400. Nth Digit

The solution consists of three steps:
- find the length of number that the Nth digit comes from
- find the number that contains Nth digit
- find the Nth digit

Note the variable "count" must be long because "count *= 10" could make it overflow.

1:  class Solution {  
2:  public:  
3:    int findNthDigit(int n) {  
4:      int len = 1;  
5:      long count = 9;  
6:      int start = 1;  
7:      while (n > len * count) {  
8:        n -= len * count;  
9:        len++;  
10:        count *= 10;  
11:        start *= 10;  
12:      }  
13:      start += (n - 1) / len;  
14:      string s = to_string(start);  
15:      return s[(n-1) % len] - '0';  
16:    }  
17:  };