[数据结构与算法]Leetcode 149. Max Points on a Line

Problem

Given an array of points where points[i] = [xi, yi] represents a point on the X-Y plane, return the maximum number of points that lie on the same straight line.

Constraints:

• $1$ <= points.length <= $300$
• points[i].length == $2$
• $?10^4$ <= xi, yi <= $10^4$
• All the points are unique.

Algorithm

Enumerates the point and slope defining the straight line and determines if the point is on the straight line.

Code

class Solution:
    def maxPoints(self, points: List[List[int]]) -> int:
        sLen = len(points)
        if sLen <= 2:
            return sLen 
        
        def gcd(a, b):
            if not b:
                return a
            return gcd(b, a % b)
        
        slope = {}
        ans = 0
        for i in range(sLen):
            for j in range(i):
                kx = points[i][0] - points[j][0]
                ky = points[i][1] - points[j][1]
                if kx and ky:
                    kr = gcd(kx, ky)
                    kx = kx // kr
                    ky = ky // kr
                elif not kx:
                    ky = 1
                else:
                    kx = 1
                index = str(points[i][0]) + "," + str(points[i][1]) + "," + str(kx) + "," + str(ky) 
                val = slope.get(index, 1)
                if ans < val + 1:
                    ans = val + 1
                slope.update({index:val+1})
                
        return ans

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