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 multiplying all the numbers divided by n.
Examples:
Input : arr[] = {100, 10, 5, 25, 35, 14}, n = 11
Output : 9
Explanation: 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 to find the remainder, But in this approach, if the number is a maximum of 2^64 then it gives the wrong answer.
An 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
# to use reduce function import reduce from functools from functools import reduce def find_remainder(arr, n): sum_1 = reduce ( lambda x, y: x * y, arr) remainder = sum_1 % n print (remainder) arr = [ 100 , 10 , 5 , 25 , 35 , 14 ] n = 11 find_remainder(arr, n) |
9
Time Complexity: O(n), where n is the number of elements in the array. This is because the reduce function iterates through the entire array and performs the lambda function on each element.
Auxiliary Space: O(1), as the reduce function only requires a single variable to store the result.
Method2#: Without using inbuilt functions
Python3
arr = [ 100 , 10 , 5 , 25 , 35 , 14 ];lens = len (arr);n = 11 mul = 1 for i in range (lens): mul = (mul * (arr[i] % n)) % n print (mul % n) |
9
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