# Count ‘d’ digit positive integers with 0 as a digit

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.

## We strongly recommend that you click here and practice it, before moving on to the solution.

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 .

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*10Now, 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:^{d-1}Non_Zero = 9Now the count of numbers having at least one zero can be obtained by subtracting Non_Zero from Total. Hence Answer would be given by:^{d}9*(10^{d-1 - 9d-1)}

Below is the program for the same.

## C++

`//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 digit` `int` `findCount(` `int` `d)` `{` ` ` `return` `9*(` `pow` `(10,d-1) - ` `pow` `(9,d-1));` `}` `// Driver Code` `int` `main()` `{` ` ` `int` `d = 1;` ` ` `cout << findCount(d) << endl;` ` ` `d = 2;` ` ` `cout << findCount(d) << endl;` ` ` `d = 4;` ` ` `cout << findCount(d) << endl;` ` ` `return` `0;` `}` |

## Java

`// Java program to find the count` `// of positive integer of a` `// given number of digits ` `// that contain atleast one zero` `import` `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.` |

## Python3

`# Python 3 program to find the` `# count of positive integer of a` `# given number of digits that` `# contain atleast one zero` `import` `math` `# Returns count of 'd' digit` `# integers have 0 as a digit` `def` `findCount(d) :` ` ` `return` `9` `*` `((` `int` `)(math.` `pow` `(` `10` `,d` `-` `1` `)) ` `-` `(` `int` `)(math.` `pow` `(` `9` `,d` `-` `1` `)));` `# Driver Code` `d ` `=` `1` `print` `(findCount(d))` ` ` `d ` `=` `2` `print` `(findCount(d))` `d ` `=` `4` `print` `(findCount(d))` `# This code is contributed by Nikita Tiwari.` |

## C#

`// 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` `// 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 digit` `function` `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` `?>` |

## Javascript

`<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

**Time Complexity** : O(logd) for given d

**Auxiliary Space: **O(1)

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.