def findconstant(num):
""" Find a constant c < 1 such that Fn ≤ 2^(c*n) for all n ≥ 0.
Show that your answer is correct.
Above equation can be written as - taking log on both sides
1. log(Fn) <= (c*n)log(2)
2. c >= log(Fn)/n # since log(2) is 1
Now lets find this ratio - log(Fn)/n for different values of n
and see if get our 'c'
"""
clist = []
for n in range(1, num, 1000):
fn = findfibopoly(n)
c = math.log(fn, 2) / n
clist.append(round(c, 2))
return clist
def findconstant(num):
""" Find a constant c < 1 such that Fn ≤ 2^(c*n) for all n ≥ 0.
Show that your answer is correct.
Above equation can be written as - taking log on both sides
1. log(Fn) <= (c*n)log(2)
2. c >= log(Fn)/n # since log(2) is 1
Now lets find this ratio - log(Fn)/n for different values of n
and see if get our 'c'
"""
clist = []
for n in range(1, num, 1000):
fn = findfibopoly(n)
c = math.log(fn, 2)/n
clist.append(round(c, 2))
return clist
def verifyc(c, num):
dealbreaker = []
for n in range(num + 1):
fn = findfibopoly(n)
cn = 2**(c * n)
fn = round(fn, 2)
cn = round(cn, 2)
if fn > cn:
dealbreaker.append((n, fn, cn))
# print ("%d:%0.2f" % (fn, cn))
print("Deal Breakers: ", dealbreaker)
if len(dealbreaker) == 0:
print("Q.E.D")
else:
print(":( - ERROR! Explore more!")
def verifyc(c, num):
dealbreaker = []
for n in range(num+1):
fn = findfibopoly(n)
cn = 2 ** (c * n)
fn = round(fn, 2)
cn = round(cn, 2)
if fn > cn:
dealbreaker.append((n, fn, cn))
# print ("%d:%0.2f" % (fn, cn))
print ("Deal Breakers: ", dealbreaker)
if len(dealbreaker) == 0:
print ("Q.E.D")
else:
print (":( - ERROR! Explore more!")
