BigInteger Class in Java

BigInteger class is used for the mathematical operation which involves very big integer calculations that are outside the limit of all available primitive data types.

In this way, BigInteger class is very handy to use because of its large method library and it is also used a lot in competitive programming. 
Now below is given a list of simple statements in primitive arithmetic and its analogous statement in terms of BigInteger objects.

Example:

int a, b;                
BigInteger A, B; 

Initialization is as follows:

a = 54;
b = 23;

A  = BigInteger.valueOf(54);
B  = BigInteger.valueOf(37); 

And for Integers available as strings you can initialize them as follows:

A  = new BigInteger(“54”);
B  = new BigInteger(“123456789123456789”); 

Some constants are also defined in BigInteger class for ease of initialization as follows:

A = BigInteger.ONE;
// Other than this, available constant are BigInteger.ZERO 
// and BigInteger.TEN 

Mathematical operations are as follows:  

int c = a + b;
BigInteger C = A.add(B); 

Other similar functions are subtract(), multiply(), divide(), remainder(), but all these functions take BigInteger as their argument so if we want this operation with integers or string convert them to BigInteger before passing them to functions as shown below: 

String str = “123456789”;
BigInteger C = A.add(new BigInteger(str));
int val  = 123456789;
BigInteger C = A.add(BigInteger.valueOf(val)); 

Extraction of value from BigInteger is as follows:

int x   =  A.intValue();   // value should be in limit of int x
long y   = A.longValue();  // value should be in limit of long y
String z = A.toString();  

Comparison 

if (a < b) {}         // For primitive int
if (A.compareTo(B) < 0)  {} // For BigInteger 

Actually compareTo returns -1(less than), 0(Equal), 1(greater than) according to values. For equality we can also use: 

if (A.equals(B)) {}  // A is equal to B 

Methods of BigInteger Class

Illustration: 

Factorial of 100 contains 158 digits in it so we can’t store it in any primitive data type available. We can store as large an Integer as we want in it. There is no theoretical limit on the upper bound of the range because memory is allocated dynamically but practically as memory is limited you can store a number that has Integer.MAX_VALUE number of bits in it which should be sufficient to store mostly all large values.

Example:

// Java program to find large factorials using BigInteger
import java.math.BigInteger;
import java.util.Scanner;

public class Example
{
    // Returns Factorial of N
    static BigInteger factorial(int N)
    {
        // Initialize result
        BigInteger f = new BigInteger("1"); // Or BigInteger.ONE

        // Multiply f with 2, 3, ...N
        for (int i = 2; i <= N; i++)
            f = f.multiply(BigInteger.valueOf(i));

        return f;
    }

    // Driver method
    public static void main(String args[]) throws Exception
    {
        int N = 20;
        System.out.println(factorial(N));
    }
}

Output: 

2432902008176640000

Tip: If we have to write above program in C++, that would be too large and complex, we can look at Factorial of Large Number. 

So after the above knowledge of the function of BigInteger class, we can solve many complex problems easily, but remember as BigInteger class internally uses an array of integers for processing, the operation on an object of BigIntegers are not as fast as on primitives that are add function on BigIntgers doesn’t take the constant time it takes time proportional to the length of BigInteger, so the complexity of program will change accordingly.

Must Read:

• Large Fibonacci Numbers in Java
• BigInteger class also provides quick methods for prime numbers.