Count Numbers with Difference Greater than Specific Value in C++

We are provided two numbers N which defines a range [1,N] and D which is a difference.The goal is to find all the numbers in the range [1,N] such that the [ number - (sum of its digits) ] > D. We will do this by traversing numbers from 1 to N and for each number we will calculate its digit sum using a while loop. Check if the number and calculated digit sum has a difference more than D.

Let’s understand with examples.

Input 

N=15 D=5

Output 

Numbers such that difference b/w no. and its digit sum greater than value D: 6

Explanation 

Numbers 10, 11, 12, 13, 14, 15 satisfy the condition. ( 10-1, 11-2, 12-3, 13-4, 14-5, 15-6 ) all differences are 9 which is greater than 5.

Input 

N=20 D=10

Output 

Only 20 satisfies the condition. 20-2=18 > 10.

Explanation 

This is list of numbers divisible by all non-zero digits : 100 101 102 104 105 110 111 112 115 120 122 124 126 128 132 135 140 144 150 155 162 168 175 184 200

Approach used in the below program is as follows

• We take integers N and D.

• Function digitSum(int n, int d) takes variables N, D and returns the count of numbers with (num-digitsum) >d.

• Take the initial variable count as 0 for such numbers.

• Take variable digsum as 0

• Traverse range of numbers using for loop. i=1 to i=n

• Now for each number num=i, using while loop check if number is >0.

• calculate digsum+=num%10. Reduce num=num/10 to add the next digit.

• At the end of the while, check if ( i - digsum > d ). If true increment count.

• At the end of all loops count will have a total number which satisfies the condition.

• Return the count as result.

Example

 Live Demo

#include <bits/stdc++.h>
using namespace std;
int digitSum(int n, int d){
   int count = 0;
   int digsum = 0;
   for (int i = 1; i <= n; i++){
      int num=i;
      digsum=0;
      while(num>0){
         digsum+=num%10; //sum of digits
         num=num/10;
      }
      if(i-digsum>d) //original number is i {
         count++;
         //cout<<i<<" ";
      }
   }
   return count;
}
int main(){
   int N = 20;
   int D = 8;
   cout <<"Numbers such that difference between number and its digit sum greater than specific value: "<<digitSum(N,D);
   return 0;
}

Output

If we run the above code it will generate the following output −

Numbers such that difference between number and its digit sum greater than specific value: 11