Find Integral Coordinates on a Straight Line in Python

Suppose, we have been provided with two points (p1, q1) and (p2, q2). We have to find out the number of integral coordinates (both the x and y values are integers) if a straight line is drawn between the two given points. The number of points is returned.

So, if the input is like p1 = 3, q1 = 3, p2 = 6, q2 = 6, then the output will be 2 If we draw the straight line, we will see that the points (5,5) and (6,6) are situated on the straight line.

To solve this, we will follow these steps −

• Define a function gcd_find() . This will take x,y
  • if y is same as 0, then
    • return x
  • return gcd_find(y, x mod y)

From the main method/function, do the following −

• return gcd_find(|p2 - p1| , |q2 - q1|) - 1

Example

Let us see the following implementation to get better understanding −

def gcd_find(x,y):
   if y == 0:
      return x
   return gcd_find(y,x % y)

def solve(p1,q1,p2,q2):
   return gcd_find(abs(p2 - p1),abs(q2 - q1)) - 1

print(solve(3,3,6,6))

Input

3,3,6,6

Output

2