Question

963. Minimum Area Rectangle II

中文文档

Description

You are given an array of points in the X-Y plane points where points[i] = [xi, yi].

Return _the minimum area of any rectangle formed from these points, with sides not necessarily parallel to the X and Y axes_. If there is not any such rectangle, return 0.

Answers within 10-5 of the actual answer will be accepted.

 

Example 1:

Input: points = [[1,2],[2,1],[1,0],[0,1]]
Output: 2.00000
Explanation: The minimum area rectangle occurs at [1,2],[2,1],[1,0],[0,1], with an area of 2.

Example 2:

Input: points = [[0,1],[2,1],[1,1],[1,0],[2,0]]
Output: 1.00000
Explanation: The minimum area rectangle occurs at [1,0],[1,1],[2,1],[2,0], with an area of 1.

Example 3:

Input: points = [[0,3],[1,2],[3,1],[1,3],[2,1]]
Output: 0
Explanation: There is no possible rectangle to form from these points.

 

Constraints:

• 1 <= points.length <= 50
• points[i].length == 2
• 0 <= xi, yi <= 4 * 104
• All the given points are unique.

Solutions

Solution 1

class Solution:
  def minAreaFreeRect(self, points: List[List[int]]) -> float:
    s = {(x, y) for x, y in points}
    n = len(points)
    ans = inf
    for i in range(n):
      x1, y1 = points[i]
      for j in range(n):
        if j != i:
          x2, y2 = points[j]
          for k in range(j + 1, n):
            if k != i:
              x3, y3 = points[k]
              x4 = x2 - x1 + x3
              y4 = y2 - y1 + y3
              if (x4, y4) in s:
                v21 = (x2 - x1, y2 - y1)
                v31 = (x3 - x1, y3 - y1)
                if v21[0] * v31[0] + v21[1] * v31[1] == 0:
                  w = sqrt(v21[0] ** 2 + v21[1] ** 2)
                  h = sqrt(v31[0] ** 2 + v31[1] ** 2)
                  ans = min(ans, w * h)
    return 0 if ans == inf else ans

class Solution {
  public double minAreaFreeRect(int[][] points) {
    int n = points.length;
    Set<Integer> s = new HashSet<>(n);
    for (int[] p : points) {
      s.add(f(p[0], p[1]));
    }
    double ans = Double.MAX_VALUE;
    for (int i = 0; i < n; ++i) {
      int x1 = points[i][0], y1 = points[i][1];
      for (int j = 0; j < n; ++j) {
        if (j != i) {
          int x2 = points[j][0], y2 = points[j][1];
          for (int k = j + 1; k < n; ++k) {
            if (k != i) {
              int x3 = points[k][0], y3 = points[k][1];
              int x4 = x2 - x1 + x3, y4 = y2 - y1 + y3;
              if (s.contains(f(x4, y4))) {
                if ((x2 - x1) * (x3 - x1) + (y2 - y1) * (y3 - y1) == 0) {
                  int ww = (x2 - x1) * (x2 - x1) + (y2 - y1) * (y2 - y1);
                  int hh = (x3 - x1) * (x3 - x1) + (y3 - y1) * (y3 - y1);
                  ans = Math.min(ans, Math.sqrt(1L * ww * hh));
                }
              }
            }
          }
        }
      }
    }
    return ans == Double.MAX_VALUE ? 0 : ans;
  }

  private int f(int x, int y) {
    return x * 40001 + y;
  }
}

class Solution {
public:
  double minAreaFreeRect(vector<vector<int>>& points) {
    auto f = [](int x, int y) {
      return x * 40001 + y;
    };
    int n = points.size();
    unordered_set<int> s;
    for (auto& p : points) {
      s.insert(f(p[0], p[1]));
    }
    double ans = 1e20;
    for (int i = 0; i < n; ++i) {
      int x1 = points[i][0], y1 = points[i][1];
      for (int j = 0; j < n; ++j) {
        if (j != i) {
          int x2 = points[j][0], y2 = points[j][1];
          for (int k = j + 1; k < n; ++k) {
            if (k != i) {
              int x3 = points[k][0], y3 = points[k][1];
              int x4 = x2 - x1 + x3, y4 = y2 - y1 + y3;
              if (x4 >= 0 && x4 < 40000 && y4 >= 0 && y4 <= 40000 && s.count(f(x4, y4))) {
                if ((x2 - x1) * (x3 - x1) + (y2 - y1) * (y3 - y1) == 0) {
                  int ww = (x2 - x1) * (x2 - x1) + (y2 - y1) * (y2 - y1);
                  int hh = (x3 - x1) * (x3 - x1) + (y3 - y1) * (y3 - y1);
                  ans = min(ans, sqrt(1LL * ww * hh));
                }
              }
            }
          }
        }
      }
    }
    return ans == 1e20 ? 0 : ans;
  }
};

func minAreaFreeRect(points [][]int) float64 {
  n := len(points)
  f := func(x, y int) int {
    return x*40001 + y
  }
  s := map[int]bool{}
  for _, p := range points {
    s[f(p[0], p[1])] = true
  }
  ans := 1e20
  for i := 0; i < n; i++ {
    x1, y1 := points[i][0], points[i][1]
    for j := 0; j < n; j++ {
      if j != i {
        x2, y2 := points[j][0], points[j][1]
        for k := j + 1; k < n; k++ {
          if k != i {
            x3, y3 := points[k][0], points[k][1]
            x4, y4 := x2-x1+x3, y2-y1+y3
            if s[f(x4, y4)] {
              if (x2-x1)*(x3-x1)+(y2-y1)*(y3-y1) == 0 {
                ww := (x2-x1)*(x2-x1) + (y2-y1)*(y2-y1)
                hh := (x3-x1)*(x3-x1) + (y3-y1)*(y3-y1)
                ans = math.Min(ans, math.Sqrt(float64(ww*hh)))
              }
            }
          }
        }
      }
    }
  }
  if ans == 1e20 {
    return 0
  }
  return ans
}

function minAreaFreeRect(points: number[][]): number {
  const n = points.length;
  const f = (x: number, y: number): number => x * 40001 + y;
  const s: Set<number> = new Set();
  for (const [x, y] of points) {
    s.add(f(x, y));
  }
  let ans = Number.MAX_VALUE;
  for (let i = 0; i < n; ++i) {
    const [x1, y1] = points[i];
    for (let j = 0; j < n; ++j) {
      if (j !== i) {
        const [x2, y2] = points[j];
        for (let k = j + 1; k < n; ++k) {
          if (k !== i) {
            const [x3, y3] = points[k];
            const x4 = x2 - x1 + x3;
            const y4 = y2 - y1 + y3;
            if (s.has(f(x4, y4))) {
              if ((x2 - x1) * (x3 - x1) + (y2 - y1) * (y3 - y1) === 0) {
                const ww = (x2 - x1) * (x2 - x1) + (y2 - y1) * (y2 - y1);
                const hh = (x3 - x1) * (x3 - x1) + (y3 - y1) * (y3 - y1);
                ans = Math.min(ans, Math.sqrt(ww * hh));
              }
            }
          }
        }
      }
    }
  }
  return ans === Number.MAX_VALUE ? 0 : ans;
}