Introdução 1 - Python

Resolução de exercícios

Modelação Numérica 2016/17

Mestrado Integrado em Engenharia da Energia e do Ambiente
Licenciatura em Meteorologia, Oceanografia e Geofísica
Licenciatura em Engenharia Geoespacial

DEGGE-FCUL
Departamento de Engenharia Geográfica, Geofísica e Energia
Faculdade de Ciências da Universidade de Lisboa

1. Funções, NumPy e Matplotlib

a) Escreve uma função que pega num vector NumPy x e em três números reais a, b e c como argumentos e calcula:

$$ f(x) = a x^2 + b x + c $$
In [1]:
############ Módulos e definições

%matplotlib inline
from __future__ import print_function
import numpy as np
import matplotlib.pyplot as plt

plt.rcParams['figure.figsize'] = 8, 6

############ Função

def parabola(x, a, b, c):
    return a * x**2 + b*x + c

b) Faz o gráfico da função para valores arbitrários de a, b e c e para valores de x entre -3 e +3.

In [2]:
# Atenção à diferença entre 'range' e 'np.arange'. 
# O valor da amostragen na função 'range' é obrigatoriamente um número inteiro.

#x=range(-3.,3.,.1)
x=np.arange(-3.,3.,.1)

a=10.
b=2.
c=5.

y=parabola(x, a, b, c)

plt.plot(x, y, color="blue", label="Parabola")
plt.legend()
plt.ylim(0, 90)
plt.title("A minha parabola")
plt.show()

2. 99 Garrafas de cerveja

(tirado de http://www.ling.gu.se/~lager/python_exercises.html)

"99 Bottles of Beer" é uma canção tradicional dos EUA e Canadá. É típico cantá-la em viagens longas, porque é repetitiva, fácil de memorizar e pode-se cantá-la durante muito tempo. A letra da canção é a seguinte:

99 bottles of beer on the wall, 99 bottles of beer.
Take one down, pass it around, 98 bottles of beer on the wall.

O mesmo verso é repetido, cada vez com uma garrafa a menos. A canção termina quando se chega às zero garrafas.

Escreve um script Python capaz de gerar todos os versos da canção.

In [3]:
x=range(1,100)
x=x[::-1]           # inverte o vector

for i in x:
    print(str(i) + ' bottles of beer on the wall, '+ str(i) +' bottles of beer.')
    print('Take one down, pass it around, '+ str(i-1) +' bottles of beer on the wall.')

