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Find the n-th number made of even digits only
• Difficulty Level : Hard
• Last Updated : 03 May, 2021

Given a number n, find out the n-th positive number made up of even digits (0, 2, 4, 6, 8) only. Firs few numbers made of even digits are 0, 2, 4, 6, 8, 20, 22, 24…….

Examples :

```Input  : 2
Output : 2
Second number made of 0, 2, 4, 6, 8 is 2

Input  : 10
Output : 28```

Naive Approach
A naive approach is to start from 0 and checking if it is made of only {0, 2, 4, 6, 8} and stop when you find n-th such number.

## C++

 `// Simple C++ program to find``// n-th number made of even``// digits only``#include``using` `namespace` `std;` `// function to calculate nth``// number made of even digits only``int` `findNthEvenDigitNumber(``int` `n )``{``    ``// variable to note how``    ``// many such numbers have``    ``// been found till now``    ``int` `count = 0;``    ``for` `(``int` `i = 0 ; ; i++)``    ``{``        ``int` `curr = i;` `        ``// bool variable to check if``        ``// 1, 3, 5, 7, 9 is there or not``        ``bool` `isCurrEvenDigit = ``true` `;` `        ``// checking each digit``        ``// of the number``        ``while` `(curr != 0)``        ``{``            ``// If 1, 3, 5, 7, 9 is found``            ``// temp is changed to false``            ``if` `(curr % 10 == 1 || curr % 10 == 3 ||``                ``curr % 10 == 5 || curr % 10 == 7 ||``                ``curr % 10 == 9)``                ``isCurrEvenDigit = ``false``;``            ``curr = curr / 10;``        ``}` `        ``// temp is true it means that it``        ``// does not have 1, 3, 5, 7, 9``        ``if` `(isCurrEvenDigit == ``true``)``            ``count++;` `        ``// If nth such number is``        ``// found return it``        ``if` `(count == n)``            ``return` `i;``    ``}``}` `// Driver Code``int` `main()``{``    ``cout << findNthEvenDigitNumber(2)``         ``<< endl;``    ``cout << findNthEvenDigitNumber(10)``         ``<< endl;``    ``return` `0;``}`

## Java

 `// Simple Java program to``// find the n-th number made``// of even digits only` `class` `GFG``{``    ``// function to calculate nth``    ``// number made of even digits only``    ``static` `int` `findNthEvenDigitNumber(``int` `n )``    ``{``        ``// variable to note how``        ``// many such numbers have``        ``// been found till now``        ``int` `count = ``0``;``        ``for` `(``int` `i = ``0` `; ; i++)``        ``{``            ``int` `curr = i;``    ` `            ``// bool variable to check if``            ``// 1, 3, 5, 7, 9 is there or not``            ``boolean` `isCurrEvenDigit = ``true` `;``    ` `            ``// checking each digit``            ``// of the number``            ``while` `(curr != ``0``)``            ``{``                ``// If 1, 3, 5, 7, 9 is found``                ``// temp is changed to false``                ``if` `(curr % ``10` `== ``1` `|| curr % ``10` `== ``3` `||``                    ``curr % ``10` `== ``5` `|| curr % ``10` `== ``7` `||``                    ``curr % ``10` `== ``9``)``                    ``isCurrEvenDigit = ``false``;``                ``curr = curr / ``10``;``            ``}``    ` `            ``// temp is true it means that it``            ``// does not have 1, 3, 5, 7, 9``            ``if` `(isCurrEvenDigit == ``true``)``                ``count++;``    ` `            ``// If nth such number``            ``// is found return it``            ``if` `(count == n)``                ``return` `i;``        ``}``    ``}``    ` `    ``// Driver Code``    ``public` `static` `void` `main (String[] args)``    ``{``        ``System.out.println(findNthEvenDigitNumber(``2``));``        ``System.out.println(findNthEvenDigitNumber(``10``));``    ``}``}`

## Python3

 `# Simple Python3 program to find nth``# number made of even digits only` `# function to calculate nth number``# made of even digits only``def` `findNthEvenDigitNumber(n):` `    ``# variable to note how many such``    ``# numbers have been found till now``    ``count ``=` `0``;``    ``i ``=` `0``;``    ``while` `(``True``):``    ` `        ``curr ``=` `i;` `        ``# bool variable to check if``        ``# 1, 3, 5, 7, 9 is there or not``        ``isCurrEvenDigit ``=` `True``;` `        ``# checking each digit of the number``        ``while` `(curr !``=` `0``):``            ` `            ``# If 1, 3, 5, 7, 9 is found``            ``# temp is changed to false``            ``if` `(curr ``%` `10` `=``=` `1` `or` `curr ``%` `10` `=``=` `3` `or``                ``curr ``%` `10` `=``=` `5` `or` `curr ``%` `10` `=``=` `7` `or``                ``curr ``%` `10` `=``=` `9``):``                ``isCurrEvenDigit ``=` `False``;``            ``curr ``=` `curr ``/``/` `10``;` `        ``# temp is true it means that it``        ``# does not have 1, 3, 5, 7, 9``        ``if` `(isCurrEvenDigit ``=``=` `True``):``            ``count ``+``=` `1``;` `        ``# If nth such number is found,``        ``# return it``        ``if` `(count ``=``=` `n):``            ``return` `i;``        ` `        ``i ``+``=` `1``;` `# Driver Code``print``(findNthEvenDigitNumber(``2``));``print``(findNthEvenDigitNumber(``10``));` `# This code is contributed by mits`

## C#

 `// Simple C# program to``// find the n-th number``// made of even digits only``using` `System;` `class` `GFG``{``    ``// function to calculate nth``    ``// number made of even digits only``    ``static` `int` `findNthEvenDigitNumber(``int` `n )``    ``{``        ``// variable to note how``        ``// many such numbers have``        ``// been found till now``        ``int` `count = 0;``        ``for` `(``int` `i = 0 ; ; i++)``        ``{``            ``int` `curr = i;``    ` `            ``// bool variable to check if``            ``// 1, 3, 5, 7, 9 is there or not``            ``bool` `isCurrEvenDigit = ``true` `;``    ` `            ``// checking each digit``            ``// of the number``            ``while` `(curr != 0)``            ``{``                ``// If 1, 3, 5, 7, 9 is found``                ``// temp is changed to false``                ``if` `(curr % 10 == 1 || curr % 10 == 3 ||``                    ``curr % 10 == 5 || curr % 10 == 7 ||``                    ``curr % 10 == 9 )``                    ``isCurrEvenDigit = ``false``;``                ``curr = curr / 10;``            ``}``    ` `            ``// temp is true it means that it``            ``// does not have 1, 3, 5, 7, 9``            ``if` `(isCurrEvenDigit == ``true``)``                ``count++;``    ` `            ``// If nth such number``            ``// is found return it``            ``if` `(count == n)``                ``return` `i;``        ``}``    ``}``    ` `    ``// Driver code``    ``public` `static` `void` `Main ()``    ``{``        ``Console.WriteLine(findNthEvenDigitNumber(2));``        ``Console.WriteLine(findNthEvenDigitNumber(10));``    ``}``}` `// This article is contributed by vt_m.`

## PHP

 ``

## Javascript

 ``

Output :

