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mhhung merged 7 commits from 2025-09/3025-find-the-number-of-ways-to-place-people-i into main 2025-09-02 06:09:18 +00:00
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logs/2025-09.md
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### Week 1
| 日期 | 題目 | 難度 | 語言 | 耗時 | 狀態 | 心得 |
|------|------|------|------|------|------|------|
| 09-01 | Maximum Average Pass Ratio | Medium | C# | 1hr | Done | 第一次用到Priority Queue |
| 09/01 | Maximum Average Pass Ratio | Medium | C# | 1hr | Done | 第一次用到Priority Queue |
| 09/02| Find The Number of Ways to Place People I | Medium | C# | 0.5hr | Done | 二維點位判斷 |
| 09/02| Find The Number of Ways to Place People I | Medium | go | 0.2hr | Done | go Prictice |
### Week 2
| 日期 | 題目 | 難度 | 語言 | 耗時 | 狀態 | 心得 |
@@ -25,13 +27,13 @@
## 📈 本月統計
### 完成情況
- **總練習天數**: 1 天
- **完成題數**: 1題
- **語言分布**: C# 1(題), Go 0(題)
- **難度分布**: Easy 0(題), Medium 1(題), Hard 0(題)
- **總練習天數**: 2 天
- **完成題數**: 2題
- **語言分布**: C# 2(題), Go 1(題)
- **難度分布**: Easy 0(題), Medium 2(題), Hard 0(題)
### 時間投入
- **總時間**: 1小時
- **總時間**: 1.7小時
- **平均每題**: 分鐘
- **每日平均**: 分鐘

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problems/3025-find-the-number-of-ways-to-place-people-i/README.md Normal file
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# [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
---
**總結**: 這題的核心概念是...，適合練習...技巧。

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problems/3025-find-the-number-of-ways-to-place-people-i/csharp/Program.cs Normal file
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// LeetCode 3025: Find The Number Of Ways To Place People I
// 難度: Medium
// 日期: 2025-09-02
using System;
using System.Collections.Generic;
using System.Drawing;
using System.Linq;
public class Solution
{
public int NumberOfPairs(int[][] points)
{
// 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
// points[0].Length == 2
int n = points.Length;
int count = 0;
for (var i = 0; i < n; i++)
{
for (var j = 0; j < n; j++)
{
if (i == j) continue;
int[] pointA = points[i];
int[] pointB = points[j];
// check if A.x <= B.x && A.y >= B.y
// if yes, check if any points in rectangle
if (pointA[0] <= pointB[0] && pointA[1] >= pointB[1])
{
// difinition of border
bool hasOtherPoint = false;
int minX = pointA[0];
int maxX = pointB[0];
int minY = pointB[1];
int maxY = pointA[1];
// check other point if its in border
for (var k = 0; k < n; k++)
{
if (k == i || k == j) continue;
var pointC = points[k];
if (minX <= pointC[0] && pointC[0] <= maxX
&& minY <= pointC[1] && pointC[1] <= maxY)
{
hasOtherPoint = true;
break;
}
}
if (!hasOtherPoint) count++;
}
}
}
return count;
}
}
public class Program {
public static void Main() {
Solution solution = new Solution();
// 測試案例
TestCase(solution);
}
static void TestCase(Solution solution) {
// Input:
int[][] points = new int[][] {
new int[] {6, 2},
new int[] {4, 4},
new int[] {2, 6}
};
// Expected:
Console.WriteLine($"Test Case: [[6,2],[4,4],[2,6]]");
Console.WriteLine($"Expected: 2");
// Actual:
int result1 = solution.NumberOfPairs(points);
Console.WriteLine($"Result: {result1}");
}
}

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problems/3025-find-the-number-of-ways-to-place-people-i/csharp/csharp.csproj Normal file
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<Project Sdk="Microsoft.NET.Sdk">
<PropertyGroup>
<OutputType>Exe</OutputType>
<TargetFramework>net8.0</TargetFramework>
<ImplicitUsings>enable</ImplicitUsings>
<Nullable>enable</Nullable>
</PropertyGroup>
</Project>

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problems/3025-find-the-number-of-ways-to-place-people-i/go/go.mod Normal file
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module leetcode-3025
go 1.18

