Nth Digit【第n个数字】

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.

SOLVE:

class Solution {
public:
    int findNthDigit(int n) {
        int len=1;    //the length of the number
        int start=1;    //the first number of different length
        long long count=9;    //number of digits before 'start' 
        while(n>count*len){
            n-=count*len;
            len++;
            start*=10;
            count*=10;
        }
        start+=(n-1)/len;
        string res=to_string(start);
        return res[(n-1)%len]-'0';
    }
};