Find the Kth smallest element in the sorted generated array

Last Updated : 31 May, 2022

Given an array arr[] of N elements and an integer K, the task is to generate an B[] with the following rules:

Copy elements arr[1...N], N times to array B[].
Copy elements arr[1...N/2], 2*N times to array B[].
Copy elements arr[1...N/4], 3*N times to array B[].
Similarly, until only no element is left to be copied to array B[].

Finally print the K^th smallest element from the array B[]. If K is out of bounds of B[] then return -1.
Examples:

Input: arr[] = {1, 2, 3}, K = 4
Output: 1
{1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 1, 1, 1, 1, 1} is the required array B[]
{1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 3, 3, 3} in the sorted form where
1 is the 4th smallest element.
Input: arr[] = {2, 4, 5, 1}, K = 13
Output: 2

Approach:

Maintain a Count_Array where we must store the count of times every element occurs in array B[]. It can be done for range of elements by adding the count at start index and subtracting the same count at end index + 1 location.
Take cumulative sum of count array.
Maintain all elements of arr[] with their count in Array B[] along with their counts and sort them based on element value.
Traverse through vector and see which element has Kth position in B[] as per their individual counts.
If K is out of bounds of B[] then return -1.

Below is the implementation of the above approach:

C++

// C++ implementation of the approach
#include <bits/stdc++.h>
using namespace std;

// Function to return the Kth element in B[]
int solve(int Array[], int N, int K)
{

    // Initialize the count Array
    int count_Arr[N + 1] = { 0 };
    int factor = 1;
    int size = N;

    // Reduce N repeatedly to half its value
    while (size) {
        int start = 1;
        int end = size;

        // Add count to start
        count_Arr[1] += factor * N;

        // Subtract same count after end index
        count_Arr[end + 1] -= factor * N;
        factor++;
        size /= 2;
    }

    for (int i = 2; i <= N; i++)
        count_Arr[i] += count_Arr[i - 1];

    // Store each element of Array[] with their count
    vector<pair<int, int> > element;
    for (int i = 0; i < N; i++) {
        element.push_back({ Array[i], count_Arr[i + 1] });
    }

    // Sort the elements wrt value
    sort(element.begin(), element.end());

    int start = 1;
    for (int i = 0; i < N; i++) {
        int end = start + element[i].second - 1;

        // If Kth element is in range of element[i]
        // return element[i]
        if (K >= start && K <= end) {
            return element[i].first;
        }

        start += element[i].second;
    }

    // If K is out of bound
    return -1;
}

// Driver code
int main()
{
    int arr[] = { 2, 4, 5, 1 };
    int N = sizeof(arr) / sizeof(arr[0]);
    int K = 13;

    cout << solve(arr, N, K);

    return 0;
}

Java

// Java implementation of the approach 
import java.util.Vector;

class GFG 
{

    // Pair class implementation to use Pair
    static class Pair
    {
        private int first;
        private int second;

        Pair(int first, int second) 
        {
            this.first = first;
            this.second = second;
        }

        public int getFirst() 
        {
            return first;
        }

        public int getSecond()
        {
            return second;
        }
    }

    // Function to return the Kth element in B[]
    static int solve(int[] Array, int N, int K)
    {

        // Initialize the count Array
        int[] count_Arr = new int[N + 2];
        int factor = 1;
        int size = N;

        // Reduce N repeatedly to half its value
        while (size > 0) 
        {
            int start = 1;
            int end = size;

            // Add count to start
            count_Arr[1] += factor * N;

            // Subtract same count after end index
            count_Arr[end + 1] -= factor * N;
            factor++;
            size /= 2;
        }

        for (int i = 2; i <= N; i++)
            count_Arr[i] += count_Arr[i - 1];

        // Store each element of Array[]
        // with their count
        Vector<Pair> element = new Vector<>();
        for (int i = 0; i < N; i++) 
        {
            Pair x = new Pair(Array[i], 
                              count_Arr[i + 1]);
            element.add(x);
        }

        int start = 1;
        for (int i = 0; i < N; i++) 
        {
            int end = start + element.elementAt(0).getSecond() - 1;

            // If Kth element is in range of element[i]
            // return element[i]
            if (K >= start && K <= end)
                return element.elementAt(i).getFirst();

            start += element.elementAt(i).getSecond();
        }

        // If K is out of bound
        return -1;
    }

    // Driver code
    public static void main(String[] args)
    {
        int[] arr = { 2, 4, 5, 1 };
        int N = arr.length;
        int K = 13;
        System.out.println(solve(arr, N, K));
    }
}    

