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Nth number made up of odd digits only

  • Difficulty Level : Hard
  • Last Updated : 31 Mar, 2021

Given an integer N, the task is to find the Nth number made up of odd digits (1, 3, 5, 7, 9) only. 
First few numbers made up of odd digits are 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 31, …

Examples:  

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Input: N = 7 
Output: 13 
1, 3, 5, 7, 9, 11, 13 
13 is the 7th number in the series

Input: N = 10 
Output: 19 



Approach 1 (Simple) : Starting from 1, keep checking if the number is made up of only odd digits (1, 3, 5, 7, 9) and stop when nth such number is found.

Below is the implementation of the above approach: 

C++




// C++ program to find nth number made up of odd digits only
#include <bits/stdc++.h>
using namespace std;
 
// Function to return nth number made up of odd digits only
int findNthOddDigitNumber(int n)
{
 
    // Variable to keep track of how many
    // such elements have been found
    int count = 0;
    for (int i = 1;; i++) {
        int num = i;
        bool isMadeOfOdd = true;
 
        // Checking each digit of the number
        while (num != 0) {
 
            // If 0, 2, 4, 6 or 8 is found
            // then the number is not made up of odd digits
            if (num % 10 == 0
                || num % 10 == 2
                || num % 10 == 4
                || num % 10 == 6
                || num % 10 == 8) {
                isMadeOfOdd = false;
                break;
            }
 
            num = num / 10;
        }
 
        // If the number is made up of odd digits only
        if (isMadeOfOdd == true)
            count++;
 
        // If it is the nth number
        if (count == n)
            return i;
    }
}
 
// Driver Code
int main()
{
    int n = 10;
    cout << findNthOddDigitNumber(n);
    return 0;
}

Java




// Java program to find nth number
// made up of odd digits only
 
import java.io.*;
 
class GFG {
    // Function to return nth number made up of odd digits only
static int findNthOddDigitNumber(int n)
{
 
    // Variable to keep track of how many
    // such elements have been found
    int count = 0;
    for (int i = 1;; i++) {
        int num = i;
        boolean isMadeOfOdd = true;
 
        // Checking each digit of the number
        while (num != 0) {
 
            // If 0, 2, 4, 6 or 8 is found
            // then the number is not made up of odd digits
            if (num % 10 == 0
                || num % 10 == 2
                || num % 10 == 4
                || num % 10 == 6
                || num % 10 == 8) {
                isMadeOfOdd = false;
                break;
            }
 
            num = num / 10;
        }
 
        // If the number is made up of odd digits only
        if (isMadeOfOdd == true)
            count++;
 
        // If it is the nth number
        if (count == n)
            return i;
    }
}
 
// Driver Code
     
    public static void main (String[] args) {
    int n = 10;
    System.out.println (findNthOddDigitNumber(n));
         
    }
//This code is contributed by ajit   
}

Python3




# Python3 program to find nth number
# made up of odd digits only
 
# Function to return nth number made
# up of odd digits only
def findNthOddDigitNumber(n) :
     
    # Variable to keep track of how many
    # such elements have been found
    count = 0
     
    i = 1
    while True :
        num = i
        isMadeOfOdd = True
         
        # Checking each digit of the number
        while num != 0 :
             
            # If 0, 2, 4, 6 or 8 is found
            # then the number is not made
            # up of odd digits
            if (num % 10 == 0 or num % 10 == 2 or
                num % 10 == 4 or num % 10 == 6 or
                num % 10 == 8) :
                     
                    isMadeOfOdd = False
                    break
         
            num /= 10
     
        # If the number is made up of
        # odd digits only
        if isMadeOfOdd == True :
            count += 1
     
        # If it is the nth number
        if count == n :
            return i
     
        i += 1
 
# Driver code
if __name__ == "__main__" :
     
    n = 10
     
    # Function call
    print(findNthOddDigitNumber(n))
     
# This code is contributed by Ryuga

C#




// C# program to find nth number
// made up of odd digits only
using System;
 
class GFG
{
     
// Function to return nth number
// made up of odd digits only
static int findNthOddDigitNumber(int n)
{
 