```2
28```

Efficient Approach
We need to find numbers made of 5 digits, 0, 2, 4, 6 and 8. When we convert a number into base 5 number, it will only be made of numbers {0, 1, 2, 3, 4}. It can be clearly seen that each digit in the required digit set {0, 2, 4, 6, 8} is double the digit in the corresponding index of the base-5 digit set. So to find the n-th number made of only even digits follow the below mentioned steps
Step 1: Convert n to n-1 this is done so as to exclude zero.
Step 2: Convert n to 5 base decimal number.
Step 3: Multiply the above found number by 2. This is the required number

## C++

 `// Efficient C++ program to``// find n-th number made of``// even digits only``#include``using` `namespace` `std;` `// function to find nth number``// made of even digits only``int` `findNthEvenDigitNumber(``int` `n)``{``    ``// If n=1 return 0``    ``if` `(n == 1)``        ``return` `0;` `    ``// vector to store the digits``    ``// when converted into base 5``    ``vector< ``int``> v;` `    ``// Reduce n to n-1 to exclude 0``    ``n = n - 1;`` ` `    ``// Reduce n to base 5``    ``// number and store digits``    ``while` `(n > 0)``    ``{``        ``// pushing the digits``        ``// into vector``        ``v.push_back(n % 5);``        ``n = n / 5;``    ``}` `    ``// variable to represent the``    ``// number after converting it``    ``// to base 5. Since the digits``    ``// are be in reverse order,``    ``// we traverse vector from back``    ``int` `result = 0;``    ``for` `(``int` `i = v.size() - 1; i >= 0; i--)``    ``{``        ``result = result * 10;``        ``result = result + v[i];``    ``}` `    ``// return 2*result (to convert``    ``// digits 0, 1, 2, 3, 4 to``    ``// 0, 2, 4, 6, 8.``    ``return` `2*result;``}` `// Driver Code``int` `main()``{``    ``cout << findNthEvenDigitNumber(2)``         ``<< endl;``    ``cout << findNthEvenDigitNumber(10)``         ``<< endl;``    ``return` `0;``}`

## Java

 `import` `java.util.*;``// Efficient Java program to``// find n-th number made of``// even digits only` `class` `GFG {` `// function to find nth number``// made of even digits only``    ``static` `int` `findNthEvenDigitNumber(``int` `n) {``        ``// If n=1 return 0``        ``if` `(n == ``1``) {``            ``return` `0``;``        ``}` `        ``// vector to store the digits``        ``// when converted into base 5``        ``Vector< Integer> v = ``new` `Vector<>();` `        ``// Reduce n to n-1 to exclude 0``        ``n = n - ``1``;` `        ``// Reduce n to base 5``        ``// number and store digits``        ``while` `(n > ``0``) {``            ``// pushing the digits``            ``// into vector``            ``v.add(n % ``5``);``            ``n = n / ``5``;``        ``}` `        ``// variable to represent the``        ``// number after converting it``        ``// to base 5. Since the digits``        ``// are be in reverse order,``        ``// we traverse vector from back``        ``int` `result = ``0``;``        ``for` `(``int` `i = v.size() - ``1``; i >= ``0``; i--) {``            ``result = result * ``10``;``            ``result = result + v.get(i);``        ``}` `        ``// return 2*result (to convert``        ``// digits 0, 1, 2, 3, 4 to``        ``// 0, 2, 4, 6, 8.``        ``return` `2` `* result;``    ``}` `// Driver Code``    ``public` `static` `void` `main(String[] args) {``        ``System.out.println(findNthEvenDigitNumber(``2``));``        ``System.out.println(findNthEvenDigitNumber(``10``));``    ``}``}``// This code is contributed by PrinciRaj1992`

