K-th Smallest in Lexicographical Order
<p>Given two integers <code>n</code> and <code>k</code>, return <em>the</em> <code>k<sup>th</sup></code> <em>lexicographically smallest integer in the range</em> <code>[1, n]</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> n = 13, k = 2
<strong>Output:</strong> 10
<strong>Explanation:</strong> The lexicographical order is [1, 10, 11, 12, 13, 2, 3, 4, 5, 6, 7, 8, 9], so the second smallest number is 10.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> n = 1, k = 1
<strong>Output:</strong> 1
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= k &lt;= n &lt;= 10<sup>9</sup></code></li>
</ul>
Trie
impl Solution {
    pub fn find_kth_number(n: i32, k: i32) -> i32 {
        fn count(mut curr: i64, n: i32) -> i32 {
            let mut next = curr + 1;
            let mut total = 0;
            let n = n as i64;
            while curr <= n {
                total += std::cmp::min(n - curr + 1, next - curr);
                curr *= 10;
                next *= 10;
            }
            total as i32
        }

        let mut curr = 1;
        let mut k = k - 1;

        while k > 0 {
            let cnt = count(curr as i64, n);
            if k >= cnt {
                k -= cnt;
                curr += 1;
            } else {
                k -= 1;
                curr *= 10;
            }
        }

        curr
    }
}
