCalc:
StatCalc calc; // Object to be used to process the data.
calc = new StatCalc();
Read numbers from the user and add them to the dataset. Use 0 as a sentinel value
(that is, stop reading numbers when the user enters 0). After all the user's non-zero
numbers have been entered, print out each of the six statistics that available
from calc.
Discussion
For the StatCalc class to handle minimums and maximums,
some of what must be added to the class is obvious. We needs two new
instance variables, min and max, and two methods to return
the values of those instance variables. So, we can add these lines to
the class definition:
private double min; // Smallest item that has been entered.
private double max; // Largest item that has been entered.
public double getMin() {
// Return the smallest item that has been entered.
return min;
}
public double getMax() {
// Return the largest item that has been entered.
return max;
}
But then there is the problem of making sure that min and
max have the right values. Every time we have a new number
to add to the dataset, we have to compare it with min.
If the new number is smaller than the current min, then
the number becomes the new value of min (since the new number
is now the smallest number we have seen so far). We do something
similar for max. This has to be done whenever a number
is entered into the dataset, so it has to be added to the enter()
method, giving:
public void enter(double num) {
// Add the number to the dataset.
count++;
sum += num;
squareSum += num*num;
if (num > max) // We have a new maximum.
max = num;
if (num < min) // We have a new minimum.
min = num;
}
Unfortunately, if this is all we do, there is a bug
in our program. For example, if the dataset consists
of the numbers 21, 17, and 4, the computer will insist that
the minimum is 0, rather than 4. The problem is that the
variables min and max are initialized to zero.
(If no initial value is provided for a numerical instance variable,
it gets the default initial value, zero.) Since min is 0,
none of the numbers in the dataset pass the test "if (num < min)",
so the value of min never changes. A similar problem holds
for max, but it will only show up if all the numbers in the
dataset are less than zero. For the other instance variables,
count, sum, and squareSum, the default initial
value of zero is correct. For min and max, we have
to do something different.
Once possible way to fix the problem is to treat the first number
entered as a special case. When only one number has been entered, it's
certainly the largest number so far and also the smallest number so far,
so it should be assigned to both min and max. This
can be handled in the enter() method:
public void enter(double num) {
// Add the number to the dataset.
// (This is NOT the version I used in my final answer.)
count++;
sum += num;
squareSum += num*num;
if (count == 1) { // This is the fist number.
max = num;
min = num;
}
else {
if (num > max) // We have a new maximum.
max = num;
if (num < min) // We have a new minimum.
min = num;
}
}
This works fine. However, I decided to use an alternative approach.
We would be OK if we could initialize min to have a value
that is bigger than any possible number. Then, when the first number
is entered, it will have to satisfy the test "if (num < min)",
and it will become the value of min. But to be bigger than any
possible number, min would have to be infinity.
The initial value for max has to be smaller than any possible
number, so max has to be initialized to negative infinity.
And that's what we'll do!
The system that is used to represent real numbers in a computer
includes special values to represent infinity and negative infinity.
Java has a standard class named Double that includes
named constants for these quantities, Double.POSITIVE_INFINITY
and Double.NEGATIVE_INFINITY. We can use these named
constants to provide initial values for the instance variables
min and max. So, the declarations become:
private double max = Double.NEGATIVE_INFINITY; // Largest item seen.
private double min = Double.POSITIVE_INFINITY; // Smallest item seen.
With this change, the StatCalc class works correctly. The
complete class is shown below. (By the way, there is another special
constant, Double.NaN, that represents an undefined value
such as the result of dividing a number by 0.0.
"NaN" stands for "Not a Number.")
The main program is fairly straightforward. The user's data are
read and entered into the StatCalc object in a loop:
do {
TextIO.put("? ");
item = TextIO.getlnDouble();
if (item != 0)
calc.enter(item);
} while ( item != 0 );
The subroutine call "calc.enter(item);" enters
the user's item. That is, it does all the processing necessary to
include this data item in the statistics it is computing.
After all the data have been entered, the statistics can be
obtained by using function calls such as "calc.getMean()".
