Last non-zero digit in factorial in Java

October 14, 2022

Last non-zero digit in factorial in Java

Here, in this page we will discuss the program to find the Last non-zero digit in factorial in Java programming Language. We will discuss various methods to solve the given problem.

Last non-zero digit in factorial in Java

Method Discussed :

  • Method 1 : Naive Approach
  • Method 2 : Efficient Approach

Let’s discuss them one by one in brief,

Method 1:

  • Run a loop till i<j, inside loop check if (arr[i]==arr[j]), then increase the value of i by 1 and decrease the value of j by 1.
  • Else if (arr[i]>arr[j]), then set arr[j-1] = arr[j-1]+arr[j] and decrease the value of j and increase the value of count by 1.
  • Else set, arr[i+1] = arr[i]+arr[i+1] and increase the value of i and count by 1.
  • After the traversal print the value of count.

Time and Space Complexity :

  • Time-Complexity : O(n)
  • Space-Complexity : O(1)

Method 1 : Code in Java

Run 
class Main {
 
    // Method to find factorial of the given number
    static int factorial(int n)
    {
        if(n==0 || n==1)
        return 1;
        
        return n*factorial(n-1);
    }
 
    // Driver method
    public static void main(String[] args)
    {
        int num = 5;
        int fact = factorial(num);
        
        int res;
        
        while(fact%10==0){
            fact /=10;
        }
        
        System.out.println(fact%10);
    }
}

Output :

2

Method 2:

  • Now divide each array element into its shortest divisible form by 2 and decrease count of such occurrences. This way we are not considering the multiplication of 2 and a 5 in our multiplication(number of 2’s present in multiplication result upto n is always more than number 0f 5’s).
  • Multiply each number(after removing pairs of 2’s and 5’s) now and store just last digit by taking remainder by 10.
  • Now call recursively for smaller numbers by (currentNumber – 1) as parameter.

Method 2 : Code in Java

Run 
import java.io.*;
 
class Main {
   
    public static void callMeFactorialLastDigit(int n, int[] result, int sumOf5)
    {
        int number = n;
        if (number == 1)
            return; 
 
        while (number % 5 == 0) {
            number /= 5;
            sumOf5++;
        }
 
        while (sumOf5 != 0 && (number & 1) == 0) {
            number >>= 1; 
            sumOf5--;
        }
 
        result[0] = (result[0] * (number % 10)) % 10;
        callMeFactorialLastDigit(n - 1, result, sumOf5);
    }
 
    public static int lastNon0Digit(int n)
    {
        int[] result = { 1 }; 
        callMeFactorialLastDigit(n, result, 0);
        return result[0];
    }
 
    public static void main(String[] args)
    {
        System.out.println(lastNon0Digit(7)); 
        
    }
}

Output :

4

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