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Find Four points such that they form a square whose sides are parallel to x and y axes in Python

Suppose we have n pair of points; we have to find four points so that they can generate a square whose sides are parallel to x and y axes otherwise return "not possible" If we can find more than one square then select the one with whose area is maximum.

So, if the input is like n = 6, points = [(2, 2), (5, 5), (4, 5), (5, 4), (2, 5), (5, 2)], then the output will be 3, points are (2, 2) (5, 2) (2, 5) (5, 5)

To solve this, we will follow these steps −

  • my_map := a new map

  • for i in range 0 to n, do

    • my_map[(points[i,0], points[i,1])] = my_map.[(points[i,0], points[i,1]], 0) + 1

  • side := -1

  • x := -1

  • y := -1

  • for i in range 0 to n, do

    • my_map[points[i, 0], points[i, 1]] := my_map[points[i, 0], points[i, 1]] - 1

    • for j in range 0 to n, do

      • my_map[points[j, 0], points[j, 1]] := my_map[points[j, 0], points[j, 1]] - 1

      • if (i is not same as j and (points[i,0]-points[j,0]) is same as (points[i,1]- points[j,1])), then

        • if my_map[(points[i,0], points[j, 1])] > 0 and my_map[(points[j,0], points[i,1])] > 0, then

          • if (side < |points[i,0] - points[j,0]| or (side is same as |points[i,0] - points[j,0]| and ((points[i,0] * points[i,0] + points[i,1] * points[i,1]) < (x * x + y * y)))) −

            • x := points[i, 0]

            • y := points[i, 1]

            • side := |points[i,0] - points[j,0]|

      • my_map[points[j, 0], points[j, 1]] := my_map[points[j, 0], points[j, 1]] + 1

    • my_map[points[i, 0], points[i, 1]] := my_map[points[i, 0], points[i, 1]] + 1

  • if side is not same as -1, then

    • display side

    • display points (x,y), (x+side, y), (x,y + side), (x+side, y+side)

  • otherwise,

    • display "No such square"

Example

Let us see the following implementation to get better understanding −

def get_square_points(points,n):
   my_map = dict()
   for i in range(n):
      my_map[(points[i][0], points[i][1])] = my_map.get((points[i][0], points[i][1]), 0) + 1
   side = -1
   x = -1
   y = -1
   for i in range(n):
      my_map[(points[i][0], points[i][1])]-=1
      for j in range(n):
         my_map[(points[j][0], points[j][1])]-=1
            if (i != j and (points[i][0]-points[j][0]) == (points[i][1]-points[j][1])):
               if (my_map[(points[i][0], points[j][1])] > 0 and my_map[(points[j][0], points[i][1])] > 0):
                  if (side < abs(points[i][0] - points[j][0]) or (side == abs(points[i][0] - points[j][0]) and ((points[i][0] * points[i][0] + points[i][1] * points[i][1]) < (x * x + y * y)))):
                     x = points[i][0]
                     y = points[i][1]
                     side = abs(points[i][0] - points[j][0])
            my_map[(points[j][0], points[j][1])] += 1
         my_map[(points[i][0], points[i][1])] += 1
      if (side != -1):
         print("Side:", side)
         print("Points:", (x,y), (x+side, y), (x,y + side), (x+side, y+side))
      else:
         print("No such square")
n = 6
points=[(2, 2), (5, 5), (4, 5), (5, 4), (2, 5), (5, 2)]
get_square_points(points, n)

Input

6, [(2, 2), (5, 5), (4, 5), (5, 4), (2, 5), (5, 2)]

Output

Side: 3 Points: (2, 2) (5, 2) (2, 5) (5, 5)