【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