【leetcode】Max Points on a Line

Max Points on a Line

题目描述：

Given n points on a 2D plane, find the maximum number of points that lie on the same straight line.

解题思路：

1.首先由这么一个O(n^3)的方法，也就是算出每条线的方程（n^2），然后判断有多少点在每条线上（N）。这个方法肯定是可行的，只是复杂度太高
2.然后想到一个O(N)的，对每一个点，分别计算这个点和其他所有点构成的斜率，具有相同斜率最多的点所构成的直线，就是具有最多点的直线。

注意的地方：

1.重合的点
2.斜率不存在的点

 1 # Definition for a point

 2 class Point:

 3     def __init__(self, a=0, b=0):

 4         self.x = a

 5         self.y = b

 6 

 7 class Solution:

 8     # @param points, a list of Points

 9     # @return an integer

10     def calcK(self,pa, pb):

11         t = ((pb.y - pa.y) * 1.0) / (pb.x - pa.x)

12         return t

13         

14     def maxPoints(self, points):

15         l = len(points)

16         res = 0

17         if l <= 2:

18             return l 

19         for i in xrange(l):

20             same = 0

21             k = {}

22             k['inf'] = 0

23             for j in xrange(l):

24                 if points[j].x == points[i].x and points[j].y != points[i].y:

25                     k['inf'] += 1

26                 elif points[j].x == points[i].x and points[j].y == points[i].y:

27                     same +=1

28                 else:

29                     t = self.calcK(points[j],points[i])

30                     if t not in k.keys():

31                         k[t] = 1

32                     else:

33                         k[t] += 1

34             res = max(res, max(k.values())+same)

35         return res

36         

37 def main():

38     points = []

39     points.append(Point(0,0))

40     points.append(Point(1,1))

41     points.append(Point(1,-1))

42     #points.append(Point(0,0))

43     #points.append(Point(1,1))

44     #points.append(Point(0,0))

45     s = Solution()

46     print s.maxPoints(points)

47     

48     

49 if __name__ == '__main__':

50     main()

51