Check if a given number can be represented in given a no. of digits in any base

Given a number and no. of digits to represent the number, find if given number can be represented in given no. of digits in any base from 2 to 32.

Examples :

Input: 8 4  
Output: Yes
Possible in base 2 as 8 in base 2 is 1000

Input: 8 2 
Output: Yes 
Possible in base 3 as 8 in base 3 is 22

Input: 8 3  
Output: No
Not possible in any base

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The idea is to check all bases one by one starting from base 2 to base 32. How do we check for a given base? Following are simple steps.
1) IF number is smaller than base and digit is 1, then return true.
2) Else if digit is more than 1 and number is more than base, then remove the last digit from num by doing num/base, reduce the number of digits and recur.
3) Else return false

Below is the implementation of above idea.

C++

// C++ program to check if a given number can be 
// represented in given number of digits in any base 
#include <iostream> 
using namespace std; 
  
// Returns true if 'num' can be represented usind 'dig' 
// digits in 'base' 
bool checkUtil(int num, int dig, int base) 
{ 
    // Base case 
    if (dig==1 && num < base) 
       return true; 
  
    // If there are more than 1 digits left and number 
    // is more than base, then remove last digit by doing 
    // num/base, reduce the number of digits and recur 
    if (dig > 1 && num >= base) 
       return checkUtil(num/base, --dig, base); 
  
    return false; 
} 
  
// return true of num can be represented in 'dig' 
// digits in any base from 2 to 32 
bool check(int num, int dig) 
{ 
    // Check for all bases one by one 
    for (int base=2; base<=32; base++) 
       if (checkUtil(num, dig, base)) 
            return true; 
    return false; 
} 
  
// Driver program 
int main() 
{ 
    int num = 8; 
    int dig = 3; 
    (check(num, dig))? cout << "Yes" : cout << "No"; 
    return 0; 
} 

Java

// Java program to check if a  
// given number can be represented  
// in given number of digits in any base 
class GFG 
{ 
    // Returns true if 'num' can be  
    // represented usind 'dig' digits in 'base' 
    static boolean checkUtil(int num, int dig, int base) 
    { 
        // Base case 
        if (dig==1 && num < base) 
        return true; 
      
        // If there are more than 1 digits 
        // left and number is more than base, 
        // then remove last digit by doing num/base, 
        //  reduce the number of digits and recur 
        if (dig > 1 && num >= base) 
        return checkUtil(num / base, --dig, base); 
      
        return false; 
    } 
      
    // return true of num can be  
    // represented in 'dig' digits  
    // in any base from 2 to 32 
    static boolean check(int num, int dig) 
    { 
        // Check for all bases one by one 
        for (int base = 2; base <= 32; base++) 
        if (checkUtil(num, dig, base)) 
                return true; 
        return false; 
    }  
      
    // Driver code 
    public static void main (String[] args) 
    { 
        int num = 8; 
        int dig = 3; 
        if(check(num, dig)) 
            System.out.print("Yes"); 
        else
            System.out.print("No"); 
    } 
} 
  
// This code is contributed by Anant Agarwal. 

Python3

# Python program to check 
# if a given number can be 
# represented in given number 
# of digits in any base 
  
# Returns true if 'num' can 
# be represented using 'dig' 
# digits in 'base' 
def checkUtil(num,dig,base): 
      
    # Base case 
    if (dig==1 and num < base): 
        return True
   
    # If there are more than 1 
    # digits left and number 
    # is more than base, then 
    # remove last digit by doing 
    # num/base, reduce the number 
    # of digits and recur 
    if (dig > 1 and num >= base): 
        return checkUtil(num/base, --dig, base) 
   
    return False
   
# return true of num can 
# be represented in 'dig' 
# digits in any base from 2 to 32 
def check(num,dig): 
  
    # Check for all bases one by one 
    for base in range(2,33): 
  
        if (checkUtil(num, dig, base)): 
            return True
    return False
  
# driver code 
num = 8
dig = 3
if(check(num, dig)==True): 
    print("Yes") 
else: 
    print("No") 
  
# This code is contributed 
# by Anant Agarwal. 

C#

// C# program to check if a given  
// number can be represented in  
// given number of digits in any base 
using System; 
  
class GFG { 
      
    // Returns true if 'num' can be  
    // represented usind 'dig' digits 
    // in 'base' 
    static bool checkUtil(int num, int dig, 
                          int i) 
    { 
          
        // Base case 
        if (dig == 1 && num < i) 
        return true; 
      
        // If there are more than 1 digits 
        // left and number is more than base, 
        // then remove last digit by doing  
        // num/base, reduce the number of  
        // digits and recur 
        if (dig > 1 && num >= i) 
        return checkUtil((num / i), --dig, i); 
      
        return false; 
    } 
      
    // return true of num can be  
    // represented in 'dig' digits  
    // in any base from 2 to 32 
    static bool check(int num, int dig) 
    { 
          
        // Check for all bases one by one 
        for (int i = 2; i <= 32; i++) 
        if (checkUtil(num, dig, i)) 
                return true; 
        return false; 
    }  
      
    // Driver code 
    public static void Main() 
    { 
        int num = 8; 
        int dig = 3; 
        if(check(num, dig)) 
            Console.WriteLine("Yes"); 
        else
            Console.WriteLine("No"); 
    } 
} 
  
// This code is contributed by Sam007. 

PHP

<?php 
// PHP program to check if a given 
// number can be represented in given 
// number of digits in any base 
  
// Returns true if 'num' can be 
// represented usind 'dig' 
// digits in 'base' 
  
function checkUtil($num, $dig, $base) 
{ 
    // Base case 
    if ($dig == 1 && $num < $base) 
    return true; 
  
    // If there are more than 1  
    // digits left and number is  
    // more than base, then remove 
    // last digit by doing num/base, 
    // reduce the number of digits and recur 
    if ($dig > 1 && $num >= $base) 
    return checkUtil($num / $base,  
                   --$dig, $base); 
  
    return false; 
} 
  
// return true of num can be  
// represented in 'dig' digits  
// in any base from 2 to 32 
function check($num, $dig) 
{ 
    // Check for all bases one by one 
    for ($base = 2; $base <= 32; $base++) 
    if (checkUtil($num, $dig, $base)) 
            return true; 
    return false; 
} 
  
// Driver Code 
$num = 8; 
$dig = 3; 
if (check($num, $dig) == true) 
echo "Yes" ; 
else
echo "No"; 
  
// This code is contributed by ajit 
?> 

Output :

No

This article is contributed by Mehboob Elahi. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above

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My Personal Notes

C++

Java

Python3

C#

PHP

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