How To Calculate Large Factorials Using Biginteger Inward Java?

Factorial of numbers greater than or equal to thirteen cannot live on institute using primitive int data type equally shown inwards our before factorial solution due to overflow. These factorials are besides large to agree inwards an int variable, whose maximum value is simply 2147483647 (2^31 -1). Even if nosotros role the long information type, factorials greater than or equal to 21 volition generate an overflow. To honor the factorial of anything higher upwards 21, you lot demand to role the BigInteger cast from java.math package. As the refer suggests, BigInteger class is designed to concur actually large integer value, something which is fifty-fifty bigger than the maximum value of long primitive e.g. 2^63 -1 or 9223372036854775807L. You also demand to alter the way nosotros calculate factorial for a smaller number. You tin non role recursion to calculate factorial of a larger let on instead nosotros demand to role for loop for that.

Also worth noting that, similar to java.lang.String and other wrapper classes BigInteger is also Immutable inwards Java, which agency it's of import to shop the resultant dorsum into the same variable, otherwise, the resultant of the calculation volition live on lost. BigInteger stores numbers equally 2's complement let on similar int primitive in addition to back upwards functioning supported past times int variables in addition to all relevant methods from java.lang.Math class.

Additionally, it also provides back upwards for modular arithmetic, chip manipulation, primality testing, prime number generation, GCD calculation in addition to other miscellaneous operations.

Java Program to Calculate Factorial of Large Number

Here is our sample Java programme to calculate factorial for large numbers, well, given let on is non just large but the factorial value is definitely large. For example, the factorial of 45 is 119622220865480194561963161495657715064383733760000000000, which is clearly out of saltation for fifty-fifty a long information type. Since theoretically BigInteger has no throttle it tin concur these values equally shown inwards the next example. You volition also notice that instead of recursion, nosotros bring used iteration to calculate factorial inwards Java.

import java.math.BigInteger;  /**  * Write a Java programme to calculate factorial of large numbers using  * BigInteger.  *  * @author WINDOWS 8  *  */ public class LargeFactorialDemo {      public static void main(String args[]) {          System.out.printf("Factorial of 32 is %s %n", factorial(32));         System.out.printf("Factorial of 0 is %s %n", factorial(0));         System.out.printf("Factorial of 1 is %s %n", factorial(1));         System.out.printf("Factorial of v is %s %n", factorial(5));         System.out.printf("Factorial of 41 is %s %n", factorial(41));         System.out.printf("Factorial of 45 is %s %n", factorial(45));      }      /*      * Java method to calculate factorial of a large let on      * @return BigInteger factorial of given let on      */     public static BigInteger factorial(int number) {         BigInteger factorial = BigInteger.ONE;          for (int i = number; i > 0; i--) {             factorial = factorial.multiply(BigInteger.valueOf(i));         }          return factorial;     }  }  Output Factorial of 32 is 263130836933693530167218012160000000 Factorial of 0 is 1 Factorial of 1 is 1 Factorial of 5 is 120 Factorial of 41 is 33452526613163807108170062053440751665152000000000 Factorial of 45 is 119622220865480194561963161495657715064383733760000000000

You tin come across that how large factorial of 45 is, clearly it's non possible to role long information type to shop such huge integral values. You demand to role BigInteger cast to shop such large values.

BTW, If you lot are looking for roughly programming practise to laid coding interview or to developer your programming logic in addition to thence you lot should cheque problems from Cracking the Coding Interview: 189 Programming Questions in addition to Solutions, ane of the best majority for preparing coding interviews.

Important things most BigInteger cast inwards Java

BigInteger cast inwards Java is designed to bargain amongst actually large numbers inwards Java, but to do that it's real of import that you lot brand yourself familiar amongst the class. Here are roughly fundamental points most java.math.BigInteger cast :

1. The BigInteger cast is used to stand upwards for arbitrarily large numbers. Overflow doesn't happen equally is the instance amongst int in addition to long primitive.

2. The BigInteger cast is immutable which agency that the object on which the multiply business office was invoked doesn't alter the integer it is holding. The multiplication is performed in addition to a novel BigInteger is returned which needs to live on stored inwards the variable fact.

3. BigInteger provides operations similar to int primitive type inwards Java, additionally, it provides back upwards for the prime number generation, chip manipulation, GCD calculations etc.

4. You tin do BigInteger object past times giving let on equally String or byte array using constructor, or you lot tin convert a long value to BigInteger using valueOf() method equally shown below :

BigInteger bigIntegerFromLong = BigInteger.valueOf(292909333L);  BigInteger bigIntegerFromString = new BigInteger("338948938948");

Remember BigInteger can tending you lot to bargain amongst actually large numbers inwards Java.

That's all most how to calculate factorial of a large let on inwards Java. Clearly later roughly scream for long is non plenty to resultant of factorial in addition to you lot demand something bigger than long but non double, BigInteger is the cast to stand upwards for large integral values. In theory, BigInteger has no throttle in addition to it tin stand upwards for whatsoever integral value till infinity.

Further Learning
The Coding Interview Bootcamp: Algorithms + Data Structures
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Questions from Coding Puzzles: Thinking inwards code By codingtmd? (see here)

Questions from Programming Interviews Exposed: Secrets to Landing Your Next Job? (see here)

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