Nth Digit

Problem

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

Note: n is positive and will fit within the range of a 32-bit signed integer (n < 231).

Example 1:
Input:
3
Output:
3

Example 2:
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.

Solution

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

Analysis

We first find the starting interval of number that contains the nth digit
We do so by checking while (n > size * count)
Then we update all vars and decrement n by n -= count * size
After that, we locate the number containing nth digit
Then we get nth digit by Character.getNumbericValue()