Between Two Sets

Problem Description:

You will be given two arrays of integers and asked to determine all integers that satisfy the following two conditions:

1. The elements of the first array are all factors of the integer being considered
2. The integer being considered is a factor of all elements of the second array

Input Format:

The first line contains two space-separated integers,  and , the number of elements in array  and the number of elements in array .
The second line contains  distinct space-separated integers describing  where .

The third line contains  distinct space-separated integers describing  where .

2 3

2 4

16 32 96

Output Format:

Print the number of integers that are considered to be between  and .

3

Approach:

The Question looks like easy but there is a small trick. That is LCM and GCD.

BUT how!! look at the words factors and multiples.

1. All numbers in  evenly divide  if and only if  is divisible by the LCM of all numbers in . Let's denote the LCM of  as .
2.  evenly divides all numbers in  if and only if  divides the GCD of all numbers in . Let's denote the GCD of  as .

Java Solution:

import java.io.*;
import java.math.*;
import java.security.*;
import java.text.*;
import java.util.*;
import java.util.concurrent.*;
import java.util.regex.*;
class Result {
    /*
     * Complete the 'getTotalX' function below.
     *
     * The function is expected to return an INTEGER.
     * The function accepts following parameters:
     *  1. INTEGER_ARRAY a
     *  2. INTEGER_ARRAY b
     */
        public static int gcd(int a, int b) {
        while (a > 0 && b > 0) {
            
            if (a >= b) {
                a = a % b;
            }
            else {
                b = b % a;
            }
        }
        return a + b;
    }
    public static int lcm(int a, int b) {
        return (a / gcd(a, b)) * b;
    }
    
    public static int getTotalX(Integer[] a, Integer[] b) {
        
        int multiple = 0;
        for(int i : b) {
            multiple = gcd(multiple, i);
        }
//        System.err.println("Multiple: " + multiple);
        
        int factor = 1;
        for(int i : a) {
            factor = lcm(factor, i);
            if (factor > multiple) {
                return 0;
            }
        }
        if (multiple % factor != 0) {
            return 0;
        }
//        System.err.println("Factor: " + factor);
        
        int value = multiple / factor;
        
        int max = Math.max(factor, value);
        int totalX = 1;
        
        for (int i = factor; i < multiple; i++) {
            if (multiple % i == 0 && i % factor == 0) {
                totalX++;
            }
        }
        return totalX;
        
    }
}
public class Solution {
    public static void main(String[] args) throws IOException {
        BufferedReader bufferedReader = new BufferedReader(new InputStreamReader(System.in));
        BufferedWriter bufferedWriter = new BufferedWriter(new FileWriter(System.getenv("OUTPUT_PATH")));
        String[] firstMultipleInput = bufferedReader.readLine().replaceAll("\\s+$", "").split(" ");
        int n = Integer.parseInt(firstMultipleInput[0]);
        int m = Integer.parseInt(firstMultipleInput[1]);
        String[] arrTemp = bufferedReader.readLine().replaceAll("\\s+$", "").split(" ");
        List<Integer> arr = new ArrayList<>();
        for (int i = 0; i < n; i++) {
            int arrItem = Integer.parseInt(arrTemp[i]);
            arr.add(arrItem);
        }
        String[] brrTemp = bufferedReader.readLine().replaceAll("\\s+$", "").split(" ");
        List<Integer> brr = new ArrayList<>();
        for (int i = 0; i < m; i++) {
            int brrItem = Integer.parseInt(brrTemp[i]);
            brr.add(brrItem);
        }
        Integer[] arrl = new Integer[arr.size()]; 
        arrl = arr.toArray(arrl); 
        Integer[] brrl = new Integer[brr.size()]; 
        brrl = brr.toArray(brrl); 
        int total = Result.getTotalX(arrl, brrl);
        bufferedWriter.write(String.valueOf(total));
        bufferedWriter.newLine();
        bufferedReader.close();
        bufferedWriter.close();
    }
}