# Find the number of positive integers less than or equal to N that have an odd number of digits

Given an integer N where 1 ≤ N ≤ 105, the task is to find the number of positive integers less than or equal to N that have an odd number of digits without leading zeros.

Examples:

Input: N = 11
Output: 9
1, 2, 3, …, 8 and 9 are the numbers ≤ 11
with odd number of digits.

Input: N = 893
Output: 803

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Naive approach: Traverse from 1 to N and for each number check if it contains odd digits or not.

Efficient approach: For the values:

• When N < 10 then the count of valid numbers will be N.
• When N / 10 < 10 then 9.
• When N / 100 < 10 then 9 + N – 99.
• When N / 1000 < 10 then 9 + 900.
• When N / 10000 < 10 then 909 + N – 9999.
• Otherwise 90909.

Below is the implementation of the above approach:

## C++

 `// C++ implementation of the approach ` `#include ` `using` `namespace` `std; ` ` `  `// Function to return the number of ` `// positive integers less than or equal ` `// to N that have odd number of digits ` `int` `odd_digits(``int` `n) ` `{ ` `    ``if` `(n < 10) ` `        ``return` `n; ` `    ``else` `if` `(n / 10 < 10) ` `        ``return` `9; ` `    ``else` `if` `(n / 100 < 10) ` `        ``return` `9 + n - 99; ` `    ``else` `if` `(n / 1000 < 10) ` `        ``return` `9 + 900; ` `    ``else` `if` `(n / 10000 < 10) ` `        ``return` `909 + n - 9999; ` `    ``else` `        ``return` `90909; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``int` `n = 893; ` ` `  `    ``cout << odd_digits(n); ` ` `  `    ``return` `0; ` `} `

## Java

 `// Java implementation of the approach ` `class` `GFG  ` `{ ` ` `  `// Function to return the number of ` `// positive integers less than or equal ` `// to N that have odd number of digits ` `static` `int` `odd_digits(``int` `n) ` `{ ` `    ``if` `(n < ``10``) ` `        ``return` `n; ` `    ``else` `if` `(n / ``10` `< ``10``) ` `        ``return` `9``; ` `    ``else` `if` `(n / ``100` `< ``10``) ` `        ``return` `9` `+ n - ``99``; ` `    ``else` `if` `(n / ``1000` `< ``10``) ` `        ``return` `9` `+ ``900``; ` `    ``else` `if` `(n / ``10000` `< ``10``) ` `        ``return` `909` `+ n - ``9999``; ` `    ``else` `        ``return` `90909``; ` `} ` ` `  `// Driver code ` `public` `static` `void` `main(String []args)  ` `{ ` `    ``int` `n = ``893``; ` ` `  `    ``System.out.println(odd_digits(n)); ` `} ` `} ` ` `  `// This code is contributed by 29AjayKumar `

## Python3

 `# Python3 implementation of the approach  ` ` `  `# Function to return the number of  ` `# positive integers less than or equal  ` `# to N that have odd number of digits  ` `def` `odd_digits(n) : ` ` `  `    ``if` `(n < ``10``) : ` `        ``return` `n;  ` `    ``elif` `(n ``/` `10` `< ``10``) : ` `        ``return` `9``;  ` `    ``elif` `(n ``/` `100` `< ``10``) : ` `        ``return` `9` `+` `n ``-` `99``;  ` `    ``elif` `(n ``/` `1000` `< ``10``) : ` `        ``return` `9` `+` `900``;  ` `    ``elif` `(n ``/` `10000` `< ``10``) :  ` `        ``return` `909` `+` `n ``-` `9999``;  ` `    ``else` `: ` `        ``return` `90909``;  ` ` `  `# Driver code  ` `if` `__name__ ``=``=` `"__main__"` `:  ` ` `  `    ``n ``=` `893``;  ` ` `  `    ``print``(odd_digits(n));  ` ` `  `# This code is contributed by AnkitRai01 `

## C#

 `// C# implementation of the approach ` `using` `System; ` `                     `  `class` `GFG  ` `{ ` ` `  `// Function to return the number of ` `// positive integers less than or equal ` `// to N that have odd number of digits ` `static` `int` `odd_digits(``int` `n) ` `{ ` `    ``if` `(n < 10) ` `        ``return` `n; ` `    ``else` `if` `(n / 10 < 10) ` `        ``return` `9; ` `    ``else` `if` `(n / 100 < 10) ` `        ``return` `9 + n - 99; ` `    ``else` `if` `(n / 1000 < 10) ` `        ``return` `9 + 900; ` `    ``else` `if` `(n / 10000 < 10) ` `        ``return` `909 + n - 9999; ` `    ``else` `        ``return` `90909; ` `} ` ` `  `// Driver code ` `public` `static` `void` `Main(String []args)  ` `{ ` `    ``int` `n = 893; ` ` `  `    ``Console.WriteLine(odd_digits(n)); ` `} ` `} ` ` `  `// This code is contributed by 29AjayKumar `

Output:

```803
```

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