963. Minimum Area Rectangle II

# 963. Minimum Area Rectangle II

## 刷题内容

Given a set of points in the xy-plane, determine the minimum area of any rectangle formed from these points, with sides not necessarily parallel to the x and y axes.

If there isn't any rectangle, return 0.

Example 1:

Input: [[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: [[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: [[0,3],[1,2],[3,1],[1,3],[2,1]]
Output: 0
Explanation: There is no possible rectangle to form from these points.
Example 4:

Input: [[3,1],[1,1],[0,1],[2,1],[3,3],[3,2],[0,2],[2,3]]
Output: 2.00000
Explanation: The minimum area rectangle occurs at [2,1],[2,3],[3,3],[3,1], with an area of 2.

Note:

1 <= points.length <= 50
0 <= points[i][0] <= 40000
0 <= points[i][1] <= 40000
All points are distinct.
Answers within 10^-5 of the actual value will be accepted as correct.

## 解题方案

- 时间复杂度: O(N^3)- 空间复杂度: O(N)

（其实一共有三种组合方式，p2-p3,p1-p2,p1-p3都可以作为对角线）

1. 如果互相垂直，那么算出最后一个点的坐标看看是否在lookup里面
• 如果在，算出面积，更新
• 如果不在，continue
2. 如果不相互垂直，continue

`python
class Solution(object):
def minAreaFreeRect(self, points):
"""
:type points: List[List[int]]
:rtype: float
"""
lookup = {}
for p in points:
x, y = p
lookup[(x,y)] = 1