Nth Digit

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.

方法：分步骤进行考虑。首先确定在哪个区间(1~9 或 10~99 或 100 ～999….)，然后确定在这个区间的具体数字,最后确定这个数字的第几位。
注意精度范围！

class Solution {
public:
    int findNthDigit(int n) {
        if(n>=1&&n<=9)
            return n;

        long start = 1, end = 9, level = 1;
        long count = 0 ;
        while(count < n){
            count += (end - start + 1)*level;
            start *= 10;
            end = end *10 + 9;
            ++level;
        }

        start/=10;
        end = (end - 9 )/10;
        --level;
        count = count - (end - start + 1)*level;

        count = n - count;
        int cur = start + count/level-1;
        int remain = count % level;
        if(remain==0)
            return cur%10;
        else 
            ++cur;
        int weight = level-remain;
        while(weight--)
            cur/=10;

        return cur%10;


    }
};