440. K-th Smallest in Lexicographical Order

Given integers n and k, find the lexicographically k-th smallest integer in the range from 1 to n.

Note: 1 ≤ k ≤ n ≤ 109.

Example:

Input:
n: 13   k: 2

Output:
10

Explanation:
The lexicographical order is [1, 10, 11, 12, 13, 2, 3, 4, 5, 6, 7, 8, 9], so the second smallest number is 10.

思路：
比如10 ~ 20在这一层有10个数，如果20小于n，那么再找第三层100 ~ 200，每层step就min(n + 1, n2) - n1。

class Solution {
    public int findKthNumber(int n, int k) {  
        int cur = 1;  
        int step;  
        k--;  
        while (k > 0) {  
            step = calStep(n, cur, cur + 1);  
            if (step <= k) {  
                k -= step;  
                cur++;  
            } else {  
                k--;  
                cur *= 10;  
            }  
        }  
        return cur;  
    }  

    private int calStep(int n, long n1, long n2) {  
        int step = 0;  
        while (n1 <= n) {  
            step += Math.min(n + 1, n2) - n1;  
            n1 *= 10;  
            n2 *= 10;  
        }  
        return