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:

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

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