Find the K closest points to origin using Priority Queue

Last Updated : 15 Jul, 2025

Given a list of n points on 2D plane, the task is to find the K (k < n) closest points to the origin O(0, 0).
Note: The distance between a point P(x, y) and O(0, 0) using the standard Euclidean Distance.
Examples:

Input: [(1, 0), (2, 1), (3, 6), (-5, 2), (1, -4)], K = 3
Output: [(1, 0), (2, 1), (1, -4)]
Explanation:
Square of Distances of points from origin are
(1, 0) : 1
(2, 1) : 5
(3, 6) : 45
(-5, 2) : 29
(1, -4) : 17
Hence for K = 3, the closest 3 points are (1, 0), (2, 1) & (1, -4).
Input: [(1, 3), (-2, 2)], K = 1
Output: [(-2, 2)]
Explanation:
Square of Distances of points from origin are
(1, 3) : 10
(-2, 2) : 8
Hence for K = 1, the closest point is (-2, 2).

Approach using sorting based on distance: This approach is explained in this article.
Approach using Priority Queue for comparison: To solve the problem mentioned above, the main idea is to store the coordinates of the point in a priority queue of pairs, according to the distance of the point from the origin. For assigning the maximum priority to the least distant point from the origin, we use the Comparator class in Priority Queue. Then print the first K elements of the priority queue.
Below is the implementation of above approach:

C++

// C++ implementation to find the K
// closest points to origin
// using Priority Queue

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

// Comparator class to assign
// priority to coordinates
class comp {

public:
    bool operator()(pair<int, int> a,
                    pair<int, int> b)
    {
        int x1 = a.first * a.first;
        int y1 = a.second * a.second;
        int x2 = b.first * b.first;
        int y2 = b.second * b.second;

        // return true if distance
        // of point 1 from origin
        // is greater than distance of
        // point 2 from origin
        return (x1 + y1) > (x2 + y2);
    }
};

// Function to find the K closest points
void kClosestPoints(int x[], int y[],
                    int n, int k)
{
    // Create a priority queue
    priority_queue<pair<int, int>,
                   vector<pair<int, int> >,
                   comp>
        pq;

    // Pushing all the points
    // in the queue
    for (int i = 0; i < n; i++) {
        pq.push(make_pair(x[i], y[i]));
    }

    // Print the first K elements
    // of the queue
    for (int i = 0; i < k; i++) {

        // Store the top of the queue
        // in a temporary pair
        pair<int, int> p = pq.top();

        // Print the first (x)
        // and second (y) of pair
        cout << p.first << " "
             << p.second << endl;

        // Remove top element
        // of priority queue
        pq.pop();
    }
}

// Driver code
int main()
{
    // x coordinate of points
    int x[] = { 1, -2 };

    // y coordinate of points
    int y[] = { 3, 2 };
    int K = 1;

    int n = sizeof(x) / sizeof(x[0]);

    kClosestPoints(x, y, n, K);

    return 0;
}

Java

// Java implementation to find the K
// closest points to origin
// using Priority Queue
import java.util.*;

// Point class to store
// a point
class Pair implements Comparable<Pair>
{
    int first, second;
    Pair(int a, int b)
    {
        first = a;
        second = b;
    }
    
    public int compareTo(Pair o)
    {
        int x1 = first * first;
        int y1 = second * second;
        int x2 = o.first * o.first;
        int y2 = o.second * o.second;
        return (x1 + y1) - (x2 + y2);
    }
}

class GFG{
    
// Function to find the K closest points
static void kClosestPoints(int x[], int y[], 
                           int n, int k)
{
    // Create a priority queue
    PriorityQueue<Pair> pq = new PriorityQueue<>();

    // Pushing all the points
    // in the queue
    for(int i = 0; i < n; i++)
    {
        pq.add(new Pair(x[i], y[i]));
    }

    // Print the first K elements
    // of the queue
    for(int i = 0; i < k; i++) 
    {

        // Remove the top of the queue
        // and store in a temporary pair
        Pair p = pq.poll();

