Count numbers up to N having digit D in its octal representation

Given a positive integer N and an integer D representing a digit, the task is to count the numbers in the range[1, N] such that at least one digit in octal representation of the number is d.

Examples:

Input: N = 20, D = 7
Output: 2
Explanation:
The numbers in the range [1, 20] having digit 7 in their octal representation are 7 and 15. 
Therefore, the required output is 2.

Input: N = 40, D = 5
Output: 6
Explanation:
The numbers in the range [1, 40] having digit 5 in their octal representation are 5, 13, 21, 29, 37, and 40. 
Therefore, the required output is 6

Approach: Follow the steps below to solve the problem:

• Iterate over the range [1, N]. For every i^th number check if at least one digit in octal representation of the number is d or not. If found to be true, then increment the count.
• Finally, print the count obtained.

Below is the implementation of the above approach:

C++

// C++ program to implement
// the above approach
#include <bits/stdc++.h>
using namespace std;

// Function to count the numbers in given
// range whose octal representation
// contains atleast digit, d
void countNumbers(int n, int d)
{
    // Store count of numbers up to n
    // whose octal representation
    // contains digit d
    int total = 0;

    // Iterate over the range[1, n]
    for (int i = 1; i <= n; i++) {

        int x = i;

        // Calculate digit of i in
        // octal representation
        while (x > 0) {


            // Check if octal representation
            // of x contains digit d
            if (x % 8 == d) {

                // Update total
                total++;
                break;
            }

            // Update x
            x = x / 8;
        }
    }


    // Print the answer
    cout << total;
}



// Driver Code
int main()
{
    // Given N and D
    int n = 20, d = 7;

    // Counts and prints numbers
// up to N having D as a digit
// in its octal representation
    countNumbers(n, d);

    return 0;
}

Java

// Java program to implement
// the above approach
import java.io.*;
import java.util.*;

class GFG{

// Function to count the numbers in given
// range whose octal representation
// contains atleast digit, d
static void countNumbers(int n, int d)
{

    // Store count of numbers up to n
    // whose octal representation
    // contains digit d
    int total = 0;

    // Iterate over the range[1, n]
    for(int i = 1; i <= n; i++)
    {
        int x = i;

        // Calculate digit of i in
        // octal representation
        while (x > 0)
        {

            // Check if octal representation
            // of x contains digit d
            if (x % 8 == d)
            {

                // Update total
                total++;
                break;
            }

            // Update x
            x = x / 8;
        }
    }

    // Print the answer
    System.out.println(total);
}

// Driver code
public static void main(String[] args)
{

    // Given N and D
    int n = 20, d = 7;

    // Counts and prints numbers
    // up to N having D as a digit
    // in its octal representation
    countNumbers(n, d);
}
}

// This code is contributed by sanjoy_62

Python3

# Python3 program to implement
# the above approach

# Function to count the numbers in given
# range whose octal representation
# contains atleast digit, d
def countNumbers(n, d):

    # Store count of numbers up to n
    # whose octal representation
    # contains digit d
    total = 0

    # Iterate over the range[1, n]
    for i in range(1, n + 1):
        x = i

        # Calculate digit of i in
        # octal representation
        while (x > 0):


            # Check if octal representation
            # of x contains digit d
            if (x % 8 == d):

                # Update total
                total += 1
                break

            # Update x
            x = x // 8

    # Print the answer
    print (total)

# Driver Code
if __name__ == '__main__':

    # Given N and D
    n , d = 20, 7

    # Counts and prints numbers
    # up to N having D as a digit
    # in its octal representation
    countNumbers(n, d)

# This code is contributed by mohit kumr 29

C#

// C# program to implement
// the above approach
using System;

class GFG{

// Function to count the numbers in given
// range whose octal representation
// contains atleast digit, d
static void countNumbers(int n, int d)
{

    // Store count of numbers up to n
    // whose octal representation
    // contains digit d
    int total = 0;

    // Iterate over the range[1, n]
    for(int i = 1; i <= n; i++)
    {
        int x = i;

        // Calculate digit of i in
        // octal representation
        while (x > 0)
        {

            // Check if octal representation
            // of x contains digit d
            if (x % 8 == d)
            {

                // Update total
                total++;
                break;
            }

            // Update x
            x = x / 8;
        }
    }

    // Print the answer
    Console.WriteLine(total);
}

// Driver Code
static void Main()
{

    // Given N and D
    int n = 20, d = 7;

    // Counts and prints numbers
    // up to N having D as a digit
    // in its octal representation
    countNumbers(n, d);
}
}

// This code is contributed by susmitakundugoaldanga

Javascript

<script>
// Javascript program to implement
// the above approach

// Function to count the numbers in given
// range whose octal representation
// contains atleast digit, d
function countNumbers(n, d)
{

    // Store count of numbers up to n
    // whose octal representation
    // contains digit d
    let total = 0;

    // Iterate over the range[1, n]
    for(let i = 1; i <= n; i++)
    {
        let x = i;

        // Calculate digit of i in
        // octal representation
        while (x > 0)
        {

            // Check if octal representation
            // of x contains digit d
            if (x % 8 == d)
            {

                // Update total
                total++;
                break;
            }

            // Update x
            x = x / 8;
        }
    }

    // Print the answer
    document.write(total);
}

// Driver Code

    // Given N and D
    let n = 20, d = 7;

    // Counts and prints numbers
    // up to N having D as a digit
    // in its octal representation
    countNumbers(n, d);

    // This code is contributed by souravghosh0416.
</script>

Output:

2

Time Complexity: O(N * log₈N)
Auxiliary Space: O(1)