How hard is LeetCode 593. Valid Square?

LeetCode 593. Valid Square is rated Medium on LeetCode.

What topics does LeetCode 593. Valid Square cover?

LeetCode 593. Valid Square is tagged Geometry and Math on LeetCode.

Valid Square — LeetCode 593 Python Solution

MediumGeometryMath

Problem: #593
Pattern: Math and Number Theory
Reading time: 4 min
Source: leetcode.com

The problem

Given the coordinates of four points in 2D space p1, p2, p3 and p4, return true if the four points construct a square. The coordinate of a point pi is represented as [xi, yi].

Example

Input: p1 = [0,0], p2 = [1,1], p3 = [1,0], p4 = [0,1]
Output: true

Python solution

Python

class Solution:
    def validSquare(
        self, p1: List[int], p2: List[int], p3: List[int], p4: List[int]
    ) -> bool:
        def check(a, b, c):
            (x1, y1), (x2, y2), (x3, y3) = a, b, c
            d1 = (x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2)
            d2 = (x1 - x3) * (x1 - x3) + (y1 - y3) * (y1 - y3)
            d3 = (x2 - x3) * (x2 - x3) + (y2 - y3) * (y2 - y3)
            return any(
                [
                    d1 == d2 and d1 + d2 == d3 and d1,
                    d2 == d3 and d2 + d3 == d1 and d2,
                    d1 == d3 and d1 + d3 == d2 and d1,
                ]
            )

        return (
            check(p1, p2, p3)
            and check(p2, p3, p4)
            and check(p1, p3, p4)
            and check(p1, p2, p4)
        )

Complexity

Measure	Complexity
Time	O(n) or O(1)
Space	O(1) auxiliary

Pattern: Math and Number Theory

Find the closed form, the invariant, or the modular identity — and skip the loop entirely. LeetCode 593. Valid Square is filed here on both counts: the reference solution below belongs to the algorithm family this hub collects, and LeetCode tags it Math and Geometry.

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 593. Valid Square?: LeetCode 593. Valid Square is rated Medium on LeetCode.
What topics does LeetCode 593. Valid Square cover?: LeetCode 593. Valid Square is tagged Geometry and Math on LeetCode.