Python Program for 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 number is maximum of 2^64 then it give 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

# Python3 program to # find remainder when # all array elements # are multiplied.    # Find remainder of arr[0] * arr[1] # * .. * arr[n-1] def findremainder(arr, lens, n):     mul = 1        # find the individual     # remainder and      # multiple with mul.     for i in range(lens):          mul = (mul * (arr[i] % n)) % n            return mul % n    # Driven code arr = [ 100, 10, 5, 25, 35, 14 ] lens = len(arr) n = 11    # print the remainder # of after multiple # all the numbers print( findremainder(arr, lens, n))    # This code is contributed by "rishabh_jain".

Output:

9