400. Nth Digit – Leetcode Solutions

Example 1:

Input: n = 3
Output: 3
Example 2:

Input: n = 11
Output: 0
Explanation: The 11th digit of the sequence 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, ... is a 0, which is part of the number 10.

class Solution:
    def findNthDigit(self, n: int) -> int:
        # Step 1: Determine the range where the nth digit lies
        digit_length = 1  # Current digit length (1 for 1-9, 2 for 10-99, etc.)
        count = 9         # Number of integers with the current digit length
        start = 1         # Starting number of the current digit length
        
        # Reduce n until it fits within a digit range
        while n > digit_length * count:
            n -= digit_length * count
            digit_length += 1
            count *= 10
            start *= 10
        
        # Step 2: Identify the exact number containing the nth digit
        number_index = (n - 1) // digit_length  # Zero-based index of the number
        digit_index = (n - 1) % digit_length    # Zero-based index of the digit within the number
        target_number = start + number_index    # The actual number containing the digit
        
        # Step 3: Extract the desired digit
        return int(str(target_number)[digit_index])

class Solution {
public:
    int findNthDigit(int n) {
        // Step 1: Determine the range of numbers where the nth digit is located
        long long digitLength = 1; // Start with single-digit numbers
        long long count = 9;       // Total digits in this range (9 for single digits)
        long long start = 1;       // Starting number in this range

        // Keep incrementing the range until the nth digit is found
        while (n > digitLength * count) {
            n -= digitLength * count; // Subtract the total digits in the current range
            digitLength++;            // Move to the next range (e.g., 2-digit numbers)
            count *= 10;              // Update the count (e.g., 90 for 2-digit numbers)
            start *= 10;              // Update the starting number (e.g., 10 for 2-digit numbers)
        }

        // Step 2: Locate the exact number and the digit within that number
        long long number = start + (n - 1) / digitLength; // Find the number
        int digitIndex = (n - 1) % digitLength;           // Find the digit's index in the number

        // Step 3: Extract the digit from the number
        std::string numberStr = std::to_string(number);   // Convert the number to a string
        return numberStr[digitIndex] - '0';              // Convert the character to an integer
    }
};

var findNthDigit = function(n) {
    // Step 1: Define variables to track the digit range, count, and starting number for each digit length
    let digitLength = 1; // Start with single-digit numbers
    let count = 9; // There are 9 single-digit numbers (1 to 9)
    let start = 1; // Single-digit numbers start at 1

    // Step 2: Narrow down the range where the nth digit falls
    while (n > digitLength * count) {
        n -= digitLength * count; // Subtract the digits covered by the current range
        digitLength += 1; // Move to the next digit length (e.g., 2-digit, 3-digit, etc.)
        count *= 10; // Update count (e.g., 90 for 2-digit numbers, 900 for 3-digit numbers)
        start *= 10; // Update start (e.g., 10 for 2-digit numbers, 100 for 3-digit numbers)
    }

    // Step 3: Determine the exact number and digit within the identified range
    const targetNumber = start + Math.floor((n - 1) / digitLength); // Calculate the target number
    const digitIndex = (n - 1) % digitLength; // Determine the position of the digit within the number

    // Step 4: Return the nth digit
    return Number(String(targetNumber)[digitIndex]); // Convert the number to a string, extract the digit, and return it
};

class Solution {
    public int findNthDigit(int n) {
        // Step 1: Determine the range of digits (1-digit, 2-digit, etc.)
        // Initialize variables
        int digitLength = 1; // The length of numbers in this range
        long count = 9;      // The count of numbers in this range
        long start = 1;      // The starting number of this range
        
        // While `n` is greater than the total digits in the current range
        while (n > digitLength * count) {
            n -= digitLength * count; // Move past this range
            digitLength++;            // Move to the next range (e.g., 1-digit -> 2-digit)
            count *= 10;              // Update the count of numbers in this range
            start *= 10;              // Update the starting number of this range
        }
        
        // Step 2: Identify the exact number that contains the nth digit
        long number = start + (n - 1) / digitLength; // Calculate the actual number
        
        // Step 3: Find the specific digit within the number
        String numberString = Long.toString(number); // Convert the number to a string
        int digitIndex = (n - 1) % digitLength;      // Determine the index of the digit in the string
        
        // Return the digit as an integer
        return Character.getNumericValue(numberString.charAt(digitIndex));
    }
}