Smallest N digit number which is a perfect fourth power

Last Updated : 10 Mar, 2022

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 N^th term will be pow(ceil( (pow(pow(10, (n – 1)), 1 / 4) ) ), 4).
Below is the implementation of the above approach:

C++

// 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

Java

// 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

Python3

# 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))

C#

// 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

Javascript

<script>
 
// Javascript implementation of the approach
 
// Function to return the smallest n-digit
// number which is a perfect fourth power
function cal(n)
{
    var res = Math.pow(Math.ceil((Math.pow(Math.pow(10,
                          (n - 1)), 1 / 4) )), 4);
    return parseInt(res);
}
 
// Driver code
var n = 1;
document.write(cal(n));
 
// This code is contributed by rutvik_56.
</script>

Output:

Time Complexity: O(log n)

Auxiliary Space: O(1)

My Personal Notes

Related Articles

Table of Contents

Smallest N digit number which is a perfect fourth power

C++

Java

Python3

C#

Javascript

Start Your Coding Journey Now!