149. Maximum Points on a Line - Explanation

class Solution:
    def maxPoints(self, points: List[List[int]]) -> int:
        n = len(points)
        if n <= 2:
            return n

        def get_slope(p1, p2):
            if p1[0] == p2[0]:
                return float("inf")
            return (p2[1] - p1[1]) / (p2[0] - p1[0])

        res = 1
        for i in range(n):
            for j in range(i + 1, n):
                slope = get_slope(points[i], points[j])
                cnt = 2
                for k in range(j + 1, n):
                    if slope == get_slope(points[i], points[k]):
                        cnt += 1
                res = max(res, cnt)

        return res

class Solution:
    def maxPoints(self, points: List[List[int]]) -> int:
        res = 1
        for i in range(len(points)):
            p1 = points[i]
            count = defaultdict(int)
            for j in range(i + 1, len(points)):
                p2 = points[j]
                if p2[0] == p1[0]:
                    slope = float("inf")
                else:
                    slope = (p2[1] - p1[1]) / (p2[0] - p1[0])
                count[slope] += 1
                res = max(res, count[slope] + 1)
        return res

class Solution:
    def maxPoints(self, points: List[List[int]]) -> int:
        if len(points) <= 2:
            return len(points)

        def gcd(a, b):
            return gcd(b, a % b) if b else a

        res = 1
        for i in range(len(points) - 1):
            count = defaultdict(int)
            for j in range(i + 1, len(points)):
                dx = points[j][0] - points[i][0]
                dy = points[j][1] - points[i][1]
                g = gcd(dx, dy)
                dx //= g
                dy //= g
                slope = (dx, dy)
                count[slope] += 1
            res = max(res, max(count.values()) + 1)
        return res