README.md

400. Nth Digit

Find the n^th 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.

Solutions (Rust)

1. Mathematical

impl Solution {
    pub fn find_nth_digit(n: i32) -> i32 {
        let mut n = n;
        let mut a = 0;
        let mut b = 0;
        let mut c = 9;

        for i in 0..8 {
            a += 9 * (i + 1) * 10_i32.pow(i as u32);
            if a >= n {
                c = i + 1;
                break;
            }
            b = a;
        }

        n -= b + 1;
        match n % c {
            0 => 1 + n / (c * 10_i32.pow(c as u32 - 1)),
            d => n % (c * 10_i32.pow(c as u32 - d as u32)) / (c * 10_i32.pow(c as u32 - d as u32 - 1)),
        }
    }
}