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import numpy as np
import matplotlib.pyplot as plt
import matplotlib
%matplotlib inline
%config InlineBackend.figure_format = 'png'
matplotlib.rcParams['figure.figsize'] = (15,12)
matplotlib.rcParams['xtick.labelsize'] = 35
matplotlib.rcParams['ytick.labelsize'] = 35
matplotlib.rcParams['font.size'] = 35
matplotlib.rcParams['axes.labelsize'] = 50
matplotlib.rcParams['axes.facecolor'] = 'white'
matplotlib.rcParams['axes.edgecolor'] = 'black'
matplotlib.rcParams['axes.linewidth'] = 5
matplotlib.rcParams['lines.linewidth'] = 10.0 # line width in points
#matplotlib.rcParams['lines.color'] = 'blue' # has no affect on plot(); see axes.prop_cycle
matplotlib.rcParams['image.cmap'] = 'gray'
matplotlib.rcParams['lines.markersize'] = 8 #
One guessing game, called “squeezed”, is very common in parties. It consists of a player, the chooser, who writes down a number between 00–99. The other players then take turns guessing numbers, with a catch: if one says the chosen number, he loses and has to do something daft. If the guessed number is not the chosen one, it splits the range. The chooser then states the part which contains the chosen number. If the new region only has one number, the chooser is said to be “squeezed” and is punished. An example of gameplay would be:
Chooser writes down (secretly) his number (let’s say, 30).
Chooser: “State a number between 26 and 42.”
$\vdots$
Chooser: “State a number between 29 and 32.”
Implement this game in Python, where the computer is the chooser.
Useful: $\mathtt{random.randint()}$ and $\mathtt{input()}$.
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from random import randint
secret_num = randint(0,99)
print(secret_num)
interval = [0,99]
while 1:
guessed_num = int(input("State a number between %d and %d: " % tuple(interval)))
if guessed_num > interval[1]:
print("Number is to large, we said between %d and %d" % tuple(interval))
elif guessed_num < interval[0]:
print("Number is to small, we said between %d and %d" % tuple(interval))
elif guessed_num == secret_num:
print("Soooory, you hit the number - haha, you have to kiss your neighbor! Okay, let's say only on the cheek.")
break
elif guessed_num < secret_num:
interval[0] = guessed_num
elif guessed_num > secret_num:
interval[1] = guessed_num
if interval[0]+1 == secret_num and interval[1]-1 == secret_num:
print("Okay, you won. I'll do the silly dance for you if you provide me with legs.")
break
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numbers = [[1,2,3],[4,5,6],[7,8,9]]
words = ['if','i','could','just','go','outside','and','have','an','ice','cream']
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numbers_flattened = [item for sublist in numbers for item in sublist]
print(numbers_flattened)
numbers_odd = [n for n in numbers_flattened if n%2 != 0]
print(numbers_odd)
new_words1 = [w for w in words if 'i' not in w]
print(new_words1)
vowels = ['a','e','i','o','u']
new_words2 = [w for w in words if sum([v in w for v in vowels]) < 2]
print(new_words2)
prime = [i for i in range(2,100) if 0 not in [i%p for p in range(2,i)]]
print(prime)
Points may be given in polar $(r, \theta)$ or cartesian coordinates $(x, y)$, see Figure 1.
Figure 1. Relationship between polar and cartesian coordinates.
Write a function $\mathtt{pol2cart}$, that takes a tuple $\mathtt{(r, θ)}$ in polar coordinates and returns a tuple in cartesian coordinates.
Write the inverse function $\mathtt{cart2pol}$, such that $\mathtt{pol2cart( cart2pol( ( x,y) ) )}$ is $\mathtt{(x, y)}$ for any input $\mathtt{(x, y)}$.
such that they can in addition handle lists of tuples.
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from math import sqrt, atan, cos, sin
def pol2cart( pts ):
if isinstance( pts, tuple ):
pts=[pts];
c=[ (r*cos(th), r*sin(th)) for (r,th) in pts ];
return c if len(c)>1 else c[0]
def cart2pol( pts ):
if isinstance( pts, tuple ):
pts=[pts];
p=[ (sqrt(x**2+y**2), atan(float(y)/x)) for (x,y) in pts ];
return p if len(p)>1 else p[0]
pts=[(2,1), (3.4, 5.3)];
print("Cartesian : ",pts)
print("Polar : ",cart2pol( pts ))
print("And Back : ",pol2cart(cart2pol( pts )))
Draw $N=10000$ unifromly distributed random numbers (use np.random.uniform, for example). Plot it's histogram and check that it looks uniform.
Now draw another such sample, and sum the two. How does the histogram of the sum look like?
Continue to sum $3,4,5,..$ such samples and keep plotting the histogram. It should quickly start to look like a gaussian.
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sample_size = 10000
n_max = 100
num_hists = 5
num_repeats = np.arange(1, n_max, n_max//num_hists)
num_repeats = [1,2,5, 10, 20]
variances = []
for repeat in num_repeats:
data = np.random.uniform(size = (repeat, sample_size))
means = data.mean(axis = 0)
variances.append(means.var())
plt.hist(means, label ="n = %d"%repeat,\
normed = True, histtype = 'step', lw = 3)
plt.legend()
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import scipy.ndimage
im = scipy.ndimage.imread("images/ill.png")
plt.imshow(im)
plt.grid(0)
plt.yticks([])
plt.xticks([])
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plt.imshow(im[:80, :])
plt.grid(0)
plt.yticks([])
plt.xticks([])
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x = np.arange(-1,1, 0.01)
y = np.arange(-1,1, 0.01)
X,Y = np.meshgrid(x,y)
Z = X**2 + Y**2
Z = np.where(Z<1, 1, 0)
plt.matshow(Z)
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np.argwhere(Z).shape[0]*4/Z.size
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mos = scipy.ndimage.imread("images/mosaic_grey.png")
plt.imshow(mos)
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l = mos.shape[0]
N = mos.copy()
N[:l//2,:l//2] = mos[l//2:0:-1,l//2:0:-1]
N[l//2:,l//2:] = mos[-1:l//2-1:-1,-1:l//2-1:-1]
N[l//2:,:l//2] = mos[-1:l//2-1:-1,l//2:0:-1]
N[:l//2,l//2:] = mos[l//2:0:-1,-1:l//2-1:-1]
N = np.where(N==255,0,N)
#N[l//4:3*l//4, l//4:3*l//4] = 1-N[l//4:3*l//4, l//4:3*l//4]
plt.matshow(N)
plt.axis('off')
plt.savefig("images/mosaic_conv.png", bbox_inches = 'tight')
plt.grid(False)
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