C++ Exercises: Find the nth digit of number 1 to n

Last update on April 12 2025 12:58:34 (UTC/GMT +8 hours)

15. Find the nth Digit in the Infinite Sequence

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.
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.

Sample Solution:

C++ Code :

#include <iostream>
#include <cmath>
using namespace std;

// Function to find the nth digit of an infinite integer sequence
int find_Nth_Digit(int n) {
    int digit_length = 1;

    // Loop to determine the length of the digit where the nth digit exists
    while (n > digit_length * 9 * pow(10, digit_length - 1)) {
        n -= digit_length * 9 * pow(10, digit_length - 1);
        ++digit_length;
    }

    // Calculate the specific number containing the nth digit
    const int num = pow(10, digit_length - 1) + (n - 1) / digit_length;

    // Calculate the actual nth digit of the number
    int result = num / pow(10, (digit_length - 1) - (n - 1) % digit_length);
    result %= 10; // Obtain the last digit of the calculated number

    return result;
}

int main() {
    // Testing the find_Nth_Digit function for different values of n
    int n = 7;
    cout << "\n " <<  n << "th digit of the infinite integer sequence is " << find_Nth_Digit(n) << endl;

    n = 13;
    cout << "\n " <<  n << "th digit of the infinite integer sequence is " << find_Nth_Digit(n) << endl;    

    return 0;
}

Sample Output:

7th digit of the infinite integer sequence is 7

 13th digit of the infinite integer sequence is 1

Flowchart:

For more Practice: Solve these Related Problems:

• Write a C++ program to compute the nth digit in the concatenated sequence of all natural numbers by calculating digit positions.
• Write a C++ program that reads n and finds the corresponding digit in the infinite sequence by iterating through number lengths.
• Write a C++ program to implement an algorithm that determines the nth digit of the sequence without constructing the entire sequence.
• Write a C++ program that uses mathematical formulas to compute the nth digit in the concatenated natural numbers and then prints it.

C++ Code Editor:

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