    // Variable to keep track of
    // how many such elements have
    // been found
    int count = 0;
    for (int i = 1;; i++)
    {
        int num = i;
        bool isMadeOfOdd = true;
 
        // Checking each digit
        // of the number
        while (num != 0)
        {
 
            // If 0, 2, 4, 6 or 8 is found
            // then the number is not made
            // up of odd digits
            if (num % 10 == 0 || num % 10 == 2 ||
                num % 10 == 4 || num % 10 == 6 ||
                num % 10 == 8)
            {
                isMadeOfOdd = false;
                break;
            }
 
            num = num / 10;
        }
 
        // If the number is made up of
        // odd digits only
        if (isMadeOfOdd == true)
            count++;
 
        // If it is the nth number
        if (count == n)
            return i;
    }
}
 
// Driver Code
static public void Main ()
{
    int n = 10;
    Console.WriteLine(findNthOddDigitNumber(n));
}
}
 
// This code is contributed
// by Ajit Deshpal

PHP




<?php
// PHP program to find nth number
// made up of odd digits only
 
// Function to return nth number
// made up of odd digits only
function findNthOddDigitNumber($n)
{
    // Variable to keep track of how many
    // such elements have been found
    $count = 0;
     
    $i = 1;
    while (true)
    {
        $num = $i;
        $isMadeOfOdd = true;
         
        // Checking each digit of
        // the number
        while ($num != 0)
        {
             
            // If 0, 2, 4, 6 or 8 is found
            // then the number is not made
            // up of odd digits
            if ($num % 10 == 0 or $num % 10 == 2 or
                $num % 10 == 4 or $num % 10 == 6 or
                $num % 10 == 8)
            {
                $isMadeOfOdd = false;
                break;
            }
            $num = (int)($num / 10);
        }
     
        // If the number is made up of
        // odd digits only
        if ($isMadeOfOdd == true)
            $count += 1;
     
        // If it is the nth number
        if ($count == $n)
            return $i;
     
        $i += 1;
    }
}
 
// Driver code
$n = 10;
 
// Function call
print(findNthOddDigitNumber($n));
     
// This code is contributed by mits
?>

Javascript




<script>
 
// JavaScript program to find nth
// number made up of odd digits only
 
// Function to return nth number
// made up of odd digits only
function findNthOddDigitNumber(n)
{
     
    // Variable to keep track of how many
    // such elements have been found
    let count = 0;
    for(let i = 1;; i++)
    {
        let num = i;
        let isMadeOfOdd = true;
 
        // Checking each digit of the number
        while (num != 0)
        {
             
            // If 0, 2, 4, 6 or 8 is found
            // then the number is not made
            // up of odd digits
            if (num % 10 == 0 ||
                num % 10 == 2 ||
                num % 10 == 4 ||
                num % 10 == 6 ||
                num % 10 == 8)
            {
                isMadeOfOdd = false;
                break;
            }
            num = Math.floor(num / 10);
        }
 
        // If the number is made up of
        // odd digits only
        if (isMadeOfOdd == true)
            count++;
 
        // If it is the nth number
        if (count === n)
            return i;
    }
}
 
// Driver Code
let n = 10;
 
document.write(findNthOddDigitNumber(n));
 
// This code is contributed by Manoj.
 
</script>
Output: 
19

 

Approach 2 (Queue Based): The idea is to generate all numbers (smaller than n) containing odd digits only. How to generate all numbers smaller than n with odd digits? We use queue for this. Initially we push ‘1’, ‘3’, ‘5’, ‘7’ and ‘9’ to the queue. Then we run a loop while count of processed elements is smaller than n. We pop an item one by one and for every popped item x, we generate next numbers x*10 + 1, x*10 + 3, x*10 + 5, x*10 + 7 and x*10 + 9. We enqueue these new numbers. Time complexity of this approach is O(n)
Please refer below post for implementation of this approach. 
Count of Binary Digit numbers smaller than N
 




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