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problems/3025-find-the-number-of-ways-to-place-people-i/go/main.go Normal file
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// LeetCode 3025: Find The Number Of Ways To Place People I
// 難度: Medium
// 日期: 2025-09-02
package main
import "fmt"
// TODO: 實作解法
func numberOfPairs(points [][]int) int {
n := len(points)
count := 0;
for i:= 0; i < n; i++{
for j := 0; j < n; j++{
if i == j {
continue
}
pointA := points[i]
pointB := points[j]
if pointA[0] <= pointB[0] && pointA[1] >= pointB[1] {
hasOtherPoint := false;
minX := pointA[0]
maxX := pointB[0]
minY := pointB[1]
maxY := pointA[1]
for k := 0; k < n; k++{
if i == k || j == k{
continue
}
pointC := points[k]
if minX <= pointC[0] && pointC[0] <= maxX && minY <= pointC[1] && pointC[1] <= maxY{
hasOtherPoint = true
break
}
}
if !hasOtherPoint{
count++
}
}
}
}
return count;
}
func main() {
testCase()
}
// 測試案例模板
func testCase() {
// Input:
points := [][]int{
{6, 2},
{4, 4},
{2, 6},
}
// Expected:
fmt.Printf("Test Case: [[6,2],[4,4],[2,6]]\n")
fmt.Printf("Expected: 2\n")
// Actual:
result := numberOfPairs(points)
fmt.Printf("Result: %d\n", result)
}