The statistics are output in statements such as:
TextIO.putln(" Average: " + calc.getMean());
Note that a function call represents a value, and so can be used
anyplace where a variable or literal value could be used. I don't have
to assign the value of the function to a variable. I can use the function
call directly in the output statement.
The complete main program is shown below.
Although that completes the exercise, one might wonder: Instead of
modifying the source code of StatCalc, could we make a subclass
of StatCalc and put the modifications in that? The answer is yes,
but we need to use the slightly obscure special variable super that
was discussed in Section 5.5.
The new instance variables and instance methods can simply be put into the
subclass. The problem arises with the enter() method. We have to
redefine this method so that it will update the values of min and
max. But it also has to do all the processing that is done
by the original enter() method in the StatCalc class.
This is what super is for. It lets us call a method from
the superclass of the class we are writing. So, the subclass can be written:
class StatCalcWithMinMax extends StatCalc {
private double max = Double.NEGATIVE_INFINITY; // Largest item seen.
private double min = Double.POSITIVE_INFINITY; // Smallest item seen.
public void enter(double num) {
// Add the number to the dataset.
super.enter(num); // Call the enter method from the StatCalc class.
if (num > max) // Then do the extra processing for min and max.
max = num;
if (num < min)
min = num;
}
public double getMin() {
// Return the smallest item that has been entered.
// Value will be infinity if no items have been entered.
return min;
}
public double getMax() {
// Return the largest item that has been entered.
// Value will be -infinity if no items have been entered.
return max;
}
} // end class StatCalcWithMinMax
The Solution
Revised StatCalc Class
/*
An object of class StatCalc can be used to compute several simple statistics
for a set of numbers. Numbers are entered into the dataset using
the enter(double) method. Methods are provided to return the following
statistics for the set of numbers that have been entered: The number
of items, the sum of the items, the average, the standard deviation,
the maximum, and the minimum.
*/
public class StatCalc {
private int count; // Number of numbers that have been entered.
private double sum; // The sum of all the items that have been entered.
private double squareSum; // The sum of the squares of all the items.
private double max = Double.NEGATIVE_INFINITY; // Largest item seen.
private double min = Double.POSITIVE_INFINITY; // Smallest item seen.
public void enter(double num) {
// Add the number to the dataset.
count++;
sum += num;
squareSum += num*num;
if (num > max)
max = num;
if (num < min)
min = num;
}
public int getCount() {
// Return number of items that have been entered.
return count;
}
public double getSum() {
// Return the sum of all the items that have been entered.
return sum;
}
public double getMean() {
// Return average of all the items that have been entered.
// Value is Double.NaN if count == 0.
return sum / count;
}
public double getStandardDeviation() {
// Return standard deviation of all the items that have been entered.
// Value will be Double.NaN if count == 0.
double mean = getMean();
return Math.sqrt( squareSum/count - mean*mean );
}
public double getMin() {
// Return the smallest item that has been entered.
// Value will be infinity if no items have been entered.
return min;
}
public double getMax() {
// Return the largest item that has been entered.
// Value will be -infinity if no items have been entered.
return max;
}
} // end class StatCalc
Main Program
/*
Computes and display several statistics for a set of non-zero
numbers entered by the user. (Input ends when user enters 0.)
This program uses StatCalc.java.0
*/
public class SimpleStats {
public static void main(String[] args) {
StatCalc calc; // Computes stats for numbers entered by user.
calc = new StatCalc();
double item; // One number entered by the user.
TextIO.putln("Enter your numbers. Enter 0 to end.");
TextIO.putln();
do {
TextIO.put("? ");
item = TextIO.getlnDouble();
if (item != 0)
calc.enter(item);
} while ( item != 0 );
TextIO.putln("\nStatistics about your calc:\n");
TextIO.putln(" Count: " + calc.getCount());
TextIO.putln(" Sum: " + calc.getSum());
TextIO.putln(" Minimum: " + calc.getMin());
TextIO.putln(" Maximum: " + calc.getMax());
TextIO.putln(" Average: " + calc.getMean());
TextIO.putln(" Standard Deviation: " + calc.getStandardDeviation());
} // end main()
} // end SimpleStats
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