How hard is LeetCode 963. Minimum Area Rectangle II?

LeetCode 963. Minimum Area Rectangle II is rated Medium on LeetCode.

What is the time complexity of LeetCode 963. Minimum Area Rectangle II?

The Python solution on this page runs in O(n^3).

What is the space complexity of LeetCode 963. Minimum Area Rectangle II?

The Python solution on this page uses O(n), where n is the length of the array \textit{points} auxiliary space.

What topics does LeetCode 963. Minimum Area Rectangle II cover?

LeetCode 963. Minimum Area Rectangle II is tagged Geometry, Array, Hash Table and Math on LeetCode.

Minimum Area Rectangle II — LeetCode 963 Python Solution

MediumGeometryArrayHash TableMath

Problem: #963
Pattern: Math and Number Theory
Reading time: 4 min
Source: leetcode.com

The problem

You are given an array of points in the X-Y plane points where points[i] = [xi, yi]. Return the minimum area of any rectangle formed from these points, with sides not necessarily parallel to the X and Y axes.

Example

Input: points = [[1,2],[2,1],[1,0],[0,1]]
Output: 2.00000
Explanation: The minimum area rectangle occurs at [1,2],[2,1],[1,0],[0,1], with an area of 2.

Python solution

Python

class Solution:
    def minAreaFreeRect(self, points: List[List[int]]) -> float:
        s = {(x, y) for x, y in points}
        n = len(points)
        ans = inf
        for i in range(n):
            x1, y1 = points[i]
            for j in range(n):
                if j != i:
                    x2, y2 = points[j]
                    for k in range(j + 1, n):
                        if k != i:
                            x3, y3 = points[k]
                            x4 = x2 - x1 + x3
                            y4 = y2 - y1 + y3
                            if (x4, y4) in s:
                                v21 = (x2 - x1, y2 - y1)
                                v31 = (x3 - x1, y3 - y1)
                                if v21[0] * v31[0] + v21[1] * v31[1] == 0:
                                    w = sqrt(v21[0] ** 2 + v21[1] ** 2)
                                    h = sqrt(v31[0] ** 2 + v31[1] ** 2)
                                    ans = min(ans, w * h)
        return 0 if ans == inf else ans

Complexity

Measure	Complexity
Time	O(n^3)
Space	O(n), where n is the length of the array \textit{points} auxiliary

Pattern: Math and Number Theory

Find the closed form, the invariant, or the modular identity — and skip the loop entirely. LeetCode 963. Minimum Area Rectangle II is filed here because LeetCode tags it Math and Geometry, which is the vocabulary this hub collects.

The math and number theory guide has the Python template for the pattern and the 485 LeetCode problems that use it.

Frequently asked questions

How hard is LeetCode 963. Minimum Area Rectangle II?: LeetCode 963. Minimum Area Rectangle II is rated Medium on LeetCode.
What is the time complexity of LeetCode 963. Minimum Area Rectangle II?: The Python solution on this page runs in O(n^3).
What is the space complexity of LeetCode 963. Minimum Area Rectangle II?: The Python solution on this page uses O(n), where n is the length of the array \textit{points} auxiliary space.
What topics does LeetCode 963. Minimum Area Rectangle II cover?: LeetCode 963. Minimum Area Rectangle II is tagged Geometry, Array, Hash Table and Math on LeetCode.