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# 939.Minimum-Area-Rectangle

## 939. Minimum Area Rectangle

## 题目地址

<https://leetcode.com/problems/minimum-area-rectangle/>

## 题目描述

```
Given a set of points in the xy-plane, determine the minimum area of a rectangle formed from these points, with sides parallel to the x and y axes.

If there isn't any rectangle, return 0.

Example 1:
Input: [[1,1],[1,3],[3,1],[3,3],[2,2]]
Output: 4

Example 2:
Input: [[1,1],[1,3],[3,1],[3,3],[4,1],[4,3]]
Output: 2

Note:
1 <= points.length <= 500
0 <= points[i][0] <= 40000
0 <= points[i][1] <= 40000
All points are distinct.
```

## 代码

### Approach #1 Sort by Column

Time: O(N^2) && Space: O(N)

```java
class Solution {
  public int minAreaRect(int[][] points) {
        Map<Integer, List<Integer>> rows = new TreeMap();
    for (int[] point: points) {
      int x = point[0], y = point[1];
      rows.computeIfAbsent(x, z-> new ArrayList()).add(y);
    }

    int ans = Integer.MAX_VALUE;
    Map<Integer, Integer> lastx = new HashMap();
    for (int x: rows.keySet()) {
      List<Integer> row = rows.get(x);
      Collections.sort(row);
      for (int i = 0; i < row.size(); i++) {
        for (int j = i + 1; j < row.size(); j++) {
          int y1 = row.get(i), y2 = row.get(j);
          int code = 40001 * y1 + y2;
          if (lastx.containsKey(code)) {
            ans = Math.min(ans, (x - lastx.get(code)) * (y2 - y1));
          }
          lastx.put(code, x);
        }
      }
    }

    return ans < Integer.MAX_VALUE ? ans : 0;
  }
}
```


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