You are given npoints in the plane that are all distinct, where points[i] = [xi, yi]. A boomerang is a tuple of points (i, j, k) such that the distance between i and j equals the distance between i and k(the order of the tuple matters).
Return the number of boomerangs.
Example 1:
Input: points = [[0,0],[1,0],[2,0]]
Output: 2
Explanation: The two boomerangs are [[1,0],[0,0],[2,0]] and [[1,0],[2,0],[0,0]].
Example 2:
Input: points = [[1,1],[2,2],[3,3]]
Output: 2
Example 3:
Input: points = [[1,1]]
Output: 0
Constraints:
n == points.length
1 <= n <= 500
points[i].length == 2
-104 <= xi, yi <= 104
All the points are unique.
Solutions
Solution 1: Enumeration + Counting
We can enumerate each point in points as the boomerang's point $i$, and then use a hash table $cnt$ to record the number of times the distance from other points to $i$ appears.
If there are $x$ points with equal distance to $i$, then we can arbitrarily select two of them as the boomerang's $j$ and $k$. The number of schemes is $A_x^2 = x \times (x - 1)$. Therefore, for each value $x$ in the hash table, we calculate and accumulate $A_x^2$, which gives us the total number of boomerangs that meet the problem's requirements.
The time complexity is $O(n^2)$, and the space complexity is $O(n)$, where $n$ is the length of the array points.