2025-09/3025-find-the-number-of-ways-to-place-people-i #6
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# [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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- 這題主要考察什麼概念?
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- 有什麼關鍵限制條件?
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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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1. **暴力解法**:
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- 思路:
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- 時間複雜度:O(?)
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- 空間複雜度:O(?)
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2. **優化解法**:
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- 思路:
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- 時間複雜度:O(?)
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- 空間複雜度:O(?)
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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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-
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### 遇到的困難
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-
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### 改善方向
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-
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### 相關題目
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- [題目編號] 題目名稱 - 相似概念
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- [題目編號] 題目名稱 - 進階版本
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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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// LeetCode 3025: Find The Number Of Ways To Place People I
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// 難度: Medium
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// 日期: 2025-09-02
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using System;
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using System.Collections.Generic;
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using System.Linq;
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public class Solution {
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public void Solve() {
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// TODO: 實作解法
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Console.WriteLine("Hello LeetCode 3025!");
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}
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}
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// 測試程式
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public class Program {
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public static void Main() {
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Solution sol = new Solution();
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sol.Solve();
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// TODO: 加入測試案例
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// TestCase1();
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// TestCase2();
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}
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// 測試案例模板
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/*
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static void TestCase1() {
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// Input:
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// Expected:
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// Actual:
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Console.WriteLine("Test 1: ");
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}
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*/
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}
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<Project Sdk="Microsoft.NET.Sdk">
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<PropertyGroup>
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<OutputType>Exe</OutputType>
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<TargetFramework>net8.0</TargetFramework>
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<ImplicitUsings>enable</ImplicitUsings>
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<Nullable>enable</Nullable>
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</PropertyGroup>
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</Project>
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// LeetCode 3025 單元測試
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// 使用 xUnit 框架
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using Xunit;
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using System;
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using System.Collections.Generic;
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public class SolutionTests {
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private readonly Solution _solution;
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public SolutionTests() {
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_solution = new Solution();
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}
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[Fact]
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public void TestCase1() {
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// Arrange
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// TODO: 設定輸入資料
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// var input = ;
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// var expected = ;
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// Act
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// var result = _solution.YourMethod(input);
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// Assert
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// Assert.Equal(expected, result);
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Assert.True(true); // 暫時通過,等待實作
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}
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[Fact]
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public void TestCase2() {
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// TODO: 第二個測試案例
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Assert.True(true);
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}
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[Fact]
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public void TestEdgeCases() {
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// TODO: 邊界情況測試
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// 空陣列、單一元素、最大值、最小值等
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Assert.True(true);
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}
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}
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<Project Sdk="Microsoft.NET.Sdk">
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<PropertyGroup>
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<TargetFramework>net8.0</TargetFramework>
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<Nullable>enable</Nullable>
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<IsPackable>false</IsPackable>
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</PropertyGroup>
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<ItemGroup>
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<PackageReference Include="Microsoft.NET.Test.Sdk" Version="17.1.0" />
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<PackageReference Include="xunit" Version="2.4.1" />
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<PackageReference Include="xunit.runner.visualstudio" Version="2.4.3">
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<IncludeAssets>runtime; build; native; contentfiles; analyzers; buildtransitive</IncludeAssets>
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<PrivateAssets>all</PrivateAssets>
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</PackageReference>
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</ItemGroup>
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<ItemGroup>
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<ProjectReference Include="../csharp/csharp.csproj" />
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</ItemGroup>
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</Project>
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# 邊界情況清單
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## 需要測試的邊界情況
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- [ ] 空輸入 (空陣列、空字串等)
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- [ ] 單一元素
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- [ ] 重複元素
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- [ ] 最大值/最小值
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- [ ] 負數情況
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- [ ] 超大資料量
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- [ ] 特殊字符 (如果是字串題目)
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## 額外測試案例
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### 案例 1:
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**輸入**:
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**輸出**:
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**說明**:
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### 案例 2:
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**輸入**:
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**輸出**:
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**說明**:
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