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Find the Kth smallest element in the sorted generated array

• Last Updated : 08 Jun, 2021

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

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

Finally print the Kth 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, 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:

Approach:

1. 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.
2. Take cumulative sum of count array.
3. Maintain all elements of arr[] with their count in Array B[] along with their counts and sort them based on element value.
4. Traverse through vector and see which element has Kth position in B[] as per their individual counts.
5. 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 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 > 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 codeint 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 approachimport 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 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 contiributed 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 codeif __name__ == "__main__" :     arr = [ 2, 4, 5, 1 ];    N = len(arr);    K = 13;     print(solve(arr, N, K));     # This code is contributed by AnkitRai01

C#

 // C# implementation of the approachusing 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 element = new List();        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


Output:
2

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