## Python3

 `# Efficient Python 3 program to find n-th``# number made of even digits only` `# function to find nth number made of``# even digits only``def` `findNthEvenDigitNumber( n):` `    ``# If n = 1 return 0``    ``if` `(n ``=``=` `1``):``        ``return` `0` `    ``# vector to store the digits``    ``# when converted into base 5``    ``v ``=` `[]` `    ``# Reduce n to n-1 to exclude 0``    ``n ``=` `n ``-` `1` `    ``# Reduce n to base 5 number and``    ``# store digits``    ``while` `(n > ``0``):``        ` `        ``# pushing the digits into vector``        ``v.append(n ``%` `5``)``        ``n ``=` `n ``/``/` `5` `    ``# variable to represent the number ``    ``# after converting it to base 5.``    ``# Since the digits are be in reverse``    ``# order, we traverse vector from back``    ``result ``=` `0``    ``for` `i ``in` `range``(``len``(v) ``-` `1``, ``-``1``, ``-``1``):``        ``result ``=` `result ``*` `10``        ``result ``=` `result ``+` `v[i]` `    ``# return 2*result (to convert``    ``# digits 0, 1, 2, 3, 4 to``    ``# 0, 2, 4, 6, 8.``    ``return` `2` `*` `result` `# Driver Code``if` `__name__ ``=``=` `"__main__"``:``    ` `    ``print``(findNthEvenDigitNumber(``2``))``    ``print``(findNthEvenDigitNumber(``10``))` `# This code is contributed by ita_c`

## C#

 `// Efficient C# program to``// find n-th number made of``// even digits only``using` `System;``using` `System.Collections;` `class` `GFG {` `    ``// function to find nth number``    ``// made of even digits only``    ``static` `int` `findNthEvenDigitNumber(``int` `n)``    ``{``        ``// If n=1 return 0``        ``if` `(n == 1)``        ``{``            ``return` `0;``        ``}` `        ``// vector to store the digits``        ``// when converted into base 5``        ``ArrayList v = ``new` `ArrayList();` `        ``// Reduce n to n-1 to exclude 0``        ``n = n - 1;` `        ``// Reduce n to base 5``        ``// number and store digits``        ``while` `(n > 0)``        ``{``            ``// pushing the digits``            ``// into vector``            ``v.Add(n % 5);``            ``n = n / 5;``        ``}` `        ``// variable to represent the``        ``// number after converting it``        ``// to base 5. Since the digits``        ``// are be in reverse order,``        ``// we traverse vector from back``        ``int` `result = 0;``        ``for` `(``int` `i = v.Count - 1; i >= 0; i--)``        ``{``            ``result = result * 10;``            ``result = result + (``int``)v[i];``        ``}` `        ``// return 2*result (to convert``        ``// digits 0, 1, 2, 3, 4 to``        ``// 0, 2, 4, 6, 8.``        ``return` `2 * result;``    ``}` `    ``// Driver Code``    ``public` `static` `void` `Main()``    ``{``        ``Console.WriteLine(findNthEvenDigitNumber(2));``        ``Console.WriteLine(findNthEvenDigitNumber(10));``    ``}``}` `// This code is contributed by 29AjayKumar`

## PHP

 ` 0)``    ``{``        ``// pushing the digits``        ``// into vector``        ``array_push``(``\$v``, ``\$n` `% 5);``        ``\$n` `= (int)(``\$n` `/ 5);``    ``}` `    ``// variable to represent the number``    ``// after converting it to base 5.``    ``// Since the digits are be in``    ``// reverse order, we traverse vector``    ``// from back``    ``\$result` `= 0;``    ``for` `(``\$i` `= ``count``(``\$v``) - 1; ``\$i` `>= 0; ``\$i``--)``    ``{``        ``\$result` `= ``\$result` `* 10;``        ``\$result` `= ``\$result` `+ ``\$v``[``\$i``];``    ``}` `    ``// return 2*result (to convert``    ``// digits 0, 1, 2, 3, 4 to``    ``// 0, 2, 4, 6, 8.``    ``return` `2 * ``\$result``;``}` `// Driver Code``echo` `findNthEvenDigitNumber(2) . ``"\n"``;``echo` `findNthEvenDigitNumber(10) . ``"\n"` `// This code is contributed by mits``?>`

## Javascript

 ``

Output :

```2
28```

Time Complexity : O(log5(n))

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