# [3025] Find The Number Of Ways To Place People I

## 題目資訊
- **難度**: Medium
- **標籤**: Array, Math, Geometry, Sorting, Enumeration
- **題目連結**: [LeetCode](https://leetcode.com/problems/find-the-number-of-ways-to-place-people-i/)
- **練習日期**: 2025-09-02

## 題目描述
You are given a 2D array `points` of size `n x 2` representing integer coordinates of some points on a 2D plane, where `points[i] = [xi, yi]`.

Count the number of pairs of points `(A, B)`, where
 - `A` is on **the upper** left side of `B`, and
 - there are no other points in the rectangle (or line) they make (**including the border**).

Return the count.

## 解題思路

### 初步分析
- 核心概念
   幾何關係判斷 + 區域內點的檢測
- 關鍵限制條件
   1. A必須在B的左上方, A.x <= B.x, A.y >= B.y
   2. 矩形區域內（包含邊界）不能有其他點
- 預期時間/空間複雜度？

### 解法概述
**解法**: 
   - 思路：
      - 遍歷所有點對 (A, B)
      - 檢查每個pair形成的矩形, 裡面跟邊界會不會包含其他點
   - 時間複雜度：O(N^3)
   - 空間複雜度：O(1)

## 測試案例

### 範例輸入輸出
```
Input: points = [[6,2],[4,4],[2,6]]
Output: 2
Explanation:
 - The left one is the pair (points[1], points[0]), where points[1] is on the upper left side of points[0] and the rectangle is empty.
 - The left one is the pair (points[1], points[0]), where points[1] is on the upper left side of points[0] and the rectangle is empty.
 - The right one is the pair (points[2], points[0]), where points[2] is on the upper left side of points[0], but points[1] is inside the rectangle so it's not a valid pair.
```

### 邊界情況
- `2 <= n <= 50`
- `points[i].length == 2`
- `0 <= points[i][0], points[i][1] <= 50`
- All `points[i]` are distinct.

## 學習筆記

### 今天學到什麼？
- 二維空間判斷點大小

### 遇到的困難
- 無

### 改善方向
- 無

### 相關題目
- [#223](https://leetcode.com/problems/rectangle-area/) Rectangle Area

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**總結**: 這題的核心概念是...，適合練習...技巧。