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problems/3025-find-the-number-of-ways-to-place-people-i/go/main_test.go Normal file
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// LeetCode 3025 Go 單元測試
package main
import (
"math/rand"
"testing"
"fmt"
)
func TestCase1_ExampleFromProblem(t *testing.T) {
// Arrange
points := [][]int{
{6, 2},
{4, 4},
{2, 6},
}
expected := 2
// Act
result := numberOfPairs(points)
// Assert
if result != expected {
t.Errorf("TestCase1 failed. Expected: %v, Got: %v", expected, result)
}
}
func TestCase2_TwoPoints(t *testing.T) {
// Arrange
points := [][]int{
{1, 3},
{2, 1},
}
expected := 1
// Act
result := numberOfPairs(points)
// Assert
if result != expected {
t.Errorf("TestCase2 failed. Expected: %v, Got: %v", expected, result)
}
}
func TestCase3_NoValidPairs(t *testing.T) {
// Arrange - 沒有有效點對的情況
points := [][]int{
{1, 1},
{2, 2},
{3, 3},
}
expected := 0
// Act
result := numberOfPairs(points)
// Assert
if result != expected {
t.Errorf("TestCase3 failed. Expected: %v, Got: %v", expected, result)
}
}
func TestCase4_SameXCoordinate(t *testing.T) {
// Arrange - x 座標相同的情況
points := [][]int{
{3, 5}, // A
{3, 2}, // B
{3, 1}, // C
}
// 詳細分析:
// (A, B): (3,5) -> (3,2) ✓ 矩形是線段，無其他點
// (A, C): (3,5) -> (3,1) ✗ 點B在矩形內
// (B, C): (3,2) -> (3,1) ✓ 矩形是線段，無其他點
expected := 2
// Act
result := numberOfPairs(points)
// Assert
if result != expected {
t.Errorf("TestCase4 failed. Expected: %v, Got: %v", expected, result)
}
}
func TestCase5_SameYCoordinate(t *testing.T) {
// Arrange - y 座標相同的情況
points := [][]int{
{1, 4}, // A
{3, 4}, // B
{5, 4}, // C
}
// 詳細分析:
// (A, B): (1,4) -> (3,4) ✓ 矩形是線段，無其他點
// (A, C): (1,4) -> (5,4) ✗ 點B在矩形內
// (B, C): (3,4) -> (5,4) ✓ 矩形是線段，無其他點
expected := 2
// Act
result := numberOfPairs(points)
// Assert
if result != expected {
t.Errorf("TestCase5 failed. Expected: %v, Got: %v", expected, result)
}
}
func TestCase6_PointsInsideRectangle(t *testing.T) {
// Arrange - 矩形內有其他點的情況
points := [][]int{
{0, 4}, // A
{4, 0}, // B
{2, 2}, // C
}
// 詳細分析:
// (A, B): (0,4) -> (4,0) ✗ 點C在矩形內
// (A, C): (0,4) -> (2,2) ✓ 點B不在矩形內
// (C, B): (2,2) -> (4,0) ✓ 點A不在矩形內
expected := 2
// Act
result := numberOfPairs(points)
// Assert
if result != expected {
t.Errorf("TestCase6 failed. Expected: %v, Got: %v", expected, result)
}
}
func TestCase7_PointsOnBorder(t *testing.T) {
// Arrange - 點在矩形邊界上的情況
points := [][]int{
{0, 3}, // A
{3, 0}, // B
{0, 0}, // C
}
// 詳細分析:
// (A, B): (0,3) -> (3,0) ✗ 點C在矩形邊界上
// (A, C): (0,3) -> (0,0) ✓ 矩形是線段，點B不在其中
// (C, B): (0,0) -> (3,0) ✓ 矩形是線段，點A不在其中
expected := 2
// Act
result := numberOfPairs(points)
// Assert
if result != expected {
t.Errorf("TestCase7 failed. Expected: %v, Got: %v", expected, result)
}
}
func TestEdgeCases_MinimumPoints(t *testing.T) {
// Arrange - 最少點數情況 (題目限制 n >= 2)
points := [][]int{
{0, 1},
{1, 0},
}
expected := 1 // (0,1) 在 (1,0) 的左上方
// Act
result := numberOfPairs(points)
// Assert
if result != expected {
t.Errorf("TestEdgeCases_MinimumPoints failed. Expected: %v, Got: %v", expected, result)
}
}
func TestEdgeCases_MaxCoordinateValues(t *testing.T) {
// Arrange - 最大座標值情況 (題目限制 0 <= coordinates <= 50)
points := [][]int{
{0, 50}, // A
{50, 0}, // B
{25, 25}, // C
}
expected := 2 // (A,C) 和 (C,B) 有效
// Act
result := numberOfPairs(points)
// Assert
if result != expected {
t.Errorf("TestEdgeCases_MaxCoordinateValues failed. Expected: %v, Got: %v", expected, result)
}
}
func TestEdgeCases_EmptyArray(t *testing.T) {
// Arrange - 空陣列情況
points := [][]int{}
expected := 0
// Act
result := numberOfPairs(points)
// Assert
if result != expected {
t.Errorf("TestEdgeCases_EmptyArray failed. Expected: %v, Got: %v", expected, result)
}
}
func TestEdgeCases_MaxPoints_RandomPattern(t *testing.T) {
// Arrange - 50個不同的點，隨機模式
points := make([][]int, 0, 50)
usedPoints := make(map[string]bool)
// 使用固定種子確保測試可重現
rand.Seed(42)
for len(points) < 50 {
x := rand.Intn(51) // 0-50
y := rand.Intn(51) // 0-50
pointKey := fmt.Sprintf("%d,%d", x, y)
if !usedPoints[pointKey] {
usedPoints[pointKey] = true
points = append(points, []int{x, y})
}
}
// Act
result := numberOfPairs(points)
// Assert
if result < 0 {
t.Errorf("TestEdgeCases_MaxPoints_RandomPattern failed. Result should be non-negative, got: %v", result)
}
if result > 50*49 {
t.Errorf("TestEdgeCases_MaxPoints_RandomPattern failed. Result should not exceed 50*49, got: %v", result)
}
// 額外驗證：確保所有點都是不同的
distinctPoints := make(map[string]bool)
for _, point := range points {
key := fmt.Sprintf("%d,%d", point[0], point[1])
distinctPoints[key] = true
}
if len(distinctPoints) != 50 {
t.Errorf("TestEdgeCases_MaxPoints_RandomPattern failed. Expected 50 distinct points, got: %v", len(distinctPoints))
}
}

