Syntax error Program to sort given set of Cartesian points based on polar angles in Python

Program to sort given set of Cartesian points based on polar angles in Python

Suppose we have a set of Cartesian points in a list called points. We have to sort them based on their polar angles. The polar angles vary in range 0 and 2*PI. If some points have same polar angles, then arrange them based on the distance of that point from the origin.

So, if the input is like points = [(1,1), (1,-2),(-2,2),(5,4),(4,5),(2,3),(-3,4)],

then the output will be [(5, 4), (1, 1), (4, 5), (2, 3), (-3, 4), (-2, 2), (1, -2)]

To solve this, we will follow these steps −

  • Define a comparator function key() . This will take x
  • atan := tan-inverse of x[1]/x[0]
  • return pair (atan, x[1]^2+x[0]^2) if atan >= 0 otherwise (2*pi + atan, x[0]^2+x[1]^2)
  • then sort points using comparator function key()

Example

Let us see the following implementation to get better understanding −

import math
def solve(points):
   def key(x):
      atan = math.atan2(x[1], x[0])
      return (atan, x[1]**2+x[0]**2) if atan >= 0 else (2*math.pi + atan, x[0]**2+x[1]**2)

   return sorted(points, key=key)

points = [(1,1), (1,-2),(-2,2),(5,4),(4,5),(2,3),(-3,4)]
print(solve(points))

Input

[(1,1), (1,-2),(-2,2),(5,4),(4,5),(2,3),(-3,4)]

Output

[(5, 4), (1, 1), (4, 5), (2, 3), (-3, 4), (-2, 2), (1, -2)]
Updated on: 2021-10-11T07:05:51+05:30

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