Smallest N digit number which is a perfect fourth power

Given an integer N, the task is to find the smallest N-digit number which is a perfect fourth power.

Examples:

Input: N = 2
Output: 16
Only valid numbers are 24 = 16
and 34 = 81 but 16 is the minimum.



Input: N = 3
Output: 256
44 = 256

Approach: It can be observed that for the values of N = 1, 2, 3, …, the series will go on like 1, 16, 256, 1296, 10000, 104976, 1048576, … whose Nth term will be pow(ceil( (pow(pow(10, (n – 1)), 1 / 4) ) ), 4).

Below is the implementation of the above approach:

C++

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// C++ implementation of the approach
#include <bits/stdc++.h>
  
using namespace std;
  
// Function to return the smallest n-digit
// number which is a perfect fourth power
int cal(int n)
{
    double res = pow(ceil((pow(pow(10, 
                          (n - 1)), 1 / 4) )), 4);
    return (int)res;
}
  
// Driver code
int main()
{
    int n = 1;
    cout << (cal(n));
}
  
// This code is contributed by Mohit Kumar

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Java

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// Java implementation of the approach
class GFG
{
  
// Function to return the smallest n-digit
// number which is a perfect fourth power
static int cal(int n)
{
    double res = Math.pow(Math.ceil((
                 Math.pow(Math.pow(10
                (n - 1)), 1 / 4) )), 4);
    return (int)res;
}
  
// Driver code
public static void main(String[] args)
{
    int n = 1;
    System.out.println(cal(n));
}
}
  
// This code is contributed by CodeMech

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Python3

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# Python3 implementation of the approach
from math import *
  
# Function to return the smallest n-digit 
# number which is a perfect fourth power
def cal(n):
    res = pow(ceil( (pow(pow(10, (n - 1)), 1 / 4) ) ), 4)
    return int(res)
  
# Driver code
n = 1
print(cal(n))

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C#

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// C# implementation of the approach
using System;
  
class GFG
{
  
// Function to return the smallest n-digit
// number which is a perfect fourth power
static int cal(int n)
{
    double res = Math.Pow(Math.Ceiling((
                 Math.Pow(Math.Pow(10, 
                 (n - 1)), 1 / 4) )), 4);
    return (int)res;
}
  
// Driver code
public static void Main()
{
    int n = 1;
    Console.Write(cal(n));
}
}
  
// This code is contributed 
// by Akanksha_Rai

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Output:

1


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