Count 'd' digit positive integers with 0 as a digit - GeeksforGeeks

06 Nov, 2021
Given a number d, representing the number of digits of a positive integer. Find the total count of positive integer (consisting of d digits exactly) which have at-least one zero in them.Examples: 
Input : d = 1
Output : 0
There's no natural number of 1 digit that
contains a zero.

Input : d = 2
Output : 9
The numbers are, 10, 20, 30, 40, 50, 60, 
                 70, 80 and 90.
 
One Simple Solution is to traverse through all d digit positive numbers. For every number, traverse through its digits and if there is any 0 digit, increment count (similar to this).Following are some observations: 
There are exactly d digits.The number at most significant place can’t be a zero (no leading zeroes allowed).All the other places except the most significant one can contain zero .
There are exactly d digits.
The number at most significant place can’t be a zero (no leading zeroes allowed).
All the other places except the most significant one can contain zero .
 
So considering the above points, let’s find the total count of numbers having d digits: 
We can place any of {1, 2, ... 9} in D1
Hence D1 can be filled in 9 ways.

Apart from D1 all the other places can be  10 ways. 
(we can place 0 as well)
Hence the total numbers having d digits can be given as: 
Total =  9*10d-1

Now, let's find the numbers having d digits, that
don't contain zero at any place. 
In this case, all the places can be filled in 9 ways.
Hence count of such numbers is given by:
Non_Zero = 9d

Now the count of numbers having at least one zero 
can be obtained by subtracting Non_Zero from Total.
Hence Answer would be given by:
9*(10d-1 - 9d-1) 
Below is the program for the same.  
C++
Java
Python3
C#
PHP
Javascript
//C++ program to find the count of positive integer of a// given number of digits that contain atleast one zero#include<bits/stdc++.h>using namespace std; // Returns count of 'd' digit integers have 0 as a digitint findCount(int d){    return 9*(pow(10,d-1) - pow(9,d-1));} // Driver Codeint main(){    int d = 1;    cout << findCount(d) << endl;     d = 2;    cout << findCount(d) << endl;     d = 4;    cout << findCount(d) << endl;    return 0;}
// Java program to find the count// of positive integer of a// given number of digits// that contain atleast one zeroimport java.io.*; class GFG {         // Returns count of 'd' digit    // integers have 0 as a digit    static int findCount(int d)    {        return 9 * ((int)(Math.pow(10, d - 1))                 - (int)(Math.pow(9, d - 1)));    }         // Driver Code    public static void main(String args[])    {        int d = 1;        System.out.println(findCount(d));                 d = 2;        System.out.println(findCount(d));                 d = 4;        System.out.println(findCount(d));             }} // This code is contributed by Nikita Tiwari.
# Python 3 program to find the# count of positive integer of a# given number of digits that# contain atleast one zeroimport math # Returns count of 'd' digit# integers have 0 as a digitdef findCount(d) :    return 9*((int)(math.pow(10,d-1)) - (int)(math.pow(9,d-1)));  # Driver Coded = 1print(findCount(d))     d = 2print(findCount(d)) d = 4print(findCount(d))  # This code is contributed by Nikita Tiwari.
// C# program to find the count// of positive integer of a// given number of digits// that contain atleast one zero.using System; class GFG {         // Returns count of 'd' digit    // integers have 0 as a digit    static int findCount(int d)    {        return 9 * ((int)(Math.Pow(10, d - 1))                 - (int)(Math.Pow(9, d - 1)));    }         // Driver Code    public static void Main()    {        int d = 1;        Console.WriteLine(findCount(d));                 d = 2;        Console.WriteLine(findCount(d));                 d = 4;        Console.WriteLine(findCount(d));             }} // This code is contributed by nitin mittal.
<?php// PHP program to find the count// of positive integer of a given// number of digits that contain// atleast one zero // Returns count of 'd' digit// integers have 0 as a digitfunction findCount($d){    return 9 * (pow(10, $d - 1) -                pow(9, $d - 1));} // Driver Code{    $d = 1;    echo findCount($d),"\n";     $d = 2;    echo findCount($d),"\n";     $d = 4;    echo findCount($d), "\n";    return 0;} // This code is contributed by nitin mittal?>
<script> // JavaScript program to find the count// of positive integer of a// given number of digits// that contain atleast one zero     // Returns count of 'd' digit    // integers have 0 as a digit    function findCount(d)    {        return 9 * ((Math.pow(10, d - 1))                 - (Math.pow(9, d - 1)));    } // Driver Code         let d = 1;        document.write(findCount(d) + "<br/>");                   d = 2;        document.write(findCount(d) + "<br/>");                   d = 4;        document.write(findCount(d) + "<br/>");            // This code is contributed by target_2.</script>
Output : 
0
9
2439
This article is contributed by Ashutosh Kumar. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above. 
nitin mittal
target_2
bassivedant
Amazon
Mathematical
Amazon
Mathematical
Writing code in comment?
Please use ide.geeksforgeeks.org,
generate link and share the link here.
Comments
Old Comments
Modulo Operator (%) in C/C++ with Examples
Program to find sum of elements in a given array
The Knight's tour problem | Backtracking-1
Program for factorial of a number
Find all factors of a natural number | Set 1
Operators in C / C++
Minimum number of jumps to reach end
Find minimum number of coins that make a given value
Write a program to calculate pow(x,n)
Euclidean algorithms (Basic and Extended)