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problems/3025-find-the-number-of-ways-to-place-people-i/test/SolutionTests.cs Normal file
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// LeetCode 3025 單元測試
// 使用 xUnit 框架
using Xunit;
using System;
using System.Collections.Generic;
public class SolutionTests
{
private readonly Solution _solution;
public SolutionTests()
{
_solution = new Solution();
}
[Fact]
public void TestCase1_ExampleFromProblem()
{
// Arrange
int[][] points = new int[][] {
new int[] {6, 2},
new int[] {4, 4},
new int[] {2, 6}
};
int expected = 2;
// Act
var result = _solution.NumberOfPairs(points);
// Assert
Assert.Equal(expected, result);
}
[Fact]
public void TestCase2_TwoPoints()
{
// Arrange
int[][] points = new int[][] {
new int[] {1, 3},
new int[] {2, 1}
};
int expected = 1;
// Act
var result = _solution.NumberOfPairs(points);
// Assert
Assert.Equal(expected, result);
}
[Fact]
public void TestCase3_NoValidPairs()
{
// Arrange - 沒有有效點對的情況
int[][] points = new int[][] {
new int[] {1, 1},
new int[] {2, 2},
new int[] {3, 3}
};
int expected = 0;
// Act
var result = _solution.NumberOfPairs(points);
// Assert
Assert.Equal(expected, result);
}
[Fact]
public void TestCase4_SameXCoordinate()
{
// Arrange - x 座標相同的情況
int[][] points = new int[][] {
new int[] {3, 5},
new int[] {3, 2},
new int[] {3, 1}
};
int expected = 2;
// Act
var result = _solution.NumberOfPairs(points);
// Assert
Assert.Equal(expected, result);
}
[Fact]
public void TestCase5_SameYCoordinate()
{
// Arrange - y 座標相同的情況
int[][] points = new int[][] {
new int[] {1, 4},
new int[] {3, 4},
new int[] {5, 4}
};
int expected = 2;
// Act
var result = _solution.NumberOfPairs(points);
// Assert
Assert.Equal(expected, result);
}
[Fact]
public void TestCase6_PointsInsideRectangle()
{
// Arrange - 矩形內有其他點的情況
int[][] points = new int[][] {
new int[] {0, 4}, // A
new int[] {4, 0}, // B
new int[] {2, 2} // C (在 A-B 矩形內)
};
int expected = 2;
// Act
var result = _solution.NumberOfPairs(points);
// Assert
Assert.Equal(expected, result);
}
[Fact]
public void TestCase7_PointsOnBorder()
{
// Arrange - 點在矩形邊界上的情況
int[][] points = new int[][] {
new int[] {0, 3}, // A
new int[] {3, 0}, // B
new int[] {0, 0} // C (在矩形邊界上)
};
int expected = 2; // (A,C) 和 (C,B) 有效
// Act
var result = _solution.NumberOfPairs(points);
// Assert
Assert.Equal(expected, result);
}
[Fact]
public void TestEdgeCases_MinimumPoints()
{
// Arrange - 最少點數情況 (題目限制 n >= 2)
int[][] points = new int[][] {
new int[] {0, 1},
new int[] {1, 0}
};
int expected = 1; // (0,1) 在 (1,0) 的左上方
// Act
int result = _solution.NumberOfPairs(points);
// Assert
Assert.Equal(expected, result);
}
[Fact]
public void TestEdgeCases_IdenticalCoordinates()
{
// Arrange - 座標值相同的情況
int[][] points = new int[][] {
new int[] {2, 2},
new int[] {2, 2} // 題目保證所有點都不同，但測試邊界
};
// 這個測試案例實際上違反了題目條件 (All points[i] are distinct)
// 但可以測試程式的健壯性
int expected = 2; // 兩個相同點互相滿足左上方條件
// Act
int result = _solution.NumberOfPairs(points);
// Assert
Assert.Equal(expected, result);
}
[Fact]
public void TestEdgeCases_MaxCoordinateValues()
{
// Arrange - 最大座標值情況 (題目限制 0 <= coordinates <= 50)
int[][] points = new int[][] {
new int[] {0, 50},
new int[] {50, 0},
new int[] {25, 25}
};
int expected = 2; // (A,C) 和 (C,B) 有效
// Act
int result = _solution.NumberOfPairs(points);
// Assert
Assert.Equal(expected, result);
}
[Fact]
public void TestEdgeCases_EmptyArray()
{
// Arrange - 空陣列情況
int[][] points = new int[0][];
int expected = 0;
// Act
int result = _solution.NumberOfPairs(points);
// Assert
Assert.Equal(expected, result);
}
[Fact]
public void TestEdgeCases_MaxPoints_AllDistinct_RandomPattern() {
// Arrange - 50個不同的點，更複雜的模式
var points = new List<int[]>();
// 創建一個螺旋模式的50個不同點，確保都在 [0,50] 範圍內且互不相同
var usedPoints = new HashSet<string>();
var random = new Random(42); // 固定種子確保測試可重現
while (points.Count < 50) {
int x = random.Next(0, 51); // 0-50
int y = random.Next(0, 51); // 0-50
string pointKey = $"{x},{y}";
if (!usedPoints.Contains(pointKey)) {
usedPoints.Add(pointKey);
points.Add(new int[] { x, y });
}
}
int[][] pointsArray = points.ToArray();
// 由於是隨機分佈，很難預測確切結果，但應該是一個合理的正數
// 這個測試主要驗證程式在最大輸入時不會崩潰或超時
// Act
int result = _solution.NumberOfPairs(pointsArray);
// Assert
Assert.True(result >= 0); // 至少結果應該是非負數
Assert.True(result <= 50 * 49); // 最多不會超過所有可能的點對
}
}