// This code is contributed by
// sanjeev2552

Python3

# Python3 implementation of the approach 

# Function to return the Kth element in B[] 
def solve(Array, N, K) : 

    # Initialize the count Array 
    count_Arr = [0]*(N + 2) ; 
    factor = 1; 
    size = N; 

    # Reduce N repeatedly to half its value 
    while (size) :
        start = 1; 
        end = size; 

        # Add count to start 
        count_Arr[1] += factor * N; 

        # Subtract same count after end index 
        count_Arr[end + 1] -= factor * N; 
        factor += 1; 
        size //= 2; 

    for i in range(2, N + 1) : 
        count_Arr[i] += count_Arr[i - 1]; 

    # Store each element of Array[] with their count 
    element = [];
    
    for i in range(N) :
        element.append(( Array[i], count_Arr[i + 1] )); 

    # Sort the elements wrt value 
    element.sort(); 

    start = 1; 
    for i in range(N) :
        end = start + element[i][1] - 1; 

        # If Kth element is in range of element[i] 
        # return element[i] 
        if (K >= start and K <= end) :
            return element[i][0]; 

        start += element[i][1]; 

    # If K is out of bound 
    return -1; 


# Driver code 
if __name__ == "__main__" : 

    arr = [ 2, 4, 5, 1 ]; 
    N = len(arr); 
    K = 13; 

    print(solve(arr, N, K)); 

    # This code is contributed by AnkitRai01

// C# implementation of the approach
using System;
using System.Collections.Generic;
    
class GFG 
{

    // Pair class implementation to use Pair
    public class Pair
    {
        public int first;
        public int second;

        public Pair(int first, int second) 
        {
            this.first = first;
            this.second = second;
        }

        public int getFirst() 
        {
            return first;
        }

        public int getSecond()
        {
            return second;
        }
    }

    // Function to return the Kth element in B[]
    static int solve(int[] Array, int N, int K)
    {

        // Initialize the count Array
        int[] count_Arr = new int[N + 2];
        int factor = 1;
        int size = N;

        // Reduce N repeatedly to half its value
        while (size > 0) 
        {
            int end = size;

            // Add count to start
            count_Arr[1] += factor * N;

            // Subtract same count after end index
            count_Arr[end + 1] -= factor * N;
            factor++;
            size /= 2;
        }

        for (int i = 2; i <= N; i++)
            count_Arr[i] += count_Arr[i - 1];

        // Store each element of Array[]
        // with their count
        List<Pair> element = new List<Pair>();
        for (int i = 0; i < N; i++) 
        {
            Pair x = new Pair(Array[i], 
                              count_Arr[i + 1]);
            element.Add(x);
        }

        int start = 1;
        for (int i = 0; i < N; i++) 
        {
            int end = start + element[0].getSecond() - 1;

            // If Kth element is in range of element[i]
            // return element[i]
            if (K >= start && K <= end)
                return element[i].getFirst();

            start += element[i].getSecond();
        }

        // If K is out of bound
        return -1;
    }

    // Driver code
    public static void Main(String[] args)
    {
        int[] arr = { 2, 4, 5, 1 };
        int N = arr.Length;
        int K = 13;
        Console.WriteLine(solve(arr, N, K));
    }
}

// This code is contributed by Rajput-Ji

JavaScript

<script>

// JavaScript implementation of the approach

// Function to return the Kth element in B[]
function solve(arr, N, K) {

    // Initialize the count Array
    let count_Arr = new Array(N + 1).fill(0);
    let factor = 1;
    let size = N;

    // Reduce N repeatedly to half its value
    while (size) {
        let start = 1;
        let end = size;

        // Add count to start
        count_Arr[1] += factor * N;

        // Subtract same count after end index
        count_Arr[end + 1] -= factor * N;
        factor++;
        size = Math.floor(size / 2);
    }

    for (let i = 2; i <= N; i++)
        count_Arr[i] += count_Arr[i - 1];

    // Store each element of Array[] with their count
    let element = [];
    for (let i = 0; i < N; i++) {
        element.push([arr[i], count_Arr[i + 1]]);
    }

    // Sort the elements wrt value
    element.sort((a, b) => a - b);

    let start = 1;
    for (let i = 0; i < N; i++) {
        let end = start + element[i][1] - 1;

        // If Kth element is in range of element[i]
        // return element[i]
        if (K >= start && K <= end) {
            return element[i][0];
        }

        start += element[i][1];
    }

    // If K is out of bound
    return -1;
}

// Driver code

let arr = [2, 4, 5, 1];
let N = arr.length;
let K = 13;

document.write(solve(arr, N, K));


// This code is contributed by gfgking

</script>

Output:

Time Complexity: O(N * log N)

Auxiliary Space: O(N)

Find the Kth smallest element in the sorted generated array

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