def fun(x):
  val = x**4-14*x**3+60*x**2-70*x
  return val

# Importting required python libraries
import math
import numpy as np
from termcolor import colored

# Golden section search function 
def golden_section_search(a,b,ro):
  
    ''' The number of iterations needed to reach the given range between two values,i.e|a-b|< epsilon
         (1-ro)^N <= 0.3(final range)/2(given initial range)'''

    N=math.ceil(np.log10(0.3/2)/np.log10(0.6181))
  
    ''' We will use iteration to arrive at the required range.
      Since, for the first time we need to calculate 2 evaluation points, we will keep the first iteration 
      out of the iteration look'''
    #Iteration : 1
    a1 = a + ro*(b-a)
    b1 = a + (1-ro)*(b-a)
    f1= fun(a1)
    print("Value of function evaluation on the left of the minimum:",f1,"\t")
    f2 = fun(b1)
    print("Value of function evaluation on the right of the minimum:",f1,"\t")

    for i in range(1,N+2):
      f1= fun(a1)
      f2= fun(b1)
      if abs(a-b) <= 0.3:
        print("The final range between a & b : ",abs(b-a))
        return
      if f1 <= f2:
        print("Current values of a & b","a:",a,"b:",b,"\t")
        print("Iteration :",i,"value of function evaluation","f1: ",f1," f2: ",f2,"\t")
        b=b1
        b1=a1
        a1 = a + ro*(b-a) 
      else:
        print("Current values of a & b","a:",a,"b:",b,"\t")
        print("Iteration :",i,"value of function evaluation","f1: ",f1," f2: ",f2,"\t")
        a = a1
        a1 = b1
        b1 =  a + (1-ro)*(b-a)