Find K closest elements to given Value in Unsorted Array

Given an unsorted array arr[] and two numbers X and K, the task is to find K closest values to X in arr[].

Examples:

Input: arr[] = {10, 2, 14, 4, 7, 6}, X = 5, K = 3 
Output: 4 6 7
Explanation: Three closest values of x are 4, 6 and 7.

Input: arr[] = {-10, -50, 20, 17, 80}, X = 20, K = 2
Output: 17 20

Find K closest Element by Sorting the Array: 

The simple idea is to sort the array. Then apply the method discussed to K closest values in a sorted array.

Find K closest Element using Heap:

An efficient approach is to use a max heap data structure of size K. 

Find the absolute difference of the array elements with X and push them in the heap. If at any position the heap gets filled then only push elements when it has an absolute difference less than the first element of the max heap.

Follow the steps mentioned below to implement the idea:

• Build a max heap of size K.
• Initially push the first K elements of the array with their absolute difference from X.
• Now traverse from K+1 to N:
  • If the absolute difference is less than the maximum difference stored in the heap, then remove the maximum difference and insert the current difference.
• After the traversal is over, the K elements stored in the heap are the required K closest elements. 

Below is the implementation of the above approach. 

C++

// C++ program to find k closest elements

#include <bits/stdc++.h>
using namespace std;

// Function to find the K closest elements
void printKclosest(int arr[], int n, int x,
                   int k)
{
    // Make a max heap of difference with
    // first k elements.
    priority_queue<pair<int, int> > pq;
    for (int i = 0; i < k; i++)
        pq.push({ abs(arr[i] - x), i });

    // Now process remaining elements.
    for (int i = k; i < n; i++) {

        int diff = abs(arr[i] - x);

        // If difference with current
        // element is more than root,
        // then ignore it.
        if (diff > pq.top().first)
            continue;

        // Else remove root and insert
        pq.pop();
        pq.push({ diff, i });
    }

    // Print contents of heap.
    while (pq.empty() == false) {
        cout << arr[pq.top().second] << " ";
        pq.pop();
    }
}

// Driver code
int main()
{
    int arr[] = { -10, -50, 20, 17, 80 };
    int X = 20, K = 2;
    int N = sizeof(arr) / sizeof(arr[0]);

    // Function call
    printKclosest(arr, N, X, K);
    return 0;
}

Java

// Java program to find k closest elements

import java.util.Comparator;
import java.util.PriorityQueue;

class Pair {
    Integer key;
    Integer value;

    public Pair(Integer key, Integer value)
    {
        this.key = key;
        this.value = value;
    }
    public Integer getKey() {
        return key;
    }
    public void setKey(Integer key) {
        this.key = key;
    }
    public Integer getValue() {
        return value;
    }
    public void setValue(Integer value)
    {
        this.value = value;
    }
}

class GFG {

    public static void printKclosest(int[] arr, int n,
                                     int x, int k)
    {
        // Make a max heap.
        PriorityQueue<Pair> pq
            = new PriorityQueue<>(new Comparator<Pair>() {
                  public int compare(Pair p1, Pair p2)
                  {
                      return p2.getValue().compareTo(
                          p1.getValue());
                  }
              });

        // Build heap of difference with
        // first k elements
        for (int i = 0; i < k; i++) {
            pq.offer(
                new Pair(arr[i], Math.abs(arr[i] - x)));
        }

        // Now process remaining elements.
        for (int i = k; i < n; i++) {
            int diff = Math.abs(arr[i] - x);

            // If difference with current
            // element is more than root,
            // then ignore it.
            if (diff > pq.peek().getValue())
                continue;

            // Else remove root and insert
            pq.poll();
            pq.offer(new Pair(arr[i], diff));
        }

        // Print contents of heap.
        while (!pq.isEmpty()) {
            System.out.print(pq.poll().getKey() + " ");
        }
    }

    // Driver code
    public static void main(String[] args)
    {
        int arr[] = { -10, -50, 20, 17, 80 };
        int X = 20, K = 2;
        int N = arr.length;

        printKclosest(arr, N, X, K);
    }
}

// This code is contributed by Ashok Borra

Python3

# Python3 program to find k closest elements

import math
import sys
from queue import PriorityQueue

# Function to find the K closest elements
def printKclosest(arr,n,x,k):

    # Make a max heap of difference with
    # first k elements.
    pq = PriorityQueue()
    for i in range(k):
        pq.put((-abs(arr[i]-x),i))

    # Now process remaining elements
    for i in range(k,n):
        diff = abs(arr[i]-x)
        p,pi = pq.get()
        curr = -p

        # If difference with current
        # element is more than root,
        # then put it back.
        if diff>curr:
            pq.put((-curr,pi))
            continue
        else:

            # Else remove root and insert
            pq.put((-diff,i))

    # Print contents of heap.
    while(not pq.empty()):
        p,q = pq.get()
        print("{} ".format(arr[q]),end = "")

# Driver code
if __name__ == '__main__':
    arr = [-10,-50,20,17,80]
    X, K = 20,2
    N = len(arr)
    printKclosest(arr, N, X, K)

C#

// C# program to find k closest elements

using System;
using System.Collections.Generic;

class GFG {

    // Function to find the K closest elements
    static void printKclosest(int[] arr, int n, int x,
                              int k)
    {
        // Make a max heap of difference with
        // first k elements.
        List<Tuple<int, int> > pq
            = new List<Tuple<int, int> >();
        for (int i = 0; i < k; i++) {
            pq.Add(new Tuple<int, int>(Math.Abs(arr[i] - x),
                                       i));
        }

        pq.Sort();
        pq.Reverse();

        // Now process remaining elements.
        for (int i = k; i < n; i++) {

            int diff = Math.Abs(arr[i] - x);

            // If difference with current
            // element is more than root,
            // then ignore it.
            if (diff > pq[0].Item1)
                continue;

            // Else remove root and insert
            pq.RemoveAt(0);
            pq.Add(new Tuple<int, int>(diff, i));
            pq.Sort();
            pq.Reverse();
        }

        // Print contents of heap.
        while (pq.Count > 0) {
            Console.Write(arr[pq[0].Item2] + " ");
            pq.RemoveAt(0);
        }
    }

    // Driver code
    static void Main()
    {
        int[] arr = { -10, -50, 20, 17, 80 };
        int X = 20, K = 2;
        int N = arr.Length;
        printKclosest(arr, N, X, K);
    }
}

// This code is contributed by divyesh072019.

Output

17 20 

Time Complexity: O(N * logK)
Auxiliary Space: O(K)