Question

447. Number of Boomerangs

中文文档

Description

You are given n points 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.

class Solution:
  def numberOfBoomerangs(self, points: List[List[int]]) -> int:
    ans = 0
    for p1 in points:
      cnt = Counter()
      for p2 in points:
        d = dist(p1, p2)
        ans += cnt[d]
        cnt[d] += 1
    return ans << 1

class Solution {
  public int numberOfBoomerangs(int[][] points) {
    int ans = 0;
    for (int[] p1 : points) {
      Map<Integer, Integer> cnt = new HashMap<>();
      for (int[] p2 : points) {
        int d = (p1[0] - p2[0]) * (p1[0] - p2[0]) + (p1[1] - p2[1]) * (p1[1] - p2[1]);
        ans += cnt.getOrDefault(d, 0);
        cnt.merge(d, 1, Integer::sum);
      }
    }
    return ans << 1;
  }
}

class Solution {
public:
  int numberOfBoomerangs(vector<vector<int>>& points) {
    int ans = 0;
    for (auto& p1 : points) {
      unordered_map<int, int> cnt;
      for (auto& p2 : points) {
        int d = (p1[0] - p2[0]) * (p1[0] - p2[0]) + (p1[1] - p2[1]) * (p1[1] - p2[1]);
        ans += cnt[d];
        cnt[d]++;
      }
    }
    return ans << 1;
  }
};

func numberOfBoomerangs(points [][]int) (ans int) {
  for _, p1 := range points {
    cnt := map[int]int{}
    for _, p2 := range points {
      d := (p1[0]-p2[0])*(p1[0]-p2[0]) + (p1[1]-p2[1])*(p1[1]-p2[1])
      ans += cnt[d]
      cnt[d]++
    }
  }
  ans <<= 1
  return
}

function numberOfBoomerangs(points: number[][]): number {
  let ans = 0;
  for (const [x1, y1] of points) {
    const cnt: Map<number, number> = new Map();
    for (const [x2, y2] of points) {
      const d = (x1 - x2) ** 2 + (y1 - y2) ** 2;
      ans += cnt.get(d) || 0;
      cnt.set(d, (cnt.get(d) || 0) + 1);
    }
  }
  return ans << 1;
}

Solution 2

class Solution:
  def numberOfBoomerangs(self, points: List[List[int]]) -> int:
    ans = 0
    for p1 in points:
      cnt = Counter()
      for p2 in points:
        d = dist(p1, p2)
        cnt[d] += 1
      ans += sum(x * (x - 1) for x in cnt.values())
    return ans

class Solution {
  public int numberOfBoomerangs(int[][] points) {
    int ans = 0;
    for (int[] p1 : points) {
      Map<Integer, Integer> cnt = new HashMap<>();
      for (int[] p2 : points) {
        int d = (p1[0] - p2[0]) * (p1[0] - p2[0]) + (p1[1] - p2[1]) * (p1[1] - p2[1]);
        cnt.merge(d, 1, Integer::sum);
      }
      for (int x : cnt.values()) {
        ans += x * (x - 1);
      }
    }
    return ans;
  }
}

class Solution {
public:
  int numberOfBoomerangs(vector<vector<int>>& points) {
    int ans = 0;
    for (auto& p1 : points) {
      unordered_map<int, int> cnt;
      for (auto& p2 : points) {
        int d = (p1[0] - p2[0]) * (p1[0] - p2[0]) + (p1[1] - p2[1]) * (p1[1] - p2[1]);
        cnt[d]++;
      }
      for (auto& [_, x] : cnt) {
        ans += x * (x - 1);
      }
    }
    return ans;
  }
};

func numberOfBoomerangs(points [][]int) (ans int) {
  for _, p1 := range points {
    cnt := map[int]int{}
    for _, p2 := range points {
      d := (p1[0]-p2[0])*(p1[0]-p2[0]) + (p1[1]-p2[1])*(p1[1]-p2[1])
      cnt[d]++
    }
    for _, x := range cnt {
      ans += x * (x - 1)
    }
  }
  return
}

function numberOfBoomerangs(points: number[][]): number {
  let ans = 0;
  for (const [x1, y1] of points) {
    const cnt: Map<number, number> = new Map();
    for (const [x2, y2] of points) {
      const d = (x1 - x2) ** 2 + (y1 - y2) ** 2;
      cnt.set(d, (cnt.get(d) || 0) + 1);
    }
    for (const [_, x] of cnt) {
      ans += x * (x - 1);
    }
  }
  return ans;
}