# Program to count number of points that lie on a line in Python

Suppose we have a list of coordinates. Each coordinate has two values x and y, representing a point on the Cartesian plane. Now find the maximum number of points that lie on some line.

So, if the input is like coordinates = [[6, 2],[8, 3],[10, 4],[1, 1],[2, 2],[6, 6],[7, 7]], then the output will be 4, as the points are [1, 1], [2, 2], [6, 6], [7, 7]] that lies on a line.

To solve this, we will follow these steps −

• res := 0

• for i in range 0 to size of points list, do

• (x1, y1) := points[i]

• slopes := a new map

• same := 1

• for j in range i + 1 to size of points, do

• (x2, y2) := points[j]

• if x2 is same as x1, then

• slopes[inf] := 1 + (slopes[inf] if exits otherwise 0)

• otherwise when x1 is same as x2 and y1 is same as y2, then

• same := same + 1

• otherwise,

• slope :=(y2 - y1) /(x2 - x1)

• slopes[slope] := 1 + (slopes[slope] if exits otherwise 0)

• if slopes is not empty, then

• res := maximum of res and (same + maximum of list of all values of slopes)

• return res

## Example

Let us see the following implementation to get better understanding −

Live Demo

class Solution:
def solve(self, points):
res = 0
for i in range(len(points)):
x1, y1 = points[i][0], points[i][1]
slopes = {}
same = 1
for j in range(i + 1, len(points)):
x2, y2 = points[j][0], points[j][1]
if x2 == x1:
slopes[float("inf")] = slopes.get(float("inf"), 0) + 1
elif x1 == x2 and y1 == y2:
same += 1
else:
slope = (y2 - y1) / (x2 - x1)
slopes[slope] = slopes.get(slope, 0) + 1
if slopes:
res = max(res, same + max(slopes.values()))
return res
ob = Solution()
coordinates = [[6, 2],[8, 3],[10, 4],[1, 1],[2, 2],[6, 6],[7, 7]]
print(ob.solve(coordinates))

## Input

[[6, 2],[8, 3],[10, 4],[1, 1],[2, 2],[6, 6],[7, 7]]

## Output

4

Updated on: 22-Dec-2020

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