coding-practice/problems/3025-find-the-number-of-ways-to-place-people-i/README.md

[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
• 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

1. 暴力解法:

   • 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(?)

2. 優化解法:

   • 思路：
   • 時間複雜度：O(?)
   • 空間複雜度：O(?)

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 Rectangle Area

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總結: 這題的核心概念是...，適合練習...技巧。