Program to find common fraction between min and max using given constraint in Python

Suppose we have two long integer values maximum and minimum. We have to find a common fraction n/d such that min

So, if the input is like minimum = 1 maximum = 10, then the output will be 22/7.

To solve this, we will follow these steps −

• P := a fraction (5706674932067741 / 1816491048114374) - 3
• a := 0, b := 1, c := 1, d := 1
• farey := an array of pairs, it has two pairs initially (a, b) and (c, d)
• Loop through the following unconditionally -
  • f := b + d
  • if f > maximum - minimum, then
    • come out from the loop
  • e := a + c
  • insert pair (e, f) at the end of farey
  • if P
  • c := e and d := f
• therwise,
  • a := e and b := f

Example

Let us see the following implementation to get better understanding −

from fractions import Fraction

def solve(minimum, maximum):
   P = Fraction(5706674932067741, 1816491048114374) - 3

   a, b, c, d = 0, 1, 1, 1
   farey = [(a,b),(c,d)]

   while True:
      f = b + d
      if f > maximum - minimum:
         break

      e = a + c
      farey.append((e, f))
      if P  maximum:
            break
         if abs(Fraction(p_min + a, minimum + b).real - P) 
Input
4, 27
Output
22/7