440. K-th Smallest in Lexicographical Order

Posted on Edited on In

440. K-th Smallest in Lexicographical Order

Description

Given two integers n and k, return the k^th lexicographically smallest integer in the range [1, n].

Example 1:

1
2
3
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.

Example 2:

1
2
Input: n = 1, k = 1
Output: 1

Constraints:

  • 1 <= k <= n <= 10^9

Hints/Notes

Solution

Language: C++

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
class Solution {
public:
    int findKthNumber(int n, int k) {
        int cur = 1;
        k--;

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

    int countSteps(int n, long prefix1, long prefix2) {
        int steps = 0;
        while (prefix1 <= n) {
            steps += min((long)(n + 1), prefix2) - prefix1;
            prefix1 *= 10;
            prefix2 *= 10;
        }
        return steps;
    }
};