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++
// 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:
1
Time Complexity: O(log n)
Auxiliary Space: O(1)