C++ Exercises: Count the total number of digit 1 appearing in all positive integers less than or equal to a given integer n

C++ Math: Exercise-10 with Solution

Write a C++ program to count the total number of digits 1 appearing in all positive integers less than or equal to a given integer n.

Input n = 12,
Return 5, because digit 1 occurred 5 times in the following numbers: 1, 10, 11, 12.

Sample Solution:

C++ Code :

#include <iostream>
using namespace std;

// Function to count the number of times digit 1 appears in numbers up to a given limit
int count_DigitOne(int num) {
    int m = 0, k = 0, result = 0, base = 1; // Initialize variables for calculations

    // Loop through each digit of the number
    while (num > 0) {
        k = num % 10; // Extract the rightmost digit
        num = num / 10; // Remove the rightmost digit

        // Determine the count of digit 1 in the current position
        if (k > 1) {
            result += (num + 1) * base;
        } else if (k < 1) {
            result += num * base;
        } else {
            result += num * base + m + 1;
        }

        m += k * base; // Update the value of m for the next iteration
        base *= 10; // Move to the next position (tens, hundreds, etc.)
    }
    return result; // Return the total count of digit 1 in the given number
}

int main(void) {
    // Test cases to count the occurrences of digit 1 in numbers up to a certain limit
    int n = 6;
    cout << "\nTotal number of digit 1 appearing in " << n << " (less than or equal) is " << count_DigitOne(n) << endl;

    n = 15;
    cout << "\nTotal number of digit 1 appearing in " << n << " (less than or equal) is " << count_DigitOne(n) << endl;

    n = 100;
    cout << "\nTotal number of digit 1 appearing in " << n << " (less than or equal) is " << count_DigitOne(n) << endl;

    return 0; // Return 0 to indicate successful completion
}

Sample Output:

Total number of digit 1 appearing in 6 (less than or equal) is 1

Total number of digit 1 appearing in 15 (less than or equal) is 8

Total number of digit 1 appearing in 100 (less than or equal) is 21

Flowchart:

C++ Code Editor:

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