Java Program to Find remainder of array multiplication divided by n

Given multiple numbers and a number n, the task is to print the remainder after multiply all the number divide by n.

Examples:

Input : arr[] = {100, 10, 5, 25, 35, 14}, 
            n = 11
Output : 9
100 x 10 x 5 x 25 x 35 x 14 = 61250000 % 11 = 9

Naive approach: First multiple all the number then take % by n then find the remainder, But in this approach, if the number is maximum of 2^64 then it gives the wrong answer.



Approach that avoids overflow : First take a remainder or individual number like arr[i] % n. Then multiply the remainder with current result. After multiplication, again take remainder to avoid overflow. This works because of distributive properties of modular arithmetic. ( a * b) % c = ( ( a % c ) * ( b % c ) ) % c.

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// Java program to find
// remainder when all
// array elements are
// multiplied.
import java.util.*;
import java.lang.*;
  
public class GfG {
  
    // Find remainder of arr[0] * arr[1] *
    // .. * arr[n-1]
    public static int findremainder(int arr[],
                                   int len, int n)
    {
        int mul = 1;
  
        // find the individual remainder
        // and multiple with mul.
        for (int i = 0; i < len; i++)
            mul = (mul * (arr[i] % n)) % n;
  
        return mul % n;
    }
  
    // Driver function
    public static void main(String argc[])
    {
        int[] arr = new int[] { 100, 10, 5,
                                25, 35, 14 };
        int len = 6;
        int n = 11;
  
        // print the remainder of after
        // multiple all the numbers
        System.out.println(findremainder(arr, len, n));
    }
}
  
/* This code is contributed by Sagar Shukla */

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Output:

9

Please refer complete article on Find remainder of array multiplication divided by n for more details!



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Improved By : Akanksha_Rai



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