We are going to create a class called LongInteger inheriting SignedNumeral that can store an indefinite size of an integer value beyond the primitive types such as int and long.
What is so special about primitive data types in Java?
Java SE provides a similar class called although the implementations of LongIntegerandBigIntegerare completely independent.
Field
Let us declare the member field digits that is an array of bytes holding the values of this integer:
L1: LongInteger is passed to specify the generic type T in SignedNumeral.
The i'th dimension of digits is the i'th least significant digit in the integer such that the integer 12345 would be stored as digits = {5, 4, 3, 2, 1}, which makes it convenient to implement the arithmetic methods, add() and multiply().
Is the array of bytes the most efficient way of storing a long integer?
Constructors
Let us define the following three constructors:
L2: the default constructor that initializes this integer with 0 by calling the constructor in L20.
L10: a copy constructor that initializes this integer with n.
Do the constructors in L10 and L20 call any constructor in the super class?
Arrays.copyOf() is a referenced by the class type Arrays, not an object. Java provides many classes with static methods that are commonly used (e.g., , ).
Can you call non-static methods or fields in the body of a static method?
The static keyword must not be abused to quickly fix compile errors unless it is intended.
Method: set()
Let us define the set() method that takes a string and sets the sign and the value of this integer:
L1-7: javadoc comments.
L4: this method throws if n is null.
When should we use statements over blocks for error handling and vice versa?
This type of method is called a setter. Java encourages making member fields private and creating getters and setters to access the fields for , which is not necessarily encouraged by other languages.
Method: add()
Let us override the add() method that calls two helper methods:
L3-4: adds n to this integer that has the same sign by calling addSameSign().
L5-6: adds n to this integer that has a different sign by calling addDifferentSign().
The following shows an implementation of addSameSign() based on the simple arithmetic:
L7-9: creates the byte array result by copying values in this integer.
L8: the dimension of result can be 1 more than m after the addition.
What are tradeoffs to make the size of result to be m instead of m+1 and vice versa?
The following shows addDifferentSign() that throws :
The implementation of addDifferentSign() is quite similar to addSameSign() although it involves a few more logics. We will leave this as an .
In practice, addSameSign()and addDifferentSign() should be private. We made them protected for exercise purposes.
Method: multiply()
Let us override the multiply() method:
L4: sets the sign after the multiplication.
L7-15: multiplies n to this integer:
What is the worst-case complexity of the multiply() method?
Method: main()
Let us create a runnable class called that contains the main method:
Can we define the main method in LongInteger instead without creating LongIntegerRun?
L2: the parameter args is passed from the command line.
Why does the main method need to be static?
This prints something like the following:
[: one-dimensional array.
L: the element of this array is an object.
java.lang.String
What is the hash code of an object?
Every object implicitly inherits that defines a few member methods including , which gets called automatically by the println() method to retrieve the string representation of this object. We can use the helper method that gives a more readable representation:
How is the Arrays.toString() method implemented?
Since no argument is passed to the main method at the moment, this prints an empty array:
If you set the arguments to 123 -456 using the [Run - Edit Configurations - Program arguments]setting, it prints the following array:
Given those two arguments, we can create two integers:
This prints something like the following, which are returned by a.toString():
How is the toString() method implemented in the Object class?
Method: toString()
To print a more readable representation, we need to override the toString() method in LongInteger:
L5: provides an efficient way of concatenating different data types into one string.
What are the advantages of using StringBuilder instead of concatenating values with the + operator as follows:
Given the overridden method, the above main method now prints the following:
What are the advantages of overriding toString() instead of creating a new method with the same code, and calling the new method to get the string representation of LongInteger?
Method: compareTo()
Java does not allow , so it is not possible to use logical operators to compare the two integers above, a and b:
In fact, any object that is comparable must inherit the interface as follows:
L2: LongInteger is passed to Comparable as a generic type.
Is extends always used to inherit a class whereas implements is used to inherit an interface?
The Comparable interface contains one abstract method called that returns a negative value if this object is smaller than n, a positive value if this object is greater than n, and zero if this object equals to n. The compareTo() method must be overridden by the LongInteger class:
The compareAbs() method compares the absolute values of this and n:
L7: if digits has more dimensions, its absolute value is greater.
L10-13: compares the significant digits iteratively.
Is it safe to use the same variable i to iterate both digits and n.digits?
Once LongInteger properly inherits Comparable by overriding compareTo(), objects instantiated by this class can be compared using many built-in methods.
L2: is a specific implementation of the interface .
All collections in Java inheriting uses generics.
What is the advantage of declaring list as List instead of ArrayList?
What kind of sorting algorithm does Collections.sort() use?
The above code prints the following sorted lists:
What would be the case that needs to distinguish -0 from 0?
super(): calls the corresponding constructor in the super class, SignedNumeral.
public class LongInteger extends SignedNumeral<LongInteger> {
/** The values of this integer (excluding the sign). */
protected byte[] digits;
...
/** Creates a long integer with the default value of "0". */
public LongInteger() {
this("0");
}
/**
* Creates a long integer by copying the specific object.
* @param n the object to be copied.
