714323. Binary Modulo
Binary Modulo
Slug: binary-modulo--170648 Difficulty: Easy Id: 714323 Topic Tags: Mathematical, Bit Magic Company Tags: None
Summary
The Binary Modulo problem is an easy-level mathematical problem that requires you to find the remainder of a large number when divided by another number. The key concept involved here is bit manipulation, which helps in solving this problem efficiently.
Detailed Explanation
To solve this problem, we will use bit manipulation techniques. Given two numbers n and m, our task is to find the remainder of n when divided by m. We can do this by using bitwise operators. Here's a step-by-step breakdown of the solution:
- Calculate the number of bits required to represent
m. - Use bitwise AND operation (
&) to get the least significant bit (LSB) ofm. This is because we are interested in finding the remainder at the LSB level. - If the LSB of
mis 1, then the remainder will be equal ton & m. - If the LSB of
mis 0, then the remainder will be equal ton.
Here's an example:
Let n = 17 and m = 5. The binary representation of these numbers are 10101 (17) and 0101 (5).
To find the remainder, we need to perform bitwise AND operation (&) between n and m, which gives us 00001.
So, the remainder is 1.
Time Complexity: O(1) Space Complexity: O(1)
Optimized Solutions
Java
public class Main {
public static int binaryModulo(int n, int m) {
return n & m;
}
public static void main(String[] args) {
int n = 17;
int m = 5;
System.out.println("The remainder is: " + binaryModulo(n, m));
}
}