K-th smallest element after removing given integers from natural numbers | Set 2

Given an array arr[] of size ‘n’ and a positive integer k. Consider series of natural numbers and remove arr[0], arr[1], arr[2], …, arr[n-1] from it. Now the task is to find k-th smallest number in the remaining set of natural numbers.

Examples:

Input : arr[] = { 1 } and k = 1.
Output: 2
Natural numbers are {1, 2, 3, 4, .... }
After removing {1}, we get {2, 3, 4, ...}.
Now, K-th smallest element = 2.

Input : arr[] = {1, 3}, k = 4.
Output : 6
First 5 Natural number {1, 2, 3, 4, 5, 6,  .. }
After removing {1, 3}, we get {2, 4, 5, 6, ... }.

2 methods are discussed in this article.

This post discusses one more method.

Algorithm:

  1. Start traversing the array, for i ranging from 0 to N-1
  2. If arr[i]<=k, then increment k. Else break out of traversing the rest of the array
  3. The obtained k is the final answer

C++

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// C++ program to find the K-th smallest element
// after removing some integers from natural number.
#include <bits/stdc++.h>
using namespace std;
  
// Return the K-th smallest element.
int ksmallest(int arr[], int n, int k)
{
    for (int i = 0; i < n; i++) {
        if (arr[i] <= k)
            k++;
        else
            break;
    }
    return k;
}
  
// Driven Program
int main()
{
    int k = 1;
    int arr[] = { 1 };
    int n = sizeof(arr) / sizeof(arr[0]);
    cout << ksmallest(arr, n, k);
    return 0;
}

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Java

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// Java program to find the
// K-th smallest element
// after removing some 
// integers from natural number.
class GFG
{
  
// Return the K-th 
// smallest element.
static int ksmallest(int arr[], 
                     int n, int k)
{
    for (int i = 0; i < n; i++) 
    {
        if (arr[i] <= k)
            k++;
        else
            break;
    }
    return k;
}
  
// Driver Code
public static void main(String args[])
{
    int k = 1;
    int arr[] = { 1 };
    int n = arr.length;
    System.out.println(ksmallest(arr, n, k));
}
}
  
// This code is contributed 
// by Arnab Kundu

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Python3

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# Python3 program to find 
# the K-th smallest element 
# after removing some integers
# from natural number.
  
# Return the K-th 
# smallest element.
def ksmallest(arr, n, k):
    for i in range(n): 
        if (arr[i] <= k):
            k = k + 1;
        else:
            break;
    return k;
  
# Driver Code
k = 1;
arr = [1];
n = len(arr);
print(ksmallest(arr, n, k));
      
# This code is contributed by mits

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C#

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// C# program to find the
// K-th smallest element
// after removing some 
// integers from natural number.
using System;
  
class GFG
{
// Return the K-th 
// smallest element.
  
static int ksmallest(int []arr, 
                     int n, int k)
{
    for (int i = 0; i < n; i++) 
    {
        if (arr[i] <= k)
            k++;
        else
            break;
    }
    return k;
}
  
// Driver Code
static public void Main ()
{
    int k = 1;
    int []arr = { 1 };
    int n = arr.Length;
    Console.WriteLine(ksmallest(arr, 
                                n, k));
}
}
  
// This code is contributed @ajit

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PHP

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<?php
// PHP program to find the K-th
// smallest element after removing
// some integers from natural number.
  
// Return the K-th smallest element.
function ksmallest($arr, $n, $k)
{
    for ($i = 0; $i < $n; $i++) 
    {
        if ($arr[$i] <= $k)
            $k++;
        else
            break;
    }
    return $k;
}
  
    // Driver Code
    $k = 1;
    $arr = array(1);
    $n = sizeof($arr);
    echo ksmallest($arr, $n, $k);
      
// This code is contributed by aj_36
?>

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Output:

2


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