Line Reflection — LeetCode 356 Python Solution

The problem

Given n points on a 2D plane, find if there is such a line parallel to the y-axis that reflects the given points symmetrically. In other words, answer whether or not if there exists a line that after reflecting all points over the given line, the original points' set is the same as the reflected ones.

Example

Input

points = [[1,1],[-1,1]]

Output

true

Explanation

We can choose the line x = 0.

Python solution

class Solution:
    def isReflected(self, points: List[List[int]]) -> bool:
        min_x, max_x = inf, -inf
        point_set = set()
        for x, y in points:
            min_x = min(min_x, x)
            max_x = max(max_x, x)
            point_set.add((x, y))
        s = min_x + max_x
        return all((s - x, y) in point_set for x, y in points)

Complexity

Pattern: Math and Number Theory

Find the closed form, the invariant, or the modular identity — and skip the loop entirely. LeetCode 356. Line Reflection is filed here because LeetCode tags it Math, 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.

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