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 = 9Naive 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 codearr = [100, 10, 5, 25, 35, 14]lens = len(arr)n = 11# print the remainder# of after multiple# all the numbersprint(findremainder(arr, lens, n))# This code is contributed by "rishabh_jain". |
Output:
9
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