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# Count of n digit numbers whose sum of digits equals to given sum in C++

Given a positive number as the number of digits and a sum. The goal is to find all d digit numbers that have sum of digits equal to the input sum. The numbers having leading zeros will not be considered as d digit numbers.

The ranges are digits between 1 to 100 and sum between 1 and 500.

## Let us understand with examples.

**For Example**

**Input -** digits = 3, digi_sum = 3

**Output -** Count of n digit numbers whose sum of digits equals to given sum are: 6

**Explanation -** Three digit numbers having sum of digits as 3 are:

102, 111, 120, 201, 210, and 300.

**Input -** digits = 4 digi_sum = 2

**Output -** Count of n digit numbers whose sum of digits equals to given sum are: 4

**Explanation -** Four digit numbers having sum of digits as 2 are :

1001, 1010, 1100, and 2000.

## Approach used in the below program is as follows

In this approach we will traverse from the first d digit number and find the first number whose sum of digits is equal to the given sum. Then increment numbers by 9 until we find the sum of digits more than the given sum. Once a number having digit sum greater than input sum is found then increment the number by 1 and find the next number with sum as input sum. Repeat this process till the last d digit number.

- Take the number of digits and sum of digits as input.
- Function digits_sum(int digits, int digi_sum) takes both input values and returns the count of n digit numbers whose sum of digits equals a given sum.
- Take the initial count as 0.
- Take the first number as Left = pow(10, digits - 1). And the last number of the range as right = pow(10, digits) - 1 ( i.e 10 and 99 for digits=2 ).
- Using a while loop traverse from left to right.
- Take first=0 and last=i.
- For each i ( last ), take the rightmost digit ( last % 10 ) and add to first. Reduce last by 10 for the next iteration.
- If first becomes equal to digi_sum then increment count and update i by 9 for next iteration.
- Otherwise increment i by 1.
- At the end of all loops we will have count as numbers that have digit sum equal to digi_sum.
- Return count as result.

## Example

#include <bits/stdc++.h> using namespace std; int digits_sum(int digits, int digi_sum) { int count = 0; int Left = pow(10, digits - 1); int right = pow(10, digits) - 1; int i = Left; while (i <= right) { int first = 0; int last = i; while (last != 0) { first = first + last % 10; last = last / 10; } if (first == digi_sum) { count++; i = i + 9; } else { i++; } } return count; } int main() { int digits = 5; int digi_sum = 7; cout << "Count of n digit numbers whose sum of digits equals to given sum are: " << digits_sum(digits, digi_sum); return 0; }

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

## Output

Count of n digit numbers whose sum of digits equals to given sum are: 5