Skip to content
Related Articles

Related Articles

Improve Article

Count numbers with difference between number and its digit sum greater than specific value

  • Difficulty Level : Medium
  • Last Updated : 22 Apr, 2021

Given a positive value N, we need to find the count of numbers smaller than N such that the difference between the number and sum of its digits is greater than or equal to given specific value diff. 
Examples: 
 

Input : N = 13, diff = 2
Output : 4
Then 10, 11, 12 and 13 satisfy the given
condition shown below,
10 – sumofdigit(10) = 9 >= 2
11 – sumofdigit(11) = 9 >= 2
12 – sumofdigit(12) = 9 >= 2
13 – sumofdigit(13) = 9 >= 2  
Whereas no number from 1 to 9 satisfies 
above equation so final result will be 4

 

We can solve this problem by observing a fact that for a number k less than N, 
 

 
if k – sumofdigit(k) >= diff then
above equation will be true for (k+1)
also because we know that sumofdigit(k+1)
is not greater than sumofdigit(k) + 1
so, k + 1 - sumofdigit(k + 1) >= 
k - sumofdigit(k)
but we know that right side of above 
inequality is greater than diff, 
so left side will also be greater than 
diff.

So, finally we can say that if a number k satisfies the difference condition then (k + 1) will also satisfy same equation so our job is to find the smallest number which satisfies the difference condition then all numbers greater than this and up to N will satisfy the condition so our answer will be N – smallest number we found. 
We can find the smallest number satisfying this condition using binary search so total time complexity of solution will be O(log N) 
 
 

C++




/* C++ program to count total numbers which
have difference with sum of digits greater
than specific value */
#include <bits/stdc++.h>
using namespace std;
 
// Utility method to get sum of digits of K
int sumOfDigit(int K)
{
    // loop until K is not zero
    int sod = 0;
    while (K)
    {
        sod += K % 10;
        K /= 10;
    }
    return sod;
}
 
// method returns count of numbers smaller than N,
// satisfying difference condition
int totalNumbersWithSpecificDifference(int N, int diff)
{
    int low = 1, high = N;
 
    // binary search while loop   
    while (low <= high)
    {
        int mid = (low + high) / 2;
 
        /* if difference between number and its sum
        of digit is smaller than given difference
        then smallest number will be on left side */
        if (mid - sumOfDigit(mid) < diff)       
            low = mid + 1;
         
        /* if difference between number and its sum
        of digit is greater than or equal to given
        difference then smallest number will be on
        right side */
        else       
            high = mid - 1;       
    }
 
    // return the difference between 'smallest number
    // found' and 'N' as result
    return (N - high);
}
 
// Driver code to test above methods
int main()
{
    int N = 13;
    int diff = 2;
 
    cout << totalNumbersWithSpecificDifference(N, diff);   
    return 0;
}

Java




/*  Java program to count total numbers which
   have difference with sum of digits greater
   than specific value */
 
class Test
{
    //  Utility method to get sum of digits of K
    static int sumOfDigit(int K)
    {
        //  loop until K is not zero
        int sod = 0;
        while (K != 0)
        {
            sod += K % 10;
            K /= 10;
        }
        return sod;
    }
     
    // method returns count of numbers smaller than N,
    // satisfying difference condition
    static int totalNumbersWithSpecificDifference(int N, int diff)
    {
        int low = 1, high = N;
      
        //  binary search while loop   
        while (low <= high)
        {
            int mid = (low + high) / 2;
      
            /* if difference between number and its sum
               of digit is smaller than given difference
               then  smallest number will be on left side */
            if (mid - sumOfDigit(mid) < diff)       
                low = mid + 1;
              
            /* if difference between number and its sum
               of digit is greater than or equal to given
               difference then  smallest number will be on
               right side */
            else      
                high = mid - 1;       
        }
      
        // return the difference between 'smallest number
        // found' and 'N' as result
        return (N - high);
    }
 
    // Driver method
    public static void main(String args[])
    {
        int N = 13;
        int diff = 2;
      
        System.out.println(totalNumbersWithSpecificDifference(N, diff));
    }
}

Python3




# Python program to count total numbers which
# have difference with sum of digits greater
# than specific value
 
 
# Utility method to get sum of digits of K
def sumOfDigit(K):
 
    # loop until K is not zero
    sod = 0
    while (K):
     
        sod =sod + K % 10
        K =K // 10
     
    return sod
 
 
# method returns count of
# numbers smaller than N,
# satisfying difference condition
def totalNumbersWithSpecificDifference(N,diff):
 
    low = 1
    high = N
 
    # binary search while loop   
    while (low <= high):
     
        mid = (low + high) // 2
 
        ''' if difference between number and its sum
        of digit is smaller than given difference
        then smallest number will be on left side'''
        if (mid - sumOfDigit(mid) < diff):       
            low = mid + 1
 
