# Find the occurrences of digit d in the range [0..n]

Given a number n and a digit d, count all occurrences of d in range from 0 to n.**Examples:**

Input : n = 25 d = 2 Output : 9 The occurrences are 2, 12, 20, 21 22 (Two occurrences), 23, 24, 25 Input : n = 25 d = 3 Output :3 The occurrences are 3, 13, 23 Input : n = 32 d = 3 Output : 6 The occurrences are 3, 13, 23, 30, 31, 32

The first occurrence of d cannot be before number d. So we start to iterate from d and do following check again and again. We jump the number by 10 most of the time (in step 2) except for the cases mentioned in steps 2.a and 2.b. **Step 1**: Check whether the last digit of the number is equal to the d, if it is then increment the count. **Step 2**:

a) If the number is completely divisible by 10 then increment both the count and number (For example if we reach the number 30 which is completely divisible by 10 and d=3, then we have to count all numbers from 31-39 that’s why we increment count by 1 and number by 1)

b) else if the first digit of the number is one less than d then it means that we have come to the row where we have to increment the number by 10 and subtract the d from it. For example if we reach 23 for d=3 then we increment the number by 23+10-3 = 30)

c) else increment the number by 10 only. (For example: d=3, itr=3, then increment by 10 i.e.13, 23) **Step 3:-** Return the count.

## C++

`// C++ program to count appearances of` `// a digit 'd' in range from [0..n]` `#include <bits/stdc++.h>` `using` `namespace` `std;` `int` `getOccurence(` `int` `n, ` `int` `d)` `{` ` ` `int` `result = 0; ` `// Initialize result` ` ` `// Count appearances in numbers starting` ` ` `// from d.` ` ` `int` `itr = d;` ` ` `while` `(itr <= n)` ` ` `{` ` ` `// When the last digit is equal to d` ` ` `if` `(itr%10 == d)` ` ` `result++;` ` ` `// When the first digit is equal to d then` ` ` `if` `(itr != 0 && itr/10 == d)` ` ` `{` ` ` `// increment result as well as number` ` ` `result++;` ` ` `itr++;` ` ` `}` ` ` `// In case of reverse of number such as 12 and 21` ` ` `else` `if` `(itr/10 == d-1)` ` ` `itr = itr + (10 - d);` ` ` `else` ` ` `itr = itr+10;` ` ` `}` ` ` `return` `result;` `}` `// Driver code` `int` `main(` `void` `)` `{` ` ` `int` `n = 11, d = 1;` ` ` `cout << getOccurence(n, d);` ` ` `return` `0;` `}` |

## Java

`// java program to count appearances of` `// a digit 'd' in range from [0..n]` `import` `java.*;` `public` `class` `GFG {` ` ` ` ` `static` `int` `getOccurence(` `int` `n, ` `int` `d)` ` ` `{` ` ` ` ` `// Initialize result` ` ` `int` `result = ` `0` `;` ` ` ` ` `// Count appearances in numbers` ` ` `// starting from d.` ` ` `int` `itr = d;` ` ` ` ` `while` `(itr <= n)` ` ` `{` ` ` ` ` `// When the last digit is` ` ` `// equal to d` ` ` `if` `(itr % ` `10` `== d)` ` ` `result++;` ` ` ` ` `// When the first digit is` ` ` `// equal to d then` ` ` `if` `(itr != ` `0` `&& itr/` `10` `== d)` ` ` `{` ` ` ` ` `// increment result as` ` ` `// well as number` ` ` `result++;` ` ` `itr++;` ` ` `}` ` ` ` ` `// In case of reverse of number` ` ` `// such as 12 and 21` ` ` `else` `if` `(itr/` `10` `== d-` `1` `)` ` ` `itr = itr + (` `10` `- d);` ` ` `else` ` ` `itr = itr + ` `10` `;` ` ` `}` ` ` ` ` `return` `result;` ` ` `}` ` ` ` ` `// Driver code` ` ` `public` `static` `void` `main (String[] args)` ` ` `{` ` ` `int` `n = ` `11` `, d = ` `1` `;` ` ` ` ` `System.out.println(getOccurence(n, d) );` ` ` `}` `}` `// This code is contributed by Sam007.` |

## Python3

`# Python3 program to count appearances` `# of a digit 'd' in range from [0..n]` `import` `math;` `def` `getOccurence(n, d):` ` ` ` ` `# Initialize result` ` ` `result ` `=` `0` `;` ` ` `# Count appearances in numbers` ` ` `# starting from d.` ` ` `itr ` `=` `d;` ` ` `while` `(itr <` `=` `n):` ` ` ` ` `# When the last digit is equal to d` ` ` `if` `(itr ` `%` `10` `=` `=` `d):` ` ` `result ` `+` `=` `1` `;` ` ` `# When the first digit is equal to d then` ` ` `if` `(itr !` `=` `0` `and` `math.floor(itr ` `/` `10` `) ` `=` `=` `d):` ` ` ` ` `# increment result as well as number` ` ` `result ` `+` `=` `1` `;` ` ` `itr ` `+` `=` `1` `;` ` ` `# In case of reverse of number` ` ` `# such as 12 and 21` ` ` `elif` `(math.floor(itr ` `/` `10` `) ` `=` `=` `d ` `-` `1` `):` ` ` `itr ` `=` `itr ` `+` `(` `10` `-` `d);` ` ` `else` `:` ` ` `itr ` `=` `itr ` `+` `10` `;` ` ` `return` `result;` `# Driver code` `n ` `=` `11` `;` `d ` `=` `1` `;` `print` `(getOccurence(n, d));` `# This code is contributed by mits` |

