Question

Problem: Given an integer k, find the two closest integers in absolute difference and the whole product equals k+1 or k+2. Return the two integers in any order. Write the code in java.

• You can assume the integer value will be between [1,10^9]

• You can multiple a divisor with itself.

• Description of a sample run 1:

  • The input number 8 hence, k+1 is 9 and k+2 is 10

  • The divisors for 9 are: 1,3,9 and for 10: 1,2,5,10

  • For both cases, we have 2 divisors that multiply exactly to the values (3*3=15 and 2*5=10), we also have 1*9 and 1*10, however, this will yield the largest difference

  • However, we want to pick the product with the lowest absolute value hence: 3-3=0 and 5-2=3 so our correct choice is 3,3

Sample Input:

Input: num=8

Output: [3,3]

Answer 1

import java.io.*;
import java.util.*;
import java.util.Scanner;
import java.lang.Math;
class Factors{
    public static List<List<Integer> > factComb(int n)
    {
        List<List<Integer> > r_list =
                     new ArrayList<List<Integer> >();
        List<Integer> list = new ArrayList<Integer>();
        factorsListFunc(2, 1, n, r_list, list);
        return r_list;
    }

    public static void factorsListFunc(int first, int each_prod, int n,
    List<List<Integer> > r_list, List<Integer> s_r_list)
    {
        if (first > n || each_prod > n)
            return;
        if (each_prod == n) {
            ArrayList<Integer> t =new ArrayList<Integer>(s_r_list);
            r_list.add(t);
            return;
        }
        for (int i = first; i < n; i++) {
            if (i * each_prod > n)
                break;
            if (n % i == 0) {
                s_r_list.add(i);
                factorsListFunc(i, i * each_prod, n, r_list, s_r_list);
                s_r_list.remove(s_r_list.size() - 1);
            }
        }
    }
    static void printDivisors(int n)
    {
        for (int i=1;i<=n;i++)
            if (n%i==0)
                System.out.printf("%d ",i);
    }

    public static void main(String[] args)
    {
        //Scanner value = new Scanner(System.in);
   // System.out.println("Enter integer value: ");
    int k = 8; //value.nextInt();
    System.out.println("value of k is: " + k);
    int a=k+1, b=k+2;
    System.out.println("k+1 is: " + a);
    System.out.println("k+2 is: " + b);
        System.out.println("The divisors of k+1 are: ");
        printDivisors(a);
        System.out.println("\nThe divisors of k+2 are: ");
        printDivisors(b);
        List<List<Integer> > resultant = factComb(a);
         List<List<Integer> > resultant1 = factComb(b);
       System.out.println("\ndivisors that multiply exactly to the value:");
       int m=0, d=0,c=0;
         for (List<Integer> i : resultant1) {
            for (int j : i)
               if(i.size()==2)
                  System.out.print(j + " ");
            System.out.println();
        }
        for (List<Integer> i : resultant) {
            for (int j : i)
               if(i.size()==2)
                  System.out.print(j + " ");
            System.out.println();
        }
        for (List<Integer> i : resultant) {
            for (int j : i)
               if(i.size()==2)
               d=Math.abs(i.get(0)-i.get(1));
               if(m<=d)
               m=d;
         }
           for (List<Integer> i : resultant1) {
            for (int j : i)
               if(i.size()==2)
              { c=Math.abs(i.get(0)-i.get(1)); }
              
         }
         if(c<m)
          for (List<Integer> i : resultant1) {
            for (int j : i)
               if(i.size()==2)
              {    d=Math.abs(i.get(0)-i.get(1));
                  System.out.print(j + " "); }
                   c=Math.max(m,d);
            System.out.println("absolute value is: " + c);
            System.out.println();
        }
         else
          for (List<Integer> i : resultant) {
            for (int j : i)
               if(i.size()==2)
              { d=Math.abs(i.get(0)-i.get(1));
                  System.out.print(j + " "); }
                 c=Math.min(m,d);
            System.out.println("is the output with absolute value : " + c);
            System.out.println();
        }
    }  
}