Convex Polygon Python Solution with Tests

Tested Python solution for LeetCode 469 with 12 pytest cases. Generate a practice environment with lcpy.

LeetCode 469, Medium. Topics: Geometry, Array, Math, Polygon. View on LeetCode.

Generate this problem as a practice environment: tested reference solution, 12 parametrized pytest cases, and a playground notebook:

lcpy gen -n 469   # by problem number
lcpy gen -s convex_polygon   # by problem name

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Problem

You are given an array of points on the X-Y plane points where points[i] = [x_i, y_i]. The points form a polygon when joined sequentially.

Return true if this polygon is convex and false otherwise.

You may assume the polygon formed by given points is always a simple polygon. In other words, we ensure that exactly two edges intersect at each vertex and that edges otherwise don’t intersect each other.

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Examples

Input: points = [[0,0],[0,5],[5,5],[5,0]]
Output: true

Input: points = [[0,0],[0,10],[10,10],[10,0],[5,5]]
Output: false

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Constraints

• 3 <= points.length <= 10^4
• points[i].length == 2
• -10^4 <= x_i, y_i <= 10^4
• All the given points are unique.

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Solution

Reference implementation from solution.py on GitHub, full suite in test_solution.py:

class Solution:
    # Time: O(n)
    # Space: O(1)
    def is_convex(self, points: list[list[int]]) -> bool:
        n = len(points)
        sign = 0
        for i in range(n):
            x1, y1 = points[i]
            x2, y2 = points[(i + 1) % n]
            x3, y3 = points[(i + 2) % n]
            cross = (x2 - x1) * (y3 - y2) - (y2 - y1) * (x3 - x2)
            if cross != 0:
                if sign == 0:
                    sign = 1 if cross > 0 else -1
                elif (cross > 0) != (sign > 0):
                    return False
        return True

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Complexity

Time	Space
O(n)	O(1)

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