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

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  • Difficulty Level : Easy
  • Last Updated : 02 Feb, 2022
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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

 

Recommended Practice

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 getOccurrence(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 << getOccurrence(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 getOccurrence(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(getOccurrence(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 getOccurrence(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(getOccurrence(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 getOccurrence(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(getOccurrence(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 getOccurrence($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;
    $d = 1;
    echo getOccurrence($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 getOccurrence(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(getOccurrence(n, d));
 
// This code is contributed by _saurabh_jaiswal.
</script>

Output: 
 

4

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