## C#

`// C# program to count appearances of` `// a digit 'd' in range from [0..n]` `using` `System;` ` ` `public` `class` `GFG {` ` ` ` ` `static` `int` `getOccurence(` `int` `n, ` `int` `d)` ` ` `{` ` ` ` ` `// Initialize result` ` ` `int` `result = 0;` ` ` ` ` `// Count appearances in numbers` ` ` `// starting from d.` ` ` `int` `itr = d;` ` ` `while` `(itr <= n)` ` ` `{` ` ` ` ` `// When the last digit is` ` ` `// equal to d` ` ` `if` `(itr % 10 == d)` ` ` `result++;` ` ` ` ` `// When the first digit is` ` ` `// equal to d then` ` ` `if` `(itr != 0 && itr/10 == d)` ` ` `{` ` ` ` ` `// increment result as` ` ` `// well as number` ` ` `result++;` ` ` `itr++;` ` ` `}` ` ` ` ` `// In case of reverse of number` ` ` `// such as 12 and 21` ` ` `else` `if` `(itr/10 == d-1)` ` ` `itr = itr + (10 - d);` ` ` `else` ` ` `itr = itr + 10;` ` ` `}` ` ` ` ` `return` `result;` ` ` `}` ` ` ` ` `// Driver code` ` ` `public` `static` `void` `Main()` ` ` `{` ` ` `int` `n = 11, d = 1;` ` ` ` ` `Console.Write(getOccurence(n, d));` ` ` `}` `}` `// This code is contributed by Sam007.` |

## PHP

`<?php` `// PHP program to count appearances of` `// a digit 'd' in range from [0..n]` `function` `getOccurence(` `$n` `, ` `$d` `)` `{` ` ` ` ` `// Initialize result` ` ` `$result` `= 0;` ` ` `// Count appearances in numbers` ` ` `// starting from d.` ` ` `$itr` `= ` `$d` `;` ` ` `while` `(` `$itr` `<= ` `$n` `)` ` ` `{` ` ` ` ` `// When the last digit` ` ` `// is equal to d` ` ` `if` `(` `$itr` `% 10 == ` `$d` `)` ` ` `$result` `++;` ` ` `// When the first digit` ` ` `// is equal to d then` ` ` `if` `(` `$itr` `!= 0 && ` `floor` `(` `$itr` `/ 10) == ` `$d` `)` ` ` `{` ` ` ` ` `// increment result as` ` ` `// well as number` ` ` `$result` `++;` ` ` `$itr` `++;` ` ` `}` ` ` `// In case of reverse of` ` ` `// number such as 12 and 21` ` ` `else` `if` `(` `floor` `(` `$itr` `/ 10) == ` `$d` `- 1)` ` ` `$itr` `= ` `$itr` `+ (10 - ` `$d` `);` ` ` `else` ` ` `$itr` `= ` `$itr` `+ 10;` ` ` `}` ` ` `return` `$result` `;` `}` ` ` `// Driver code` ` ` `$n` `= 11;` ` ` `$d` `= 1;` ` ` `echo` `getOccurence(` `$n` `, ` `$d` `);` `// This code is contributed by nitin mittal.` `?>` |

## Javascript

`<script>` ` ` `// Javascript program to count appearances of` `// a digit 'd' in range from [0..n]` `function` `getOccurence(n, d)` `{` ` ` ` ` `// Initialize result` ` ` `let result = 0;` ` ` `// Count appearances in numbers` ` ` `// starting from d.` ` ` `let itr = d;` ` ` `while` `(itr <= n)` ` ` `{` ` ` ` ` `// When the last digit` ` ` `// is equal to d` ` ` `if` `(itr % 10 == d)` ` ` `result++;` ` ` `// When the first digit` ` ` `// is equal to d then` ` ` `if` `(itr != 0 && Math.floor(itr / 10) == d)` ` ` `{` ` ` ` ` `// increment result as` ` ` `// well as number` ` ` `result++;` ` ` `itr++;` ` ` `}` ` ` `// In case of reverse of` ` ` `// number such as 12 and 21` ` ` `else` `if` `(Math.floor(itr / 10) == d - 1)` ` ` `itr = itr + (10 - d);` ` ` `else` ` ` `itr = itr + 10;` ` ` `}` ` ` `return` `result;` `}` ` ` `// Driver code` ` ` `let n = 11;` ` ` `let d = 1;` ` ` `document.write(getOccurence(n, d));` `// This code is contributed by _saurabh_jaiswal.` `</script>` |

**Output:**

4

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