# K-Th Smallest In Lexicographical Order Problem

## Description

LeetCode Problem 440.

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

Example 1:

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

Constraints:

• 1 <= k <= n <= 10^9

## Sample C++ Code

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class Solution {
public:
long long get_count(long long prefix, long long n){
long long upper = prefix + 1, cnt = 0;
while (prefix <= n) {
cnt += min(n + 1, upper) - prefix;
prefix *= 10;
upper *= 10;
}
return cnt;
}

int findKthNumber(int n, int k) {
int prefix = 1, cnt = 1;
while (cnt < k) {
int tmpcnt = get_count(prefix, n);
if (tmpcnt + cnt <= k) {
prefix ++;
cnt += tmpcnt;
} else {
prefix *= 10;
cnt ++;
}
}
return prefix;
}
};
``````