# K-th Smallest in Lexicographical Order in C++

C++Server Side ProgrammingProgramming

Suppose we have two values n and k. We have to find the lexicographically kth smallest integer in the range of 1 to n. So if the input is like n = 14 and k = 3, then the output will be 11, as the sequence will be [1, 10, 11, 12, 13, 14, 2, 3, 4, 5, 6, 7, 8, 9], then the kth number is 11.

To solve this, we will follow these steps −

• Define a function findKthNumber(), this will take n, k,
• curr := 1
• (decrease k by 1)
• while k is non-zero, do −
• steps := call the function calcSteps(n, curr, curr + 1)
• if steps <= k, then −
• k := k - steps
• (increase curr by 1)
• Otherwise
• curr := curr * 10
• k := k - 1
• return curr
• Define a function calcSteps(), this will take nax, n1, n2,
• ret := 0
• while n1 <= nax, do −
• ret := ret + minimum of nax + 1 and n2 – n1
• n1 := n1 * 10
• n2 := n2 * 10
• return ret

Let us see the following implementation to get better understanding −

## Example

Live Demo

#include <bits/stdc++.h>
using namespace std;
typedef long long int lli;
class Solution {
public:
int findKthNumber(int n, int k) {
int curr = 1;
k--;
while(k){
int steps = calcSteps(n, curr, curr + 1);
if(steps <= k){
k -= steps;
curr++;
}else{
curr *= 10;
k -= 1;
}
}
return curr;
}
int calcSteps(lli nax, lli n1, lli n2){
int ret = 0;
while(n1 <= nax){
ret += min(nax + 1, n2) - n1;
n1 *= 10;
n2 *= 10;
}
return ret;
}
};
main(){
Solution ob;
cout << (ob.findKthNumber(14,3));
}

## Input

14,3

## Output

11