Leetcode #1459: Rectangles Area
In this guide, we solve Leetcode #1459 Rectangles Area in Python and focus on the core idea that makes the solution efficient.
You will see the intuition, the step-by-step method, and a clean Python implementation you can use in interviews.
Problem Statement
Table: Points +---------------+---------+ | Column Name | Type | +---------------+---------+ | id | int | | x_value | int | | y_value | int | +---------------+---------+ id is the column with unique values for this table. Each point is represented as a 2D coordinate (x_value, y_value).
Quick Facts
- Difficulty: Medium
- Premium: Yes
- Tags: Database
Intuition
The task is relational in nature, which maps cleanly to DataFrame operations in Python.
By treating tables as DataFrames, joins and group-bys become concise and readable.
Approach
Load the inputs as DataFrames and apply the appropriate merge, filter, or group-by.
Select or rename the columns to match the required output.
Steps:
- Load inputs as DataFrames.
- Apply merge/groupby/filter operations.
- Select the output columns.
Example
+---------------+---------+
| Column Name | Type |
+---------------+---------+
| id | int |
| x_value | int |
| y_value | int |
+---------------+---------+
id is the column with unique values for this table.
Each point is represented as a 2D coordinate (x_value, y_value).
Python Solution
import duckdb
import pandas as pd
def solution(points: pd.DataFrame) -> pd.DataFrame:
con = duckdb.connect()
con.register("Points", points)
return con.execute("""SELECT
p1.id AS p1,
p2.id AS p2,
ABS(p1.x_value - p2.x_value) * ABS(p1.y_value - p2.y_value) AS area
FROM
Points AS p1
JOIN Points AS p2 ON p1.id < p2.id
WHERE p1.x_value != p2.x_value AND p1.y_value != p2.y_value
ORDER BY area DESC, p1, p2;""").df()
Complexity
The time complexity is O(n log n) (typical). The space complexity is O(n).
Edge Cases and Pitfalls
Watch for boundary values, empty inputs, and duplicate values where applicable. If the problem involves ordering or constraints, confirm the invariant is preserved at every step.
Summary
This Python solution focuses on the essential structure of the problem and keeps the implementation interview-friendly while meeting the constraints.