99 bottles of beer on the wall, 99 bottles of beer.
Take one down, pass it around, 98 bottles of beer on the wall.
98 bottles of beer on the wall, 98 bottles of beer.
Take one down, pass it around, 97 bottles of beer on the wall.
97 bottles of beer on the wall, 97 bottles of beer.
Take one down, pass it around, 96 bottles of beer on the wall.
96 bottles of beer on the wall, 96 bottles of beer.
Take one down, pass it around, 95 bottles of beer on the wall.
95 bottles of beer on the wall, 95 bottles of beer.
Take one down, pass it around, 94 bottles of beer on the wall.
94 bottles of beer on the wall, 94 bottles of beer.
Take one down, pass it around, 93 bottles of beer on the wall.
93 bottles of beer on the wall, 93 bottles of beer.
Take one down, pass it around, 92 bottles of beer on the wall.
92 bottles of beer on the wall, 92 bottles of beer.
Take one down, pass it around, 91 bottles of beer on the wall.
91 bottles of beer on the wall, 91 bottles of beer.
Take one down, pass it around, 90 bottles of beer on the wall.
90 bottles of beer on the wall, 90 bottles of beer.
Take one down, pass it around, 89 bottles of beer on the wall.
89 bottles of beer on the wall, 89 bottles of beer.
Take one down, pass it around, 88 bottles of beer on the wall.
88 bottles of beer on the wall, 88 bottles of beer.
Take one down, pass it around, 87 bottles of beer on the wall.
87 bottles of beer on the wall, 87 bottles of beer.
Take one down, pass it around, 86 bottles of beer on the wall.
86 bottles of beer on the wall, 86 bottles of beer.
Take one down, pass it around, 85 bottles of beer on the wall.
85 bottles of beer on the wall, 85 bottles of beer.
Take one down, pass it around, 84 bottles of beer on the wall.
84 bottles of beer on the wall, 84 bottles of beer.
Take one down, pass it around, 83 bottles of beer on the wall.
83 bottles of beer on the wall, 83 bottles of beer.
Take one down, pass it around, 82 bottles of beer on the wall.
82 bottles of beer on the wall, 82 bottles of beer.
Take one down, pass it around, 81 bottles of beer on the wall.
81 bottles of beer on the wall, 81 bottles of beer.
Take one down, pass it around, 80 bottles of beer on the wall.
80 bottles of beer on the wall, 80 bottles of beer.
Take one down, pass it around, 79 bottles of beer on the wall.
79 bottles of beer on the wall, 79 bottles of beer.
Take one down, pass it around, 78 bottles of beer on the wall.
78 bottles of beer on the wall, 78 bottles of beer.
Take one down, pass it around, 77 bottles of beer on the wall.
77 bottles of beer on the wall, 77 bottles of beer.
Take one down, pass it around, 76 bottles of beer on the wall.
76 bottles of beer on the wall, 76 bottles of beer.
Take one down, pass it around, 75 bottles of beer on the wall.
75 bottles of beer on the wall, 75 bottles of beer.
Take one down, pass it around, 74 bottles of beer on the wall.
74 bottles of beer on the wall, 74 bottles of beer.
Take one down, pass it around, 73 bottles of beer on the wall.
73 bottles of beer on the wall, 73 bottles of beer.
Take one down, pass it around, 72 bottles of beer on the wall.
72 bottles of beer on the wall, 72 bottles of beer.
Take one down, pass it around, 71 bottles of beer on the wall.
71 bottles of beer on the wall, 71 bottles of beer.
Take one down, pass it around, 70 bottles of beer on the wall.
70 bottles of beer on the wall, 70 bottles of beer.
Take one down, pass it around, 69 bottles of beer on the wall.
69 bottles of beer on the wall, 69 bottles of beer.
Take one down, pass it around, 68 bottles of beer on the wall.
68 bottles of beer on the wall, 68 bottles of beer.
Take one down, pass it around, 67 bottles of beer on the wall.
67 bottles of beer on the wall, 67 bottles of beer.
Take one down, pass it around, 66 bottles of beer on the wall.
66 bottles of beer on the wall, 66 bottles of beer.
Take one down, pass it around, 65 bottles of beer on the wall.
65 bottles of beer on the wall, 65 bottles of beer.
Take one down, pass it around, 64 bottles of beer on the wall.
64 bottles of beer on the wall, 64 bottles of beer.
Take one down, pass it around, 63 bottles of beer on the wall.
63 bottles of beer on the wall, 63 bottles of beer.
Take one down, pass it around, 62 bottles of beer on the wall.
62 bottles of beer on the wall, 62 bottles of beer.
Take one down, pass it around, 61 bottles of beer on the wall.
61 bottles of beer on the wall, 61 bottles of beer.
Take one down, pass it around, 60 bottles of beer on the wall.
60 bottles of beer on the wall, 60 bottles of beer.
Take one down, pass it around, 59 bottles of beer on the wall.
59 bottles of beer on the wall, 59 bottles of beer.
Take one down, pass it around, 58 bottles of beer on the wall.
58 bottles of beer on the wall, 58 bottles of beer.
Take one down, pass it around, 57 bottles of beer on the wall.
57 bottles of beer on the wall, 57 bottles of beer.
Take one down, pass it around, 56 bottles of beer on the wall.
56 bottles of beer on the wall, 56 bottles of beer.
Take one down, pass it around, 55 bottles of beer on the wall.
55 bottles of beer on the wall, 55 bottles of beer.
Take one down, pass it around, 54 bottles of beer on the wall.
54 bottles of beer on the wall, 54 bottles of beer.
Take one down, pass it around, 53 bottles of beer on the wall.
53 bottles of beer on the wall, 53 bottles of beer.
Take one down, pass it around, 52 bottles of beer on the wall.
52 bottles of beer on the wall, 52 bottles of beer.
Take one down, pass it around, 51 bottles of beer on the wall.
51 bottles of beer on the wall, 51 bottles of beer.
Take one down, pass it around, 50 bottles of beer on the wall.
50 bottles of beer on the wall, 50 bottles of beer.
