Find nth number that contains the digit k or divisible by k.

You have given two number n and k. You need to find the n-th number that contains the digit k or divisible by k (2 <= k <=9 ).

Examples:

Input       : n = 15, k = 3
Output      : 33
Explanation  : ( 3, 6, 9, 12, 13, 15, 18, 21, 23, 24,
27, 30, 31, 33 ). These are those number who contain 
the digit k = 3 or divisible by k and in this nth number
is 33. so output is 33.

Input       : n = 10, k = 2
Output      : 20
Explanation : ( 2, 4, 6, 8, 10, 12, 14, 16, 18, 20 )
These are those number who contain the digit k = 2 or
divisible by k and in this nth number is 20. so output 
is 20.



Approach:

Check every number from k who contains the digit k or divisible by k until we did not get nth number.

C++

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// C++ program to find nth number that contains 
// the digit k or divisible by k.
#include <bits/stdc++.h>
using namespace std;
  
// Function for checking if digit k 
// is in n or not
int checkdigit(int n, int k)
{
    while (n)
    {
        // finding remainder
        int rem = n % 10;
  
        // if digit found
        if (rem == k)
            return 1;
  
        n = n / 10;
    }
  
    return 0;
}
  
// Function for finding nth number
int findNthNumber(int n, int k)
    // since k is the first which satisfy the
    // criteria, so consider it in count making count = 1
    //  and starting from i = k + 1
    for (int i = k + 1, count = 1; count < n; i++)
    {
        // checking that the number contain
        // k digit or divisible by k
        if (checkdigit(i, k) || (i % k == 0))
            count++;
  
        if (count == n)
        return i;
    }
  
    return -1;
}
  
// Driver code
int main()
{
    int n = 10, k = 2;
    cout << findNthNumber(n, k) << endl;
    return 0;
}

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Java

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// Java program to find nth number that contains 
// the digit k or divisible by k.
import java.io.*;
  
class GFG 
{
    // Function for checking if digit k 
    // is in n or not
    public static boolean checkdigit(int n, int k)
    {
        while (n != 0)
        {
            // finding remainder
            int rem = n % 10;
      
            // if digit found
            if (rem == k)
                return true;
      
            n = n / 10;
        }
  
        return false;
    }
  
    // Function for finding nth number
    public static int findNthNumber(int n, int k)
    
        // since k is the first which satisfy th 
    // criteria, so consider it in count making count = 1
    //  and starting from i = k + 1
        for (int i = k + 1, count = 1; count < n; i++)
        {
        // checking that the number contain
        // k digit or divisible by k
        if (checkdigit(i, k) || (i % k == 0))
            count++;
  
        if (count == n)
        return i;
        }
  
    return -1;
    }
  
    // Driver code
    public static void main (String[] args) 
    {
        int n = 10, k = 2
        System.out.println(findNthNumber(n, k)); 
          
    }
}
  
// This code is contributed
// by  UPENDRA BARTWAL

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Python3

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# Python 3 program to find nth number that 
# contains the digit k or divisible by k.
  
# Function for checking if 
# digit k is in n or not
def checkdigit(n, k):
  
    while (n):
      
        # finding remainder
        rem = n % 10
  
        # if digit found
        if (rem == k):
            return 1
  
        n = n / 10
      
    return 0
  
# Function for finding nth number
def findNthNumber(n, k):
      
    i = k + 1
    count = 1
    while(count < n):
          
        # checking that the number contain
        # k digit or divisible by k
        if (checkdigit(i, k) or (i % k == 0)):
            count += 1
          
        if (count == n):
            return i
        i += 1
    return -1
  
# Driver code
n = 10
k = 2
print(findNthNumber(n, k))
  
# This code is contributed
# by Smitha Dinesh Semwal

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C#

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// C# program to find nth number that contains 
// the digit k or divisible by k.
using System;
  
class GFG 
{
      
    // Function for checking if digit k 
    // is in n or not
    public static bool checkdigit(int n, int k)
    {
        while (n != 0)
        {
              
            // finding remainder
            int rem = n % 10;
      
            // if digit found
            if (rem == k)
                return true;
      
            n = n / 10;
        }
  
        return false;
    }
  
    // Function for finding nth number
    public static int findNthNumber(int n, int k)
    
        for (int i = k + 1, count = 1; count < n; i++)
        {
              
            // checking that the number contain
            // k digit or divisible by k
            if (checkdigit(i, k) || (i % k == 0))
                count++;
      
            if (count == n)
                return i;
        }
  
    return -1;
    }
  
    // Driver code
    public static void Main () 
    {
        int n = 10, k = 2; 
          
        Console.WriteLine(findNthNumber(n, k)); 
          
    }
}
  
// This code is contributed by vt_m.

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PHP

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<?php
// PHP program to find nth number  
// that contains the digit k or 
// divisible by k.
  
// Function for checking if 
// digit k is in n or not
function checkdigit($n, $k)
{
    while ($n)
    {
        // finding remainder
        $rem = $n % 10;
  
        // if digit found
        if ($rem == $k)
            return 1;
  
        $n = $n / 10;
    }
    return 0;
}
  
// Function for finding nth number
function findNthNumber($n, $k)
    // since k is the first which 
    // satisfy the criteria, so
    // consider it in count making 
    // count = 1 and starting from
    // i = k + 1
    for ($i = $k + 1, $count = 1; 
                      $count < $n; $i++)
    {
        // checking that the number contain
        // k digit or divisible by k
        if (checkdigit($i, $k) || 
                      ($i % $k == 0))
            $count++;
  
        if ($count == $n)
        return $i;
    }
  
    return -1;
}
  
// Driver code
$n = 10; $k = 2;
echo findNthNumber($n, $k);
  
// This code is contributed 
// by inder_verma
?>

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Output:

 20 


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