C Exercises: Find the n^th digit of number 1 to n

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

17. Nth Digit in Sequence Variants

Write a C program to find the nth digit of the number 1 to n?
Infinite integer sequence: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 .. where n is a positive integer.

Example:
Input:
7
Output:
7
Input:
12
Output:
1
The 12th digit of the sequence 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, ... is 1, which is part of the number 11.

Visual Presentation:

Sample Solution:

C Code:

#include <stdio.h>

// Function to find the Nth digit in a sequence
int find_Nth_Digit(int n) {
    unsigned int i, j, k;
    i = j = 1;

    // Loop to find the appropriate position of the digit in the sequence
    while (n > 9 * i * j) {
        n -= 9 * i * j; // Decrement n based on the sequence length
        j *= 10; // Increase j to move to the next digit length
        i++; // Increment i to keep track of digit length
    }

    k = j + (n - 1) / i; // Calculate the position of the digit in the sequence

    // Loop to extract the desired digit
    for (j = (n - 1) % i; j < i - 1; j++) {
        k = k / 10; // Move to the specific digit position
    }

    return k % 10; // Return the Nth digit
}

// Main function to test the find_Nth_Digit function
int main(void) {
    int n = 7;
    printf("\n%d digit of the sequence is %d", n, find_Nth_Digit(n));
    n = 12;
    printf("\n%d digit of the sequence is %d", n, find_Nth_Digit(n));
    return 0;
}

Sample Output:

7 digit of the sequence is 7
12 digit of the sequence is 1

Flowchart:

For more Practice: Solve these Related Problems:

• Write a C program to find the nth digit in the infinite sequence formed by concatenating all positive integers.
• Write a C program to calculate the nth digit by simulating the concatenation process without storing the full sequence.
• Write a C program to determine the nth digit using mathematical formulas to jump over digit groups.
• Write a C program to compute the nth digit and optimize for very large n using logarithmic estimations.

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