Problem Analysis

This problem requires calculating the sum of all integers from 1 to N where the sum of the digits of each integer falls within the inclusive range [A, B].

For example, with N=20, A=2, and B=5, the qualiyfing numbers are 2, 3, 4, 5, 11, 12, 13, 14, 15, and 20. Their total sum is 84.

Solution Approach

1. Input Processing:

   • Read three integers: N (upper limit), A (minimum digit sum), and B (maximum digit sum).

2. Iterate Through Numbers:

   • Loop through each integer X from 1 to N.

3. Calculate Digit Sum:

   • For each integer X, compute the sum of its digits.
   • This can be done by repeatedly extracting the last digit using modulo 10 and removing it using integer division by 10.

4. Condition Check:

   • If the digit sum is between A and B (inclusive), add X to the cumulative total.

5. Output Result:

   • Print the final sum of all qualifying numbers.

Code Implementation

#include <iostream>
using namespace std;
typedef long long int_type; // Define a type alias for large integers

int main() {
    int_type upper_limit, min_sum, max_sum; // Variables for N, A, B
    int_type total_sum = 0; // Initialize sum accumulator
    cin >> upper_limit >> min_sum >> max_sum; // Read input values

    // Process each number from 1 to N
    for (int_type current_num = 1; current_num <= upper_limit; current_num++) {
        int_type digit_total = 0; // Reset digit sum for current number
        int_type number_copy = current_num; // Work with a copy to preserve original

        // Calculate sum of digits
        while (number_copy > 0) {
            digit_total += number_copy % 10; // Add last digit
            number_copy /= 10; // Remove last digit
        }

        // Check if digit sum is within specified range
        if (digit_total >= min_sum && digit_total <= max_sum) {
            total_sum += current_num; // Add qualifying number to total
        }
    }

    cout << total_sum << endl; // Output final result
    return 0;
}

Code Explanation

• Input Handling: The program reads three integers representing the problem parameters.
• Number Iteration: A loop processes each integer from 1 to N.
• Digit Sum Calculation: For each number, a while loop extracts and sums digits by repeatedly using modulo and division operations.
• Range Validation: An if statement checks whether the calculated digit sum falls within the specified inclusive bounds.
• Accumulation: Qualifying numbers are added to a running total.
• Output: The final accumulated sum is printed to standard output.