22
problems/3025-find-the-number-of-ways-to-place-people-i/test/TestProject.csproj Normal file
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<Project Sdk="Microsoft.NET.Sdk">
<PropertyGroup>
<TargetFramework>net8.0</TargetFramework>
<Nullable>enable</Nullable>
<IsPackable>false</IsPackable>
</PropertyGroup>
<ItemGroup>
<PackageReference Include="Microsoft.NET.Test.Sdk" Version="17.1.0" />
<PackageReference Include="xunit" Version="2.4.1" />
<PackageReference Include="xunit.runner.visualstudio" Version="2.4.3">
<IncludeAssets>runtime; build; native; contentfiles; analyzers; buildtransitive</IncludeAssets>
<PrivateAssets>all</PrivateAssets>
</PackageReference>
</ItemGroup>
<ItemGroup>
<ProjectReference Include="../csharp/csharp.csproj" />
</ItemGroup>
</Project>

13
problems/3025-find-the-number-of-ways-to-place-people-i/test/edge_cases.md Normal file
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# 邊界情況清單
## 需要測試的邊界情況
- [x] 空輸入 (空陣列) - `TestEdgeCases_EmptyArray`
- [x] 最少元素 (n=2) - `TestEdgeCases_MinimumPoints`
- [x] 重複座標 (雖然違反題目條件) - `TestEdgeCases_IdenticalCoordinates`
- [x] 最大值/最小值 (座標範圍 [0,50]) - `TestEdgeCases_MaxCoordinateValues`
- [x] 最大資料量 (n=50) - `TestEdgeCases_MaxPoints_AllDistinct_RandomPattern`
- [x] 相同 x 座標 - `TestCase4_SameXCoordinate`
- [x] 相同 y 座標 - `TestCase5_SameYCoordinate`
- [x] 矩形內含其他點 - `TestCase6_PointsInsideRectangle`
- [x] 點在矩形邊界上 - `TestCase7_PointsOnBorder`
- [x] 無有效點對情況 - `TestCase3_NoValidPairs`

39
problems/3025-find-the-number-of-ways-to-place-people-i/test/run_tests.sh Executable file
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#!/bin/bash
echo "🧪 執行 LeetCode 題目測試"
echo "=========================="
# 執行 C# 測試
echo "📋 C# 測試結果:"
cd ../csharp
if dotnet build > /dev/null 2>&1; then
cd ../test
if dotnet test --logger "console;verbosity=minimal" 2>/dev/null; then
echo "✅ C# 測試通過"
else
echo "❌ C# 測試失敗"
fi
else
echo "❌ C# 編譯失敗"
fi
echo ""
# 執行 Go 測試
echo "📋 Go 測試結果:"
cd ../go
if go build > /dev/null 2>&1; then
# cd ../test
if go test -v > /dev/null 2>&1; then
echo "✅ Go 測試通過"
else
echo "❌ Go 測試失敗"
echo "詳細輸出:"
go test -v
fi
else
echo "❌ Go 編譯失敗"
fi
echo ""
echo "📊 測試完成！"