Examples for Week 5¶
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# Question 1 page 507 (Gaddis)
# The program should let the user enter the name of a Galilean moon of Jupiter, then it should display
# the moon's mean radius, surface gravity, and orbital period.
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#
# The main function:
def main():
# Initialize dictionaries.
mean_radius = {'io':1821.6, 'europa':1560.8,
'ganymede':2634.1, 'callisto':2410.3}
surface_gravity = {'io':1.796, 'europa':1.314,
'ganymede':1.428, 'callisto':1.235}
orbital_period = {'io':1.769, 'europa':3.551,
'ganymede':7.154, 'callisto':16.689}
# Get input from user:
moon = input('Enter name of Galilean moon of Jupiter: ')
# Convert to lowercase for reliable matching in dictionaries:
moon = moon.lower()
# Show error message if name does not exist.
# Otherwise, display details of specified moon.
if moon not in mean_radius:
print('\n\n'+moon.title(), 'is an invalid moon name.')
else:
print('\n\nDetails of', moon.title(), 'are:')
print('-------------------------------')
print('Mean Radius:', mean_radius[moon], 'km')
print('Surface Gravity:', surface_gravity[moon], 'm/s²')
print('Orbital Period:', orbital_period[moon], 'days')
# Call the main function.
main()
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# Question 5 page 508 (Gaddis)
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import random
# The main function:
def main():
# Initialize an empty dictionary.
number_dict = dict()
# Repeat 100 times.
for i in range(100):
# Generate a random number between 1 and 10:
random_number = random.randint(1, 10)
# Establish or increment the number in the dictionary:
if random_number not in number_dict:
number_dict[random_number] = 1
else:
number_dict[random_number] += 1
# Display the results:
print('Number\tFrequency')
print('------ ---------')
# The "sorted" function produces a sorted version of
# the list of key-value pairs from the "items" method:
for number, frequency in sorted(number_dict.items()):
print(number, frequency, sep='\t')
# Call the main function.
main()
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# Question 1 from Week 5 (Mersenne primes)
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import math
# Checks whether a given number ('number') is prime or not
# returns a Boolean variable:
# TRUE (if prime) ---- or ---- FALSE (if not prime)
def check_prime(number):
for divisor in range(2, int(number**0.5) + 1):
if number % divisor == 0:
return False
return True
#
#----------------------------------------------------------------
# Checks whether the numbers 2**i - 1 are prime
# for 1 <= i <= upper_bound:
def Mersenne_Primes(upper_bound):
listM = [] # will store the Mersenne primes
iter = 1
while iter < upper_bound:
iter += 1
Mersenne = 2**iter -1
if check_prime(Mersenne):
listM.append(Mersenne)
return listM
#
#-----------------------------------------------------------------
#
nval = 1000000 # can change this value as we wish
# (2**i - 1 < nval --> take the max. val. of i)
n = math.log(nval+1,2)+1 # this is our 'upper_bound'
primes = Mersenne_Primes(n) # our list that stores the answer
for prime in primes: # display the answer on the screen
print(prime)
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# Another solution (using SETS)
import math
# this first function checks to see if a number is a prime
# it returns a boolean variable (either False or True):
def check_prime(number):
for divisor in range(2, int(number**0.5) + 1):
if number % divisor == 0:
return False
return True
#
#------------------------------------------------------------
#
def Primes(max):
listP = [] # store primes
number = 1
while number < max:
number += 1
if check_prime(number):
listP.append(number)
return listP # this list contains primes
#
#----------------------------------------------------------------
#
n = 1000000
P = set(Primes(n))
# a list of integers 2**i - 1 <=n:
A = []
for i in range(2, int(math.log(n+1, 2))+1):
A.append(2**i-1)
# The set of Mersenne primes as the intersection of A and P:
M = P.intersection(A)
# Output as a sorted list of M:
print(sorted(list(M)))
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# Question 2 from Week 5
def Cubes(nmax):
cubed = []
for i in range(2,nmax+1):
tmp = i*i*i
cubed.append(tmp)
return cubed
#
#-----------------------------------------------------------------------
#
def Sum2(nmax):
squared = [] # initialize list
for i in range(1,nmax):
for j in range(1,i+1):
tmp = i**2 + j**2
squared.append(tmp)
return squared
#
#-------------------------------------------------------------------------
#
nmax = 1000 # you can change this to smaller values....
A = set(Cubes(nmax))
B = set(Sum2(nmax))
# take the intersection of A and B:
C = A.intersection(B)
answer = len(C)
print(answer)
# OPTIONAL: if you want to know what those numbers are....
L = []
for number in C:
tmp = round(number**(1/3))
L.append(tmp)
print(sorted(L))