# K th Smallest in Lexicographical Order

This page explains Java solution to problem `K th Smallest in Lexicographical Order` using `Math`.

## Problem Statement

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

Example 1:

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.

## Solution

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``````
package com.vc.hard;

class KThSmallestInLexicographicalOrder {
public int findKthNumber(int n, int k) {
long current = 1;
k = k - 1;
while(k > 0) {
int steps = calculateSteps(n, current, current + 1);
if(k >= steps) {
k -= steps;
current = current + 1;
}
else {
k--;
current = current * 10;
}
}
return (int)current;
}

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

## Time Complexity

O(K * log N)) Where
K is index of smallest integer that we have to find.
N is Upper bound

O(1)