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

Last update on March 20 2025 12:35:38 (UTC/GMT +8 hours)

11. Count Digit 1 Occurrences Variants

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.

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

Example:
Input:
n = 12
n = 30
Output:
Total number of digit 1 appearing in 12 (less than or equal) is 5.
Total number of digit 1 appearing in 30 (less than or equal) is 13.

Visual Presentation:

Sample Solution:

C Code:

#include <stdio.h>

// Function to count the total number of occurrences of digit 1 in numbers up to the given limit
static int count_DigitOne(int n) {
    int m = 0, k = 0, x = 0, base = 1;

    // Loop to iterate through each digit of the number
    while (n > 0) {
        k = n % 10; // Get the current digit
        n = n / 10; // Update the number by removing the last digit

        // Count occurrences of digit 1 based on the current digit
        if (k > 1) {
            x += (n + 1) * base; // Increment occurrences if the digit is greater than 1
        } else if (k < 1) {
            x += n * base; // Increment occurrences if the digit is less than 1
        } else {
            x += n * base + m + 1; // Increment occurrences if the digit is equal to 1
        }

        m += k * base; // Update the count of occurrences so far
        base *= 10; // Update the base for the next digit
    }
    return x; // Return the total count of digit 1 occurrences
}

// Main function to test the count_DigitOne function with different values
int main(void) {
    int n = 12;
    printf("\nTotal number of digit 1 appearing in %d (less than or equal) is %d.", n, count_DigitOne(n));
    n = 30;
    printf("\nTotal number of digit 1 appearing in %d (less than or equal) is %d.", n, count_DigitOne(n));
    return 0;
}

Sample Output:

Total number of digit 1 appearing in 12 (less than or equal) is 5.
Total number of digit 1 appearing in 30 (less than or equal) is 13.

Flowchart:

For more Practice: Solve these Related Problems:

• Write a C program to count the occurrences of digit 1 in all numbers from 1 to n using mathematical analysis.
• Write a C program to calculate the frequency of digit 1 without iterating through every number.
• Write a C program to count digit 1 occurrences recursively and compare with iterative results.
• Write a C program to generate a histogram of digit frequencies for numbers 1 to n and highlight digit 1.

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