## Method

Here we will take nothing but a brute-force approach to solve this problem. First, we will iterate through all the points and find the corresponding distances from the origin for each point. Then we will find k shortest distances and corresponding points.

For finding the k shortest distances, we need to store the distance and index of the corresponding point. Then we sort the distances and print the first k points corresponding to distances.

## Algorithm

- Iterate over the array of points.
- Find the Euclidean distance of each point from the origin.
- Use a hashmap to store the distance and corresponding pointâ€™s index
- Sort the hashmap according to the distances
- Print the k points using the first k indices in the hash map. These are the closest points to the origin.

## Code

```
// c++ code to find k-closest-points-to-origin
#include<bits/stdc++.h>
using namespace std;
vector<vector<int>> kClosest(vector<vector<int>>& points, int k) {
vector<pair<int,int>> m;
vector<vector<int>> closest;
for(int i=0;i<points.size();i++)
{
int dist=(pow(points[i][0],2)+pow(points[i][1],2));
m.push_back({dist,i});
//using hash map to store the distance and corresponding //point's index
}
sort(m.begin(),m.end());// Sorting the hash map according to the // distances
int i=1;
//storing k points using the first k indices in the hash map
for(auto id:m)
{
if(i>k)
{
return closest;
}
closest.push_back(points[id.second]);
i++;
}
return closest;
}
// driver code
int main()
{
vector<vector<int>> points;
points.push_back({3,3});
points.push_back({5,-1});
points.push_back({-2,4});
int k=2;
vector<vector<int>> closest=kClosest(points,k);
for(auto point:closest)
{
cout<<"("<<point[0]<<","<<point[1]<<")"<<endl;
}
}
```

Output

```
(3,3)
(-2,4)
```

## Complexity analysis

Here the time complexity of the algorithm for finding k closest points is O(nlog n) where n is the number of points.

Space complexity is O(n) as we are using extra space for a hash map.

You can also explore about __GCD Euclidean Algorithm__ here.

## Frequently Asked Questions

### What is Euclidean distance?

Euclidean distance between two points (x1,y1) and (x2,y2) is

âˆš(x1 - x2)^2 + (y1 - y2)^2)

### What is a hash map?

It is a special kind of data structure that is used to store a unique key and associated value(key-value pair).

### What kind of sorting is used in the C++ STL sort() function?

It uses a hybrid sorting algorithm of insertion sort, heap sort, and quicksort.

## Conclusion

This article covered how to find K Closest Points To Origin.

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