Take one down, pass it around, 49 bottles of beer on the wall.
49 bottles of beer on the wall, 49 bottles of beer.
Take one down, pass it around, 48 bottles of beer on the wall.
48 bottles of beer on the wall, 48 bottles of beer.
Take one down, pass it around, 47 bottles of beer on the wall.
47 bottles of beer on the wall, 47 bottles of beer.
Take one down, pass it around, 46 bottles of beer on the wall.
46 bottles of beer on the wall, 46 bottles of beer.
Take one down, pass it around, 45 bottles of beer on the wall.
45 bottles of beer on the wall, 45 bottles of beer.
Take one down, pass it around, 44 bottles of beer on the wall.
44 bottles of beer on the wall, 44 bottles of beer.
Take one down, pass it around, 43 bottles of beer on the wall.
43 bottles of beer on the wall, 43 bottles of beer.
Take one down, pass it around, 42 bottles of beer on the wall.
42 bottles of beer on the wall, 42 bottles of beer.
Take one down, pass it around, 41 bottles of beer on the wall.
41 bottles of beer on the wall, 41 bottles of beer.
Take one down, pass it around, 40 bottles of beer on the wall.
40 bottles of beer on the wall, 40 bottles of beer.
Take one down, pass it around, 39 bottles of beer on the wall.
39 bottles of beer on the wall, 39 bottles of beer.
Take one down, pass it around, 38 bottles of beer on the wall.
38 bottles of beer on the wall, 38 bottles of beer.
Take one down, pass it around, 37 bottles of beer on the wall.
37 bottles of beer on the wall, 37 bottles of beer.
Take one down, pass it around, 36 bottles of beer on the wall.
36 bottles of beer on the wall, 36 bottles of beer.
Take one down, pass it around, 35 bottles of beer on the wall.
35 bottles of beer on the wall, 35 bottles of beer.
Take one down, pass it around, 34 bottles of beer on the wall.
34 bottles of beer on the wall, 34 bottles of beer.
Take one down, pass it around, 33 bottles of beer on the wall.
33 bottles of beer on the wall, 33 bottles of beer.
Take one down, pass it around, 32 bottles of beer on the wall.
32 bottles of beer on the wall, 32 bottles of beer.
Take one down, pass it around, 31 bottles of beer on the wall.
31 bottles of beer on the wall, 31 bottles of beer.
Take one down, pass it around, 30 bottles of beer on the wall.
30 bottles of beer on the wall, 30 bottles of beer.
Take one down, pass it around, 29 bottles of beer on the wall.
29 bottles of beer on the wall, 29 bottles of beer.
Take one down, pass it around, 28 bottles of beer on the wall.
28 bottles of beer on the wall, 28 bottles of beer.
Take one down, pass it around, 27 bottles of beer on the wall.
27 bottles of beer on the wall, 27 bottles of beer.
Take one down, pass it around, 26 bottles of beer on the wall.
26 bottles of beer on the wall, 26 bottles of beer.
Take one down, pass it around, 25 bottles of beer on the wall.
25 bottles of beer on the wall, 25 bottles of beer.
Take one down, pass it around, 24 bottles of beer on the wall.
24 bottles of beer on the wall, 24 bottles of beer.
Take one down, pass it around, 23 bottles of beer on the wall.
23 bottles of beer on the wall, 23 bottles of beer.
Take one down, pass it around, 22 bottles of beer on the wall.
22 bottles of beer on the wall, 22 bottles of beer.
Take one down, pass it around, 21 bottles of beer on the wall.
21 bottles of beer on the wall, 21 bottles of beer.
Take one down, pass it around, 20 bottles of beer on the wall.
20 bottles of beer on the wall, 20 bottles of beer.
Take one down, pass it around, 19 bottles of beer on the wall.
19 bottles of beer on the wall, 19 bottles of beer.
Take one down, pass it around, 18 bottles of beer on the wall.
18 bottles of beer on the wall, 18 bottles of beer.
Take one down, pass it around, 17 bottles of beer on the wall.
17 bottles of beer on the wall, 17 bottles of beer.
Take one down, pass it around, 16 bottles of beer on the wall.
16 bottles of beer on the wall, 16 bottles of beer.
Take one down, pass it around, 15 bottles of beer on the wall.
15 bottles of beer on the wall, 15 bottles of beer.
Take one down, pass it around, 14 bottles of beer on the wall.
14 bottles of beer on the wall, 14 bottles of beer.
Take one down, pass it around, 13 bottles of beer on the wall.
13 bottles of beer on the wall, 13 bottles of beer.
Take one down, pass it around, 12 bottles of beer on the wall.
12 bottles of beer on the wall, 12 bottles of beer.
Take one down, pass it around, 11 bottles of beer on the wall.
11 bottles of beer on the wall, 11 bottles of beer.
Take one down, pass it around, 10 bottles of beer on the wall.
10 bottles of beer on the wall, 10 bottles of beer.
Take one down, pass it around, 9 bottles of beer on the wall.
9 bottles of beer on the wall, 9 bottles of beer.
Take one down, pass it around, 8 bottles of beer on the wall.
8 bottles of beer on the wall, 8 bottles of beer.
Take one down, pass it around, 7 bottles of beer on the wall.
7 bottles of beer on the wall, 7 bottles of beer.
Take one down, pass it around, 6 bottles of beer on the wall.
6 bottles of beer on the wall, 6 bottles of beer.
Take one down, pass it around, 5 bottles of beer on the wall.
5 bottles of beer on the wall, 5 bottles of beer.
Take one down, pass it around, 4 bottles of beer on the wall.
4 bottles of beer on the wall, 4 bottles of beer.
Take one down, pass it around, 3 bottles of beer on the wall.
3 bottles of beer on the wall, 3 bottles of beer.
Take one down, pass it around, 2 bottles of beer on the wall.
2 bottles of beer on the wall, 2 bottles of beer.
Take one down, pass it around, 1 bottles of beer on the wall.
1 bottles of beer on the wall, 1 bottles of beer.
Take one down, pass it around, 0 bottles of beer on the wall.