*/
public LongInteger(LongInteger n) {
super(n.sign);
digits = Arrays.copyOf(n.digits, n.digits.length);
}
/**
* Creates a long integer with the specific sign and values.
* @param n the sign and values to be set.
* @see #set(String)
*/
public LongInteger(String n) {
set(n);
}
/**
* Sets the sign and values of this integer.
* @param n the sign and values to be set.
* @throws NullPointerException when `n` is null.
* @throws InvalidParameterException when `n` contains non-digit character
* except for the first character that can be [+-\d].
*/
public void set(String n) {
// 'n' must not be null
if (n == null)
throw new NullPointerException();
// set this.sign
sign = switch (n.charAt(0)) {
case '-' -> { n = n.substring(1); yield Sign.NEGATIVE; }
case '+' -> { n = n.substring(1); yield Sign.POSITIVE; }
default -> Sign.POSITIVE;
};
// set this.digits
digits = new byte[n.length()];
for (int i = 0, j = n.length() - 1; i < n.length(); i++, j--) {
byte v = (byte)(n.charAt(i) - 48);
if (0 > v || v > 9) {
String s = String.format("%d is not a valid value", v);
throw new InvalidParameterException(s);
}
digits[j] = v;
}
}
@Override
public void add(LongInteger n) {
if (sign == n.sign)
addSameSign(n);
else
addDifferentSign(n);
}
/**
* Adds the specific integer that has the same sign as this integer.
* @param n the integer to be added with the same sign.
*/
protected void addSameSign(LongInteger n) {
// copy this integer to result[]
int m = Math.max(digits.length, n.digits.length);
byte[] result = new byte[m + 1];
System.arraycopy(digits, 0, result, 0, digits.length);
// add n to result
for (int i = 0; i < n.digits.length; i++) {
if (i < n.digits.length)
result[i] += n.digits[i];
if (result[i] >= 10) {
result[i] -= 10;
result[i + 1] += 1;
}
}
// set this.digits
digits = result[m] == 0 ? Arrays.copyOf(result, m) : result;
}
/**
* Adds the specific integer that has a different sign from this integer.
* @param n the integer to be added with a different sign
*/
protected void addDifferentSign(LongInteger n) {
throw new UnsupportedOperationException();
}
@Override
public void multiply(LongInteger n) {
// set this.sign
sign = (sign == n.sign) ? Sign.POSITIVE : Sign.NEGATIVE;
// multiply this and n and save it to result
byte[] result = new byte[digits.length + n.digits.length];
for (int i = 0; i < digits.length; i++) {
for (int j = 0; j < n.digits.length; j++) {
int k = i + j, prod = digits[i] * n.digits[j];
result[k] += prod;
result[k + 1] += result[k] / 10;
result[k] %= 10;
}
}
// set this.digits
int m; for (m = result.length - 1; m > 0; m--)
if (result[m] != 0) break;
digits = ++m < result.length ? Arrays.copyOf(result, m) : result;
}
public class LongIntegerRun {
static public void main(String[] args) {
System.out.println(args);
}
}
[Ljava.lang.String;@d716361
static public void main(String[] args) {
System.out.println(Arrays.toString(args));
}
[]
[123, -456]
static public void main(String[] args) {
LongInteger a = new LongInteger(args[0]);
LongInteger b = new LongInteger(args[1]);
System.out.println(a);
System.out.println(b);
}
public class LongInteger extends SignedNumeral<LongInteger> {
...
@Override
public String toString() {
StringBuilder build = new StringBuilder();
if (sign == Sign.NEGATIVE) build.append("-");
for (int i = digits.length - 1; i >= 0; i--)
build.append(digits[i]);
return build.toString();
}
...
String s = "";
if (sign == Sign.NEGATIVE) s += "-";
for (int i = digits.length - 1; i >= 0; i--)
s += digits[i];
return s;
123
-456
boolean c = a < b; // gives a compile error
public class LongInteger extends SignedNumeral<LongInteger>
implements Comparable<LongInteger> {
...
}
@Override
public int compareTo(LongInteger n) {
if (isPositive())
return n.isNegative() ? 1 : compareAbs(n);
else
return n.isPositive() ? -1 : -compareAbs(n);
}
/**
* @param n the object to be compared.
* @return a negative integer, zero, or a positive integer as the absolute value of this object is
* less than, equal to, or greater than the absolute value of the specified object.
*/
public int compareAbs(LongInteger n) {
int diff = digits.length - n.digits.length;
if (diff == 0) {
for (int i = digits.length - 1; i >= 0; i--) {
diff = digits[i] - n.digits[i];
if (diff != 0) break;
}
}
return diff;
}
static public void main(String[] args) {
List<LongInteger> list = new ArrayList<>();
list.add(new LongInteger("78"));
list.add(new LongInteger("-45"));
list.add(new LongInteger("0"));
list.add(new LongInteger("6"));
list.add(new LongInteger("-0"));
list.add(new LongInteger("-123"));
list.sort(Comparator.naturalOrder());
System.out.println(list);
list.sort(Comparator.reverseOrder());
System.out.println(list);
}