# Program to group a set of points into k different groups in Python

Suppose we have a list of points and a number k. The points are in the form (x, y) representing Cartesian coordinates. We can group any two point p1 and p2 if the Euclidean distance between them is <= k, we have to find total number of disjoint groups.

So, if the input is like points = [[2, 2],[3, 3],[4, 4],[11, 11],[12, 12]], k = 2, then the output will be 2, as it can make two groups: ([2,2],[3,3],[4,4]) and ([11,11],[12,12])

To solve this, we will follow these steps −

• Define a function dfs() . This will take i

• if i is in seen, then

• return

• insert i into seen

• for each nb in adj[i], do

• dfs(nb)

• From the main method, do the following−

• n := size of points

• for j in range 0 to n, do

• for i in range 0 to j, do

• p1 := points[i]

• p2 := points[j]

• if Euclidean distance between p1 and p2 < k, then

• insert j at the end of adj[i]

• insert i at the end of adj[j]

• seen := a new set

• ans := 0

• for i in range 0 to n, do

• if i not seen, then

• ans := ans + 1

• dfs(i)

• return ans

Let us see the following implementation to get better understanding −

## Example

Live Demo

from collections import defaultdict
class Solution:
def solve(self, points, k):

n = len(points)
for j in range(n):
for i in range(j):
x1, y1 = points[i]
x2, y2 = points[j]
if (x1 - x2) ** 2 + (y1 - y2) ** 2 <= k ** 2:

seen = set()
def dfs(i):
if i in seen:
return
dfs(nb)

ans = 0
for i in range(n):
if i not in seen:
ans += 1
dfs(i)
return ans
ob = Solution()
points = [
[2, 2],
[3, 3],
[4, 4],
[11, 11],
[12, 12]
]
k = 2
print(ob.solve(points, k))

## Input

[[2, 2],[3, 3],[4, 4],[11, 11],[12, 12]],2

## Output

2