        # if difference between number and its sum
        # of digit greater than equal to given
        # difference then smallest number will be on
        # right side   
        else:
             
            high = mid - 1       
     
 
    # return the difference between 'smallest number
    # found' and 'N' as result
    return (N - high)
 
# Driver code to test above methods
N = 13
diff = 2
 
print(totalNumbersWithSpecificDifference(N, diff))   
     
# This code is contributed by Anant Agarwal.

C#




// C# program to count total numbers
// which have difference with sum of 
// digits greater than specific value
using System;
 
class Test {
     
    // Utility method to get sum
    // of digits of K
    static int sumOfDigit(int K)
    {
         
        // loop until K is not zero
        int sod = 0;
        while (K != 0)
        {
            sod += K % 10;
            K /= 10;
        }
        return sod;
    }
     
    // method returns count of numbers
    // smaller than N, satisfying
    // difference condition
    static int totalNumbersWithSpecificDifference(int N,
                                                  int diff)
    {
        int low = 1, high = N;
     
        // binary search while loop
        while (low <= high)
        {
            int mid = (low + high) / 2;
     
            // if difference between number and
            // its sum of digit is smaller than
            // given difference then smallest
            // number will be on left side
            if (mid - sumOfDigit(mid) < diff)    
                low = mid + 1;
             
            // if difference between number and 
            // its sum of digit is greater than 
            // or equal to given difference then 
            // smallest number will be on right side
            else   
                high = mid - 1;    
        }
     
        // return the difference between
        // 'smallest number found'
        // and 'N' as result
        return (N - high);
    }
 
    // Driver code
    public static void Main()
    {
        int N = 13;
        int diff = 2;
     
        Console.Write(totalNumbersWithSpecificDifference(N, diff));
    }
}
 
// This code is contributed by nitin mittal

PHP




<?php
// PHP program to count total numbers which
// have difference with sum of digits greater
// than specific value
 
// method to get sum of digits of K
function sumOfDigit($K)
{
     
    // loop until K is not zero
    $sod = 0;
    while ($K)
    {
        $sod += $K % 10;
        $K /= 10;
    }
    return $sod;
}
 
// method returns count of
// numbers smaller than N,
// satisfying difference condition
function totalNumbersWithSpecificDifference($N, $diff)
{
    $low = 1; $high = $N;
 
    // binary search while loop
    while ($low <= $high)
    {
        $mid = floor(($low + $high) / 2);
 
        /* if difference between number and its sum
           of digit is smaller than given difference
           then smallest number will be on left side */
        if ($mid - sumOfDigit($mid) < $diff)    
            $low = $mid + 1;
         
        /* if difference between number and its sum
           of digit is greater than or equal to given
           difference then smallest number will be on
           right side */
        else   
            $high = $mid - 1;    
    }
 
    // return the difference
    // between 'smallest number
    // found' and 'N' as result
    return ($N - $high);
}
 
// Driver Code
$N = 13;
$diff = 2;
echo totalNumbersWithSpecificDifference($N, $diff);
 
// This code is contributed by nitin mittal
?>

Javascript




<script>
 
// javascript program to
// count total numbers which
// have difference with sum
// of digits greater
// than specific value
 
// method to get sum of digits of K
function sumOfDigit(K)
{
     
    // loop until K is not zero
    let sod = 0;
    while (K)
    {
        sod += K % 10;
        K /= 10;
    }
    return sod;
}
 
// method returns count of
// numbers smaller than N,
// satisfying difference condition
function
totalNumbersWithSpecificDifference(N, diff)
{
    let low = 1;
    let high = N;
 
    // binary search while loop
    while (low <= high)
    {
        let mid = Math.floor((low + high) / 2);
 
        /* if difference between number and its sum
        of digit is smaller than given difference
        then smallest number will be on left side */
        if (mid - sumOfDigit(mid) < diff)   
            low = mid + 1;
         
        /* if difference between number and its sum
        of digit is greater than or equal to given
        difference then smallest number will be on
        right side */
        else   
            high = mid - 1;   
    }
 
    // return the difference
    // between 'smallest number
    // found' and 'N' as result
    return (N - high);
}
 
// Driver Code
let N = 13;
let diff = 2;
document.write(
totalNumbersWithSpecificDifference(N, diff)
);
 
// This code is contributed by Bobby
 
</script>

Output: 

4

This article is contributed by Utkarsh Trivedi. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.
 

Attention reader! Don’t stop learning now. Get hold of all the important mathematical concepts for competitive programming with the Essential Maths for CP Course at a student-friendly price. To complete your preparation from learning a language to DS Algo and many more,  please refer Complete Interview Preparation Course.




My Personal Notes arrow_drop_up
Recommended Articles
Page :