70 lines
2.1 KiB
Markdown
70 lines
2.1 KiB
Markdown
# [3025] Find The Number Of Ways To Place People I
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## 題目資訊
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- **難度**: Medium
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- **標籤**: Array, Math, Geometry, Sorting, Enumeration
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- **題目連結**: [LeetCode](https://leetcode.com/problems/find-the-number-of-ways-to-place-people-i/)
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- **練習日期**: 2025-09-02
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## 題目描述
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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]`.
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Count the number of pairs of points `(A, B)`, where
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- `A` is on **the upper** left side of `B`, and
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- there are no other points in the rectangle (or line) they make (**including the border**).
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Return the count.
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## 解題思路
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### 初步分析
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- 核心概念
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幾何關係判斷 + 區域內點的檢測
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- 關鍵限制條件
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1. A必須在B的左上方, A.x <= B.x, A.y >= B.y
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2. 矩形區域內（包含邊界）不能有其他點
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- 預期時間/空間複雜度？
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### 解法概述
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**解法**:
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- 思路：
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- 遍歷所有點對 (A, B)
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- 檢查每個pair形成的矩形, 裡面跟邊界會不會包含其他點
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- 時間複雜度：O(N^3)
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- 空間複雜度：O(1)
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## 測試案例
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### 範例輸入輸出
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```
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Input: points = [[6,2],[4,4],[2,6]]
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Output: 2
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Explanation:
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- 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.
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- 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.
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- 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.
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```
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### 邊界情況
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- `2 <= n <= 50`
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- `points[i].length == 2`
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- `0 <= points[i][0], points[i][1] <= 50`
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- All `points[i]` are distinct.
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## 學習筆記
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### 今天學到什麼？
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- 二維空間判斷點大小
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### 遇到的困難
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- 無
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### 改善方向
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- 無
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### 相關題目
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- [#223](https://leetcode.com/problems/rectangle-area/) Rectangle Area
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---
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**總結**: 這題的核心概念是...，適合練習...技巧。
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