85 lines
1.5 KiB
Python
85 lines
1.5 KiB
Python
# Question 1:
|
|
|
|
|
|
def tempsdevol(c):
|
|
u, n = c, 0
|
|
while u != 1:
|
|
if u % 2:
|
|
u = 3*u + 1
|
|
else:
|
|
u = u//2
|
|
n += 1
|
|
return n
|
|
|
|
# Question 2
|
|
|
|
|
|
def altitude(c):
|
|
u, umax = c, c
|
|
while u != 1:
|
|
if u % 2:
|
|
u = 3*u + 1
|
|
else:
|
|
u = u//2
|
|
if u > umax:
|
|
umax = u
|
|
return umax
|
|
|
|
# Question 3
|
|
# a)
|
|
|
|
|
|
def tempsdarret(c):
|
|
u, n, nmax = c, 0, 0
|
|
while u != 1:
|
|
n += 1
|
|
if u % 2:
|
|
u = 3*u + 1
|
|
else:
|
|
u = u//2
|
|
if u >= c:
|
|
nmax = n
|
|
return nmax
|
|
|
|
# b)
|
|
import time
|
|
|
|
|
|
def verification(m):# m=1000000 -> 60 sec
|
|
start = time.time()
|
|
for c in range(0, m+1, ):
|
|
tempsdarret(c)
|
|
return time.time() - start
|
|
|
|
# c)
|
|
|
|
# Question 4
|
|
# a)
|
|
|
|
|
|
def altitudemax(borne):
|
|
res = {"c":0, "altitude":0}
|
|
for c in range(3, borne+1, 4):
|
|
current = altitude(c)
|
|
if current > res["altitude"]:
|
|
res.update({"c":c, "altitude":current})
|
|
return res
|
|
|
|
|
|
def tempsdarretmax(borne): # {'c': 665215, 'temps': 354}
|
|
res = {"c": 0, "temps": 0}
|
|
for c in range(3, borne+1, 4):
|
|
current = tempsdarret(c)
|
|
if current > res["temps"]:
|
|
res.update({"c": c, "temps": current})
|
|
return res
|
|
|
|
def tempsdarretrecord(borne):
|
|
res = {"c": 0, "temps": 0}
|
|
L=[]
|
|
for c in range(2, borne+1):
|
|
current = tempsdarret(c)
|
|
if current > res["temps"]:
|
|
res.update({"c": c, "temps": current})
|
|
L.append({"c": c, "temps": current})
|
|
return L |