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

C++ Math: Exercise-25 with Solution

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

Sample Input: n = 10
Sample Output: Number of digit 1 present in all +ve numbers less than or equal to 10 is 2
Sample Input: n = 19
Sample Output: Number of digit 1 present in all +ve numbers less than or equal to 19 is 12

Sample Solution:

C++ Code :

#include <iostream>
#include <cmath>

using namespace std;

// Function to count the occurrence of digit 1 in positive integers up to 'n'
int count_digit_one(int n) {
    int ctr = 0; // Initialize a counter for digit '1' occurrences

    // Iterate through each digit place, starting from the ones place
    for (int i = 1; i <= n; i *= 10) {
        int a = n / i; // Get the quotient when dividing 'n' by 'i'
        int b = n % i; // Get the remainder when dividing 'n' by 'i'

        // Calculate the occurrences of digit '1' at each digit place and accumulate them
        ctr += (a + 8) / 10 * i;

        // Check if the current digit is '1' and add the count accordingly
        if (1 == a % 10) {
            ctr += b + 1;
        }
    }
    return ctr; // Return the total count of digit '1' occurrences
}

int main() {
    int n = 10;
    // Display the count of digit '1' present in all positive numbers less than or equal to 'n'
    cout << "Number of digit 1 present in all +ve numbers less than or equal to " << n << " is " << count_digit_one(n);

    n = 19;
    cout << "\nNumber of digit 1 present in all +ve numbers less than or equal to " << n << " is " << count_digit_one(n);

    n = 100;
    cout << "\nNumber of digit 1 present in all +ve numbers less than or equal to " << n << " is " << count_digit_one(n);

    return 0;    
}

Sample Output:

Number of digit 1 present in all +ve numbers less than or equal to 10 is 2
Number of digit 1 present in all +ve numbers less than or equal to 19 is 12
Number of digit 1 present in all +ve numbers less than or equal to 100 is 21

Flowchart:

C++ Code Editor:

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