import numpy as np
import matplotlib.pyplot as plt
%matplotlib inline

%reload_ext watermark
%watermark -v -m --iversions

def show_scatter(a):
    plt.figure(figsize=(8,8))
    plt.scatter(range(len(a)), a, s=10, c='black', marker=".")
    plt.show()

def show_bitmatrix(a):
    plt.figure(figsize=(8,8))
    plt.imshow(a, cmap='Greys',  interpolation='nearest')
    plt.xticks([])
    plt.yticks([])
    plt.show()

def seq_to_bitmatrix(s):
    # maximum number of bits used in this sequence
    maxbit = len(bin(max(s)))
    M = np.zeros((len(s),maxbit),dtype='uint8')
    for i,e in enumerate(s):
        bits = bin(e)[2:] # bin() -> 0b100, we drop 2 chars
        for j,b in enumerate(bits):
            M[i,maxbit-len(bits)+j] = int(b) # fill the matrix
    return M   

posint_a = list(range(50))

show_scatter(posint_a)
show_bitmatrix(seq_to_bitmatrix(posint_a).T)

sqint_a = [pow(n, 2) for n in range(50)]

show_scatter(sqint_a)
show_bitmatrix(seq_to_bitmatrix(sqint_a).T)

sqrtint_a = [int(np.sqrt(n)) for n in range(500)]

show_scatter(sqrtint_a[:50])
show_scatter(sqrtint_a)
show_bitmatrix(seq_to_bitmatrix(sqrtint_a[:50]).T)

_ = [int(2**n) for n in range(1000)]

show_scatter(_)

s = [int(n*(n+1)/2) for n in range(100)]

show_scatter(s)
show_bitmatrix(seq_to_bitmatrix(s).T)

def gen_primes():
    D = {}
    q = 2
    while True:
        if q not in D:
            yield q
            D[q * q] = [q]
        else:
            for p in D[q]:
                D.setdefault(p + q, []).append(p)
            del D[q]
        q += 1

f = gen_primes()
pa = [next(f) for i in range(100)]

show_scatter(pa)
show_bitmatrix(seq_to_bitmatrix(pa).T)

def fib(): 
    x, y = 0, 1 
    while 1: 
        yield x 
        x, y = y, x+y

f = fib()
fib_a = [next(f) for i in range(200)]

show_scatter(fib_a)
show_bitmatrix(seq_to_bitmatrix(fib_a))

from numpy import prod;
def C(n, k): 
    return prod([(n-j)/(j+1) for j in range(k)])

res=1
for r in range(15):
    print(*["{}".format('{:>5}'.format(int(C(r, i)))) for i in range(res)])
    res+=1

from itertools import islice

def pascal():
    row = [1]
    while True:
        yield row
        row = [i+j for i,j in zip([0]+row, row+[0])]

for r in islice(pascal(),0,11):
    print("{:^60}".format("".join(map(lambda n: "{:>5}".format(n), r))))

def C(n, k):
    if k<0 or k>n:
        return 0
    res=1
    for i in range(k):
        res=res*(n-i)//(i+1)
    return res

res=1
for r in range(11):
    print(*["{}".format('{:>5}'.format(int(C(r, i)))) for i in range(res)])
    res+=1

_ = [int(C(i, j)) for i in range(15) for j in range(15) if int(C(i, j)) != 0]
show_scatter(_)

def stern_n(n): 
    return n if n<2 else stern_n(n/2) if n%2==0 else stern_n((n - 1)/2) + stern_n((n + 1)/2)

stern_a = [int(stern_n(i)) for i in range(5000)]

show_scatter(stern_a)

from math import gcd
ra = {}
for n in range(1000):
    if n<=1:
        ra[n]=1
    elif gcd(int(ra[n-1]), n)==1:
        ra[n]= int(ra[n-1]+n+1)
    else:
        ra[n] = int(ra[n-1]/gcd(int(ra[n-1]), n))

show_scatter(list(ra.values()))

hofs = {}
for n in range(10000):
    if n<=2:
        hofs[n] = 1
    else:
        hofs[n] = hofs[n-hofs[n-1]]+hofs[n-hofs[n-2]]

show_scatter(list(hofs.values()))

hofsconw = {}
for n in range(5000):
    if n<=2:
        hofsconw[n] = 1
    else:
        hofsconw[n] = hofsconw[hofsconw[n-1]]+hofsconw[n-hofsconw[n-1]]

show_scatter(list(hofsconw.values()))

hofsconwc = {}
for n in range(1000):
    if n<=2:
        hofsconwc[n] = 1
    else:
        hofsconwc[n] = hofsconwc[hofsconwc[n-1]]+hofsconwc[n-hofsconwc[n-2]-1]

show_scatter(list(hofsconwc.values()))

def ant(n):
    steps = [(1, 0), (0, 1), (-1, 0), (0, -1)]
    black = set()
    x = y = 0
    position = [(x, y)]
    direction = 2
    for _ in range(n):
        if (x, y) in black:
            black.remove((x, y))
            direction += 1
        else:
            black.add((x, y))
            direction -= 1
        (dx, dy) = steps[direction%4]
        x += dx
        y += dy
        position.append((x, y))
    return position

lang_x, lang_y = zip(*[ant_p for ant_p in ant(15000)])

show_scatter(lang_x)

show_scatter(lang_y)

plt.figure(figsize=(8,8))
plt.scatter(lang_x, lang_y, s=1, c='black', marker="p")
plt.show()