Kth Largest factor Of N Problem

Kth Largest factor Of N Problem is one of the problem that was asked in previous year TCS Codevita Exam. Here in this problem two positive integers N and K are given. You have to find the kth largest factor of N.

Problem Description

A positive integer d is said to be a factor of another positive integer N if when N is divided by d, the remainder obtained is zero. For example, for number 12, there are 6 factors 1, 2, 3, 4, 6, 12. Every positive integer k has at least two factors, 1 and the number k itself.Given two positive integers N and k, write a program to print the kth largest factor of N.

Input Format:

• The input is a comma-separated list of positive integer pairs (N, k)

Output Format:

• The kth highest factor of N. If N does not have k factors, the output should be 1.

Constraints:

• 1<N<10000000000.
• 1<k<600.
• You can assume that N will have no prime factors which are larger than 13.

Example 1

• Input: 12,3
• Output: 4

Explanation: N is 12, k is 3. The factors of 12 are (1,2,3,4,6,12). The highest factor is 12 and the third largest factor is 4. The output must be 4

Example 2

• Input: 30,9
• Output: 1

Explanation: N is 30, k is 9. The factors of 30 are (1,2,3,5,6,10,15,30). There are only 8 factors. As k is more than the number of factors, the output is 1.

Solution for kth Largest factor of N Problem

`#include<bits/stdc++.h>using namespace std;vector<int> a,ans; void Find_Factor(int f,int i){    if(f>sqrt(a[0])) return;    if(a[0]%f)    {        Find_Factor(f+i,i);return;    }    ans.push_back(f);    Find_Factor(f+i,i);    if(f*f!=a[0])    ans.push_back(a[0]/f);} int main(){    string s;getline(cin,s);    int n,k;    istringstream ss(s);    for(int i;ss>>i;)    {        a.push_back(i);        if(ss.peek()==',') ss.ignore();    }    ans.push_back(1);    if((a[0]&1)==0) Find_Factor(2,1);    else Find_Factor(3,2);    ans.push_back(a[0]);    //for(auto i:ans) cout<<i<<" ";    if(ans.size()<a[1]) cout<<1;    else cout<<ans[ans.size()-a[1]];}`
`import java.util.Scanner;public class Test{  public static void main (String[]args)  {    Scanner sc = new Scanner (System.in);    int number, r, i, count = 0;      number = sc.nextInt ();      r = sc.nextInt ();    for (i = number; i >= 1; i--)      {	if ((number % i) == 0)	  count++;	if (count == r)	  {	    System.out.println (i);	    break;	  }      }    if (count != r)        System.out.println ("1");  }}`
`def Find_Factor(f,i,n,ans):    if f*f>n:        return    if (n%f):        Find_Factor(f+i,i,n,ans)        return    ans.append(f)    Find_Factor(f+i,i,n,ans)    if (f*f)!=n:        ans.append(n//f) n,k=map(int,input().split(","))ans=[]ans.append(1)if n&1:    Find_Factor(3,2,n,ans)else:    Find_Factor(2,1,n,ans)ans.append(n) if(len(ans)<k):    print(1)else:    print(ans[len(ans)-k])`