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Smallest and Largest N-digit perfect cubes

  • Difficulty Level : Medium
  • Last Updated : 23 Mar, 2021

Given an integer N, the task is to find the smallest and the largest N digit numbers which are also perfect cubes.
Examples: 
 

Input: N = 2 
Output: 27 64 
27 and 64 are the smallest and the largest 2-digit numbers which are also perfect cubes.
Input: N = 3 
Output: 125 729 
 

 

Approach: For increasing values of N starting from N = 1, the series will go on like 8, 64, 729, 9261, ….. for the largest N-digit perfect cube whose Nth term will be pow(ceil(cbrt(pow(10, (n))))-1, 3)
And 1, 27, 125, 1000, ….. for the smallest N-digit perfect cube whose Nth term will be pow(ceil(cbrt(pow(10, (n – 1)))), 3).
Below is the implementation of the above approach:
 

C++




// C++ implementation of the approach
#include <bits/stdc++.h>
using namespace std;
 
// Function to print the largest and
// the smallest n-digit perfect cube
void nDigitPerfectCubes(int n)
{
 
    // Smallest n-digit perfect cube
    cout << pow(ceil(cbrt(pow(10, (n - 1)))), 3) << " ";
 
    // Largest n-digit perfect cube
    cout << (int)pow(ceil(cbrt(pow(10, (n)))) - 1, 3);
}
 
// Driver code
int main()
{
    int n = 3;
    nDigitPerfectCubes(n);
 
    return 0;
}

Java




// Java implementation of the approach
class GFG {
 
    // Function to print the largest and
    // the smallest n-digit perfect cube
    static void nDigitPerfectCubes(int n)
    {
 
        // Smallest n-digit perfect cube
        int smallest = (int)Math.pow(Math.ceil(Math.cbrt(Math.pow(10, (n - 1)))), 3);
        System.out.print(smallest + " ");
 
        int largest = (int)Math.pow(Math.ceil(Math.cbrt(Math.pow(10, (n)))) - 1, 3);
        System.out.print(largest);
    }
 
    // Driver code
    public static void main(String args[])
    {
        int n = 3;
        nDigitPerfectCubes(n);
    }
}

Python3




# Python3 implementation of the approach
from math import ceil
 
# Function to print the largest and
# the smallest n-digit perfect cube
def nDigitPerfectCubes(n):
 
    # Smallest n-digit perfect cube
    print(pow(ceil((pow(10, (n - 1))) **
                       (1 / 3)), 3), end = " ")
 
    # Largest n-digit perfect cube
    print(pow(ceil((pow(10, (n))) **
                       (1 / 3)) - 1, 3))
 
# Driver code
if __name__ == "__main__":
 
    n = 3
    nDigitPerfectCubes(n)
 
# This code is contributed by Rituraj Jain

C#




// C# implementation of the approach
using System;
 
class GFG
{
 
    // Function to print the largest and
    // the smallest n-digit perfect cube
    static void nDigitPerfectCubes(int n)
    {
 
        // Smallest n-digit perfect cube
        int smallest = (int)Math.Pow(Math.Ceiling(MathF.Cbrt((float)Math.Pow(10, (n - 1)))), 3);
        Console.Write(smallest + " ");
 
        int largest = (int)Math.Pow(Math.Ceiling(MathF.Cbrt((float)Math.Pow(10, (n)))) - 1, 3);
        Console.Write(largest);
    }
 
    // Driver code
    static void Main()
    {
        int n = 3;
        nDigitPerfectCubes(n);
    }
}
 
// This code is contributed by mits

PHP




<?php
// PHP implementation of the approach
 
// Function to print the largest and
// the smallest n-digit perfect cube
function nDigitPerfectCubes($n)
{
 
    // Smallest n-digit perfect cube
    print(pow(ceil(pow(pow(10, ($n - 1)),1/3)), 3)." ");
 
    // Largest n-digit perfect cube
    print((int)pow(ceil(pow(pow(10, ($n)),1/3)) - 1, 3));
}
 
// Driver code
$n = 3;
nDigitPerfectCubes($n);
 
// This code is contributed by mits
?>

Javascript




<script>
 
// javascript implementation of the approach
 
// Function to print the largest and
// the smallest n-digit perfect cube
function nDigitPerfectCubes( n)
{
 
    // Smallest n-digit perfect cube
     document.write( Math.pow(Math.ceil(Math.cbrt(Math.pow(10, (n - 1)))), 3) + " ");
 
    // Largest n-digit perfect cube
     document.write( Math.pow(Math.ceil(Math.cbrt(Math.pow(10, (n)))) - 1, 3));
}
 
// Driver code
 
    let n = 3;
    nDigitPerfectCubes(n);
     
    // This code contributed by aashish1995
 
</script>
Output: 
125 729

 

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