400. Nth Digit
1. Description
Find the nth digit of the infinite integer sequence 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, …
2. Note
- n is positive and will fit within the range of a 32-bit signed integer (n < $2^{31}$).
3. Example
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.
4. Solutions
My Accepted Solution
Time complexity: O($log_{10}n$)
Space complexity: O($log_{10}n$)
class Solution
{
public:
int findNthDigit(int n)
{
int digitsPerNumber = 1;
long beginning = 1, digitsCount = 9;
// find out the target number's digits
while(n > digitsCount)
{
digitsPerNumber++;
n -= digitsCount;
beginning *= 10;
digitsCount = beginning * 9 * digitsPerNumber;
}
// find out the target number
long targetNumber = beginning + (n - 1) / digitsPerNumber;
// find out the required digit
return to_string(targetNumber)[(n - 1) % digitsPerNumber] - '0';
}
};