3. A cifra de César

(tirado de http://www.ling.gu.se/~lager/python_exercises.html)

Em criptografia, o código de César é uma técnica de encriptação muito simples, na qual cada letra do texto é substituida por uma letra que fica um número de posições fixas mais à frente no alfabeto. Por exemplo, com um passo de 3, a letra A seria substituída por D, B por E, e assim consecutivamente. O método tem o nome de Júlio César, que o utilizou para comunicar com os seus generais.
ROT-13 ("rotação com passo de 13") é um exemplo da cifra de César em que o passo é 13. Em Python, a chave do ROT-13 pode-se representar com o seguinte dicionário:

chave = {'a':'n', 'b':'o', 'c':'p', 'd':'q', 'e':'r', 'f':'s', 'g':'t', 'h':'u', 
       'i':'v', 'j':'w', 'k':'x', 'l':'y', 'm':'z', 'n':'a', 'o':'b', 'p':'c', 
       'q':'d', 'r':'e', 's':'f', 't':'g', 'u':'h', 'v':'i', 'w':'j', 'x':'k',
       'y':'l', 'z':'m', 'A':'N', 'B':'O', 'C':'P', 'D':'Q', 'E':'R', 'F':'S', 
       'G':'T', 'H':'U', 'I':'V', 'J':'W', 'K':'X', 'L':'Y', 'M':'Z', 'N':'A', 
       'O':'B', 'P':'C', 'Q':'D', 'R':'E', 'S':'F', 'T':'G', 'U':'H', 'V':'I', 
       'W':'J', 'X':'K', 'Y':'L', 'Z':'M'}

Implementa uma descodificação do ROT-13. Quando terminares, conseguirás descodificar as seguintes mensagens secretas:

Nir Prfne!
Cbe Ghgngvf, rfgrf Ebznabf fnb ybhpbf!

Bónus: Escreve um codificador!

In [4]:
# solução 1

chave = {'a':'n', 'b':'o', 'c':'p', 'd':'q', 'e':'r', 'f':'s', 'g':'t', 'h':'u', 
       'i':'v', 'j':'w', 'k':'x', 'l':'y', 'm':'z', 'n':'a', 'o':'b', 'p':'c', 
       'q':'d', 'r':'e', 's':'f', 't':'g', 'u':'h', 'v':'i', 'w':'j', 'x':'k',
       'y':'l', 'z':'m', 'A':'N', 'B':'O', 'C':'P', 'D':'Q', 'E':'R', 'F':'S', 
       'G':'T', 'H':'U', 'I':'V', 'J':'W', 'K':'X', 'L':'Y', 'M':'Z', 'N':'A', 
       'O':'B', 'P':'C', 'Q':'D', 'R':'E', 'S':'F', 'T':'G', 'U':'H', 'V':'I', 
       'W':'J', 'X':'K', 'Y':'L', 'Z':'M', ' ':' ', ',':',', '!':'!'}

code = 'Nir Prfne!'
decode=''

for i in range(len(code)):
#    print(i)
    if code[i] == ' ':
        decode = decode +' '
    elif code[i] == ',':
        decode = decode +','
    elif code[i] == '!':
        decode = decode +'!'
    else:
        decode = decode +chave[code[i]]

print(decode)

Ave Cesar!
In [5]:
### solução 2 - nesta solução alteramos a chave, juntando-lhe os caracteres não alfabéticos

chave = {'a':'n', 'b':'o', 'c':'p', 'd':'q', 'e':'r', 'f':'s', 'g':'t', 'h':'u', 
       'i':'v', 'j':'w', 'k':'x', 'l':'y', 'm':'z', 'n':'a', 'o':'b', 'p':'c', 
       'q':'d', 'r':'e', 's':'f', 't':'g', 'u':'h', 'v':'i', 'w':'j', 'x':'k',
       'y':'l', 'z':'m', 'A':'N', 'B':'O', 'C':'P', 'D':'Q', 'E':'R', 'F':'S', 
       'G':'T', 'H':'U', 'I':'V', 'J':'W', 'K':'X', 'L':'Y', 'M':'Z', 'N':'A', 
       'O':'B', 'P':'C', 'Q':'D', 'R':'E', 'S':'F', 'T':'G', 'U':'H', 'V':'I', 
       'W':'J', 'X':'K', 'Y':'L', 'Z':'M', ' ':' ', ',':',', '!':'!'}

code = 'Cbe Ghgngvf, rfgrf Ebznabf fnb ybhpbf!'
decode=''

for i in range(len(code)):
	decode = decode + chave[code[i]]

print(decode)

Por Tutatis, estes Romanos sao loucos!