Step by Step solution about How to resolve the algorithm Left factorials step by step in the Java programming language

Explanation:

1. Factorial Computation:

• factorial(BigInteger n): Calculates the factorial of n.
• It starts with ans as 1 and iterates from 1 to n, multiplying ans by x at each step.
• The result is the factorial of n, represented as a BigInteger object.

2. Left Factorial:

• leftFact(BigInteger n): Calculates the "left factorial" of n.
• It starts with ans as 0 and iterates from 0 to n-1.
• For each k, it calls factorial(k) and adds the result to ans.
• The result is the sum of factorials from 0 to n-1, which is known as the left factorial of n.

3. Main Method:

• Tests the leftFact function for various inputs:
  • Prints the left factorials of numbers from 0 to 10.
  • Prints the left factorials of numbers from 20 to 110 in steps of 10.
  • Prints the number of digits in the left factorials of numbers from 1000 to 10000 in steps of 1000.

Note: The program uses BigInteger objects to handle large factorials that cannot fit into standard data types.

import java.math.BigInteger;

public class LeftFac{
	public static BigInteger factorial(BigInteger n){
		BigInteger ans = BigInteger.ONE;
		for(BigInteger x = BigInteger.ONE; x.compareTo(n) <= 0; x = x.add(BigInteger.ONE)){
			ans = ans.multiply(x);
		}
		return ans;
	}
	
	public static BigInteger leftFact(BigInteger n){
		BigInteger ans = BigInteger.ZERO;
		for(BigInteger k = BigInteger.ZERO; k.compareTo(n.subtract(BigInteger.ONE)) <= 0; k = k.add(BigInteger.ONE)){
			ans = ans.add(factorial(k));
		}
		return ans;
	}
	
	public static void main(String[] args){
		for(int i = 0; i <= 10; i++){
			System.out.println("!" + i + " = " + leftFact(BigInteger.valueOf(i)));
		}
		
		for(int i = 20; i <= 110; i += 10){
			System.out.println("!" + i + " = " + leftFact(BigInteger.valueOf(i)));
		}
		
		for(int i = 1000; i <= 10000; i += 1000){
			System.out.println("!" + i + " has " + leftFact(BigInteger.valueOf(i)).toString().length() + " digits");
		}
	}
}