Find the Largest N digit perfect square number in Base B

Given two integers N and B, the task is to find the largest N digit numbers of Base B which is a perfect square.

Examples:

Input: N = 2, B = 10
Output: 81
Explanation:
81 is the largest 2-digit perfect square in base 10.

Input: N = 1, B = 8
Output: 4
Explanation:
4 is the largest 1 digit Octal number which is also a perfect square.

Approach: The largest number N in base B is given by B^N-1. So if we find the square root of this number in integer form and then we have to again do its square then it will be the largest perfect square of N digits which is given by the formula: \left\lfloor\sqrt{B^N-1}\right\rfloor^2.



Below is the implementation of the above approach:

C++

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// C++ implementation to find Largest
// N digit perfect square number in Base B
  
#include <bits/stdc++.h>
using namespace std;
  
// Function to find the
// largest N digit number
void nDigitPerfectSquares(int n, int b)
{
    // Largest n-digit perfect square
    int largest
        = pow(ceil(sqrt(pow(b, n))) - 1, 2);
  
    // Print the result
    cout << largest;
}
  
// Driver Code
int main()
{
    int N = 1, B = 8;
  
    nDigitPerfectSquares(N, B);
  
    return 0;
}

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Java














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// Java implementation to find largest N 


// digit perfect square number in base B 


import java.io.*;  


import java.util.*;  


  


class GFG { 


      


// Function to find the 


// largest N digit number 


static double nDigitPerfectSquares(int n, int b) 


{ 


      


    // Largest n-digit perfect square 


    double largest = Math.pow(Math.ceil 


                             (Math.sqrt 


                             (Math.pow(b, n))) - 1, 2); 


      


    // Print the result 


    return largest; 


} 


  


// Driver code  


public static void main(String[] args)  


{  


    int N = 1, B = 8; 


    System.out.println(nDigitPerfectSquares(N, B)); 


}  


}  


  


// This code is contributed by coder001 



















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Python3














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# Python3 implementation to find the largest  


# N digit perfect square number in base B  


import math 


  


# Function to find the  


# largest N digit number  


def nDigitPerfectSquares(n, b):  


  


    # Largest n-digit perfect square  


    largest = pow(math.ceil 


                 (math.sqrt(pow(b, n))) - 1, 2)  


  


    # Print the result  


    print(largest)  


  


# Driver Code  


N = 1


B = 8


  


nDigitPerfectSquares(N, B) 


  


# This code is contributed by divyamohan123 



















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C#














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// C# implementation to find largest N 


// digit perfect square number in base B 


using System; 


  


class GFG { 


      


// Function to find the 


// largest N digit number 


static double nDigitPerfectSquares(int n, int b) 


{ 


      


    // Largest n-digit perfect square 


    double largest = Math.Pow(Math.Ceiling 


                             (Math.Sqrt 


                             (Math.Pow(b, n))) - 1, 2); 


      


    // Print the result 


    return largest; 


} 


  


// Driver code  


public static void Main(String[] args)  


{  


    int N = 1, B = 8; 


      


    Console.WriteLine(nDigitPerfectSquares(N, B)); 


}  


}  


  


// This code is contributed by PrinciRaj1992 



















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Output:


4







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