Well, this is one of the most commonly asked questions from both the budding and the experienced programmer. 

Though, to know about the exact answer, you have to better go into its detailing!

In this concept, when a problem statement is given to you, you have to determine K coordinates which are closest to their origin.

However, this concept is not only limited to it! 

If you want to know more about this approach and how to find it, it’s better to stay till the end of this blog post! 

What do you know about K closest point to the origin?

First thing first, you should know about the definition of K closest points to origin. 

K closest point to origin shows that in a given array of points, x and y coordinates represent all the coordinates of XY plane. Here, the distance between the two pointers is equal to their Euclidean distance. 

Euclidean distance is a mathematical term in which the distance between two points is defined as the Euclidean space that is the length of any line segment.

So in this problem, you can return the answer in any particular order. Though, the answer you are returning should be unique. 

For example; 

Input is [ 1,3] and [ -2,2] 

K = 1 

Output would be [ -2,2] 

Explanation; 

Distance between [ 1,3] with the origin will be sqrt [10]. Whereas the distance between [-2,2] with the orion will be sqrt [8] 

Here, we want the closest k to be 1, the answer would be [-2,2] 

Finding the K Closest Point to Origin 

In order to find the k closest point to origin, the best and the most suitable approach would be by using the priority queue approach. 

In the priority queue method, you can use heap data structure for its implementation. To solve the problem using this approach and to find the distance, you have to first create a min-heap of pairs to store the distance of the point from the origin and the point itself. 

You can traverse the minimum heap using the K. Similarly you can also store all the points in your final array. In the end you can return that array. 

Some example of this approach are:

Input 

[ 1,0], [ 2,2] , [0,-4], [ 1,3] and k = 2

Output 

[ 1,0] [ 2,2] 

Explanation of this would be;

• Square of distance of [ 1,0] from its origin will be 1

• Square of distance [ 1,3] from its origin will be 10

• Square of distance [2,2] from its origin will be 8

• Square of distance from its origin will be 16 

Algorithm 

• In order to solve this problem, you have to find the k closest point to the origin with the help of priority queue approach. Create a function named K closest point (). It will take three parameters; array, its size and k’s value

• In the function, we will declare, pairs of priority queue which will store the coordinates and its distance in the increasing order 

• We will calculate the distance between each point from its origin. Then we, will store distance and the coordinates of points in your priority queue

• Then we will pick the first k elements in your priority queue to store them in final array and return them

Time Complexity of this case would be;

O[N] 

Since, we arrange single traversals so O[N] would be the time complexity. 

Space Complexity would be;

O [N]

Since we are storing all answers in another array, O[N] will be the space complexity. 

Other approaches to find K Closest Point to Origin 

The k closest point of origin problem to find all k closest points starting from the pointer [0,0] wants you to calculate the Euclidean distance. Though, you don’t need to calculate the actual distance here as you only have to compare the two point distance to its origin. 

Hence, here you can use some of the other approaches!  

There would also be another approach to find the K closest point to origin. These approaches are also discussed as follows:

Sorting

You can sort the array of distance in this approach. We use the efficient sort() method which helps in providing the in-built library. 

In this approach, you can first sort your array. After that you can return the value of your first K elements. The time complexity in this case would normally be O [nlogn] 

Quickselect Approach 

This approach is also quite helpful to find the k closest point of origin and to find the actual distance between the pointers. Quickselect is defined as an algorithm that helps to find the k smallest element in an unordered list of arrays. 

Here, you can choose one of the pivot elements and part the data based on that pivot. Here, the complexity would be O[nlogn] with its average O[n]. 

The solution will give you the best approach to find the k closest point of origin as it gives the best performance. However, this solution may be difficult to implement as you need to first remove the time and space complexity. 

Also, you need to know in-depth about the problem statement before implementing this solution. 

Longest Subsequence Palindrome 

Another important coding concept, which you should know is Longest Subsequence Palindrome. Here, in this problem, we find the maximum length or the longest substring of a given string. Here, the string is considered as plaindrome. 

For instance; Longest Subsequence Palindrome of banana would be anana. 

Though, one thing to note here is that it may be possible that the string will not be unique. 

Wrapping Up

Finding the k closest point to the origin is the important subject that you can’t definitely miss! 

We hope that by following the above-mentioned methods, you will easily find the k closest point of origin and implement that in your problem statement.