400-nth-digit

Question

https://leetcode.com/problems/nth-digit/description/

Find the nth digit of the infinite integer sequence 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, ...

Example:

Input:
3

Output:
3

Input:
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.

Thought Process

1. Math
   1. The problem can be break down into different group based on the digits, 1 - 9, 10 - 99, where the count is 9, 90, and etc
   2. Time complexity O(log n)
   3. Space complexity O(1)

Solution

class Solution {
    public int findNthDigit(int n) {
        int len = 1;
        long count = 9;
        int start = 1;
        while (n > len * count) {
            n -= len * count;
            count *= 10;
            start *= 10;
            len++;
        }
        start += (n - 1) / len;
        return Integer.toString(start).charAt((n - 1) % len) - '0';
    }
}

Additional