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Find k closest numbers in an unsorted array

  • Difficulty Level : Medium
  • Last Updated : 11 Feb, 2021

Given an unsorted array and two numbers x and k, find k closest values to x.
Examples: 
 

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

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

 

A simple solution is to sort the array. Then apply the method discussed to k closest values in a sorted array.
Time Complexity : O(n Log n)
A better solution is to use Heap Data Structure 
1) Make a max heap of differences with first k elements. 
2) For every element starting from (k+1)-th element, do following. 
…..a) Find difference of current element with x. 
…..b) If difference is more than root of heap, ignore current element. 
…..c) Else insert the current element to the heap after removing the root. 
3) Finally the heap has k closest elements. 
 

C++




// C++ program to find k closest elements
#include <bits/stdc++.h>
using namespace std;
 
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 program to test above functions
int main()
{
    int arr[] = { -10, -50, 20, 17, 80 };
    int x = 20, k = 2;
    int n = sizeof(arr) / sizeof(arr[0]);
    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
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 program to test above functions
if __name__=='__main__':
    arr = [-10,-50,20,17,80]
    x,k = 20,2
    n = len(arr)
    printKclosest(arr, n, x, k)
 
# This code is contributed by Vikash Kumar 37

C#




// C# program to find k closest elements
using System;
using System.Collections.Generic;
class GFG {
 
  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 Log k)
 

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