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Python Program for Find remainder of array multiplication divided by n

  • Difficulty Level : Basic
  • Last Updated : 23 Mar, 2021

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 numbers 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 the current result. After multiplication, again take the remainder to avoid overflow. This works because of the distributive properties of modular arithmetic. ( a * b) % c = ( ( a % c ) * ( b % c ) ) % c  

Python3




# 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 arr:
        mul = mul * (i % 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

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

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