# Smallest and Largest N-digit perfect cubes

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

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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 ` `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

 ` `

Output:

```125 729
```

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