C++ Exercises: Counts the number of combinations where the sum of the digits equals to given number

Last update on August 11 2025 12:58:03 (UTC/GMT +8 hours)

Digit Combinations with Given Sum

Write a C++ program that reads n digits chosen from 0 to 9 and counts the number of combinations where the sum of the digits equals the given number. Do not use the same digits in a combination.
For example, the combinations where n = 2 and s = 5 are as follows:
0 + 5 = 5
1 + 4 = 5
3 + 2 = 5

Visual Presentation:

C++ Exercises: Counts the number of combinations where the sum of the digits equals to given number

Sample Solution:

C++ Code :

#include <string.h> // Header file for string manipulation
#include <iostream> // Header file for input/output stream operations

using namespace std; // Using the standard namespace

int main()
{
    const int MAX_NUM  = 9; // Maximum number of digits
    const int MAX_NOS = 9; // Maximum number of sets
    const int MAX_SUM_VAL = 100; // Maximum sum value

    int n, s, dp[MAX_NOS + 1][MAX_NUM + 1][MAX_SUM_VAL + 1]; // Declaration of variables and an array for dynamic programming

    long long SUM_VAL = 0; // Initializing SUM_VAL as a long long variable

    memset(dp, 0, sizeof(dp)); // Initializing the 'dp' array to 0

    // Initializing dp array for base case of single digits
    for (int i = 0; i < MAX_NUM; i++)
    {
        dp[1][i][i] = 1;
    }

    // Dynamic programming to calculate the number of ways to form numbers with given sum and number of digits
    for (int N = 2; N <= MAX_NOS; N++)
    {
        for (int i = 1; i <= MAX_NUM; i++)
        {
            for (int j = 1; j <= MAX_SUM_VAL; j++)
            {
                if (j - i >= 0)
                {
                    for (int k = 0; k < i; k++)
                    {
                        dp[N][i][j] += dp[N - 1][k][j - i];
                    }
                }
            }
        }
    }

    cin >> n >> s; // Input for number of digits and required sum

    SUM_VAL = 0; // Reset SUM_VAL to 0

    // Calculating the total number of pairs satisfying the given conditions
    for (int i = 0; i <= MAX_NUM; i++)
    {
        SUM_VAL += dp[n][i][s];
    }

    // Outputting the result
    cout << "Number of digits " << n << " and Sum = " << s;
    cout << "\nNumber of pairs: " << SUM_VAL << endl;

    return 0; // Indicating successful completion of the program
}

Sample Output:

Sample Input: 2 5
Number of digits 2 and Sum = 5
Number of pairs: 3

Flowchart:

For more Practice: Solve these Related Problems:

Write a C++ program to count all unique combinations of n digits (0-9) that sum to a given value without repetition.
Write a C++ program that generates and prints all digit combinations where the sum of digits equals a specified value, ensuring no digit repeats.
Write a C++ program to determine the number of unique combinations of digits that add up to a target sum using backtracking.
Write a C++ program that accepts n and s, then finds and displays each combination of distinct digits that sum to s using recursion.

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C++ Code Editor:

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