Java implementation LeetCode 440 lexicographical small number of K

440. lexicographically small number of K

Given integers n and k, n are lexicographically found small numbers 1 to k.

Note: 1 ≤ k ≤ n ≤ 109.

Example:

Input:
n-: 13 is K: 2

Output:
10

Explanation: The
arrangement is lexicographically [1, 10, 11, 12, 13, 2, 3, 4, 5, 6, 7, 8, 9], the second number is smaller 10.

PS:
ten tree

class Solution {
    public int findKthNumber(int n, int k) {
        int cur = 1;
        k--;
        while (k > 0) {
            long step = 0, first = cur, last = cur + 1;
            while (first <= n) {
                step += Math.min(last, (long) (n + 1)) - first;
                first *= 10;
                last *= 10;
            }

            if (step > k) {
                //在树里
                k--;
                cur *= 10;
            }
            if (step <= k) {
                //不在树里
                k -= step;
                ++cur;
            }
        }
        return cur;
    }
}