        // Print the first (x)
        // and second (y) of pair
        System.out.println(p.first + 
                     " " + p.second);
    }
}

// Driver code
public static void main(String[] args)
{
    
    // x coordinate of points
    int x[] = { 1, -2 };

    // y coordinate of points
    int y[] = { 3, 2 };
    int K = 1;

    int n = x.length;

    kClosestPoints(x, y, n, K);
}
}

// This code is contributed by jrishabh99

Python3

# Python3 implementation to find the K
# closest points to origin
# using Priority Queue

import heapq as hq
# Function to find the K closest points
def kClosestPoints(x, y, n, k):
    # Create a priority queue
    pq=[]

    # Pushing all the points
    # in the queue
    for i in range(n):
        hq.heappush(pq, (x[i]*x[i]+y[i]*y[i],x[i],y[i]))
    
    # Print the first K elements
    # of the queue
    for i in range(k) :

        # Store the top of the queue
        # in a temporary pair
        p = hq.heappop(pq)

        # Print the first (x)
        # and second (y) of pair
        print("{} {}".format(p[1],p[2]))   


# Driver code
if __name__ == '__main__':
    # x coordinate of points
    x = [1, -2]

    # y coordinate of points
    y = [3, 2] 
    K = 1

    n=len(x)

    kClosestPoints(x, y, n, K)

// C# implementation to find the K
// closest points to origin
// using Priority Queue

using System;
using System.Collections.Generic;

// Point class to store
// a point
class Pair : IComparable<Pair> {
    public int first, second;
    public Pair(int a, int b)
    {
        first = a;
        second = b;
    }

    public int CompareTo(Pair o)
    {
        int x1 = first * first;
        int y1 = second * second;
        int x2 = o.first * o.first;
        int y2 = o.second * o.second;
        return (x1 + y1) - (x2 + y2);
    }
}

class GFG {

    // Function to find the K closest points
    static void kClosestPoints(int[] x, int[] y, int n,
                               int k)
    {
        // Create a priority queue
        List<Pair> pq = new List<Pair>();

        // Pushing all the points
        // in the queue
        for (int i = 0; i < n; i++) {
            pq.Add(new Pair(x[i], y[i]));
        }

        pq.Sort();

        // Print the first K elements
        // of the queue
        for (int i = 0; i < k; i++) {

            // Remove the top of the queue
            // and store in a temporary pair
            Pair p = pq[0];
            pq.RemoveAt(0);

            // Print the first (x)
            // and second (y) of pair
            Console.WriteLine(p.first + " " + p.second);
        }
    }

    // Driver code
    public static void Main(string[] args)
    {

        // x coordinate of points
        int[] x = { 1, -2 };

        // y coordinate of points
        int[] y = { 3, 2 };
        int K = 1;

        int n = x.Length;

        kClosestPoints(x, y, n, K);
    }
}

// This code is contributed by phasing17

JavaScript

<script>

// Javascript implementation to find the K
// closest points to origin
// using Priority Queue

// Function to find the K closest points
function kClosestPoints(x, y, n, k)
{
    // Create a priority queue
    var pq = [];

    // Pushing all the points
    // in the queue
    for (var i = 0; i < n; i++) {
        pq.push([x[i], y[i]]);
    }

    // Print the first K elements
    // of the queue
    for (var i = 0; i < k; i++) {

        // Store the top of the queue
        // in a temporary pair
        var p = pq[pq.length-1];

        // Print the first (x)
        // and second (y) of pair
        document.write( p[0] + " "
              + p[1] + "<br>");

        // Remove top element
        // of priority queue
        pq.pop();
    }
}

// Driver code
// x coordinate of points
var x = [1, -2];

// y coordinate of points
var y = [3, 2];
var K = 1;
var n = x.length;
kClosestPoints(x, y, n, K);

// This code is contributed by rutvik_56.
</script>

Output:

-2 2

Time Complexity: O(N + K * log(N))
Auxiliary Space: O(N)

Analysis of Algorithms

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