def d_fib(n):
    L = [0,1]
    if n > 1:
        i = 2
        while i <= n:
            L.append(L[-1]+L[-2])
            i += 1
    return L[n]

d_fib(10)

d_fib(100)

def fib(n):
    if n == 0 or n == 1:
        return n
    else:
        return fib(n-1) + fib(n-2)

def bulb(n):
    L = [0,1,1,2,2,3,1,2,1]
    if n > 8:
        i = 9
        while i <= n:
            L.append(min(L[i-8],L[i-6],L[i-2],L[i-1])+1)
            i += 1
    print(L)
    return L[-1]

bulb(30)

def paths(M):
    P = [[0 for columns in range(len(M[0]))] for rows in range(len(M))]
    # case where start or end is blocked
    if M[0][0] == -1 or M[-1][-1] == -1:
        return 0
    P[0][0] = 1
    # first row
    for j in range(1,len(M[0])):
        if M[0][j] == -1:
            P[0][j] = 0
        else:
            P[0][j] = P[0][j-1]
    # first column
    for i in range(1,len(M)):
        if M[i][0] == -1:
            P[i][0] = 0
        else:
            P[i][0] = P[i-1][0]
    # all other entries
    for i in range(1,len(M)):
        for j in range(1,len(M[0])):
            if M[i][j] == -1:
                P[i][j] = 0
            else:
                P[i][j] = P[i-1][j] + P[i][j-1]
    for row in P:
        print(row)
    return P[-1][-1]

maze = [[0, 0, 0, 0, 0],
        [0, 0, 0, 0, 0],
        [0, 0, 0, 0, 0],
        [0, 0, 0, 0, 0]]

paths(maze)

def largeSub(word):
    ma = 1
    M = [[1 for j in range(len(word))] for i in range(len(word))]
    for k in range(len(word)-1):
        if word[k] != word[k+1]:
            M[k][k+1] = 0
    for k in range(2,len(word)):
        for i in range(len(word)-k):
            j = k+i
            if word[i] == word[j] and M[i+1][j-1]:
                M[i][j] = 1
                ma = j-i+1
            else:
                M[i][j] = 0
    for m in M:
        print(m)
    return ma

largeSub('aabbaaccaabac')

def pizza(n):
    M = [2000]
    T = [2000]
    for i in range(n):
        M_old = M[-1]
        T_old = T[-1]
        M_new = 0.75*M_old + 0.10*T_old
        T_new = 0.15*M_old + 0.85*T_old + 50
        M.append(M_new)
        T.append(T_new)
    return M,T

pizza(0)

pizza(1)

mario, tony = pizza(15)

import matplotlib.pyplot as plt

plt.plot(mario,label="Mario's")
plt.plot(tony,label="Tony's")
plt.xlabel('Week')
plt.ylabel('Pizzas Sold')
plt.legend()
plt.show()

def eagle(n):
    j = [60]
    a = [140]
    for i in range(n):
        j_old = j[-1]
        a_old = a[-1]
        j_new = 0.05*j_old + 0.65*a_old - 52
        a_new = 0.45*j_old + 0.68*a_old + 72
        j.append(j_new)
        a.append(a_new)
    return j,a

juv, ad = eagle(25)

plt.plot(juv,label="juveniles")
plt.plot(ad,label="adults")
plt.xlabel('5 year period')
plt.ylabel('population')
plt.legend()
plt.show()

def logistic(n,r):
    x = [0.5]
    for i in range(n):
        x_old = x[-1]
        x_new = r*x_old*(1-x_old)
        x.append(x_new)
    return x

plt.scatter(range(101),logistic(100,3.8))
plt.show()

1.5, 2.3, 2.6, 3.1, 3.3, 3.5, 3.8

import numpy as np
import matplotlib.pyplot as plt

X = np.linspace(2.7,4.0,500)

def logistic(n,r):
    L = [0.35]
    for i in range(n):
        last = L[-1]
        new = r*last*(1-last)
        L.append(new)
    return np.array(L)

plt.figure(figsize=(14,10))

for x in X:
    plt.scatter([x for i in range(100)],logistic(1000,x)[-100:], alpha=0.2,s=1,c='grey')

plt.show()

import numpy as np
import matplotlib.pyplot as plt

def SIR(n):
    S = [84980]
    I = [20]
    R = [15000]
    for i in range(n):
        S_old = S[-1]
        I_old = I[-1]
        R_old = R[-1]
        S_new = S_old - 0.0000294*S_old*I_old
        I_new = I_old + 0.0000294*S_old*I_old - 0.5*I_old
        R_new = R_old + 0.5*I_old
        S.append(S_new)
        I.append(I_new)
        R.append(R_new)
    return S,I,R

s, i, r = SIR(10)

s

i

r

plt.scatter(range(len(s)),s)
plt.scatter(range(len(i)),i)
plt.scatter(range(len(r)),r)

import numpy as np

L = [1,2,3,4,5]

arr = np.array(L)

arr**2

arr.cumsum()

np.sin(arr)

m = np.array([[0,1,2],
              [0,0,0],
              [6,5,3]])

m[0,1]

m[:,2]

canvas = np.array([[0 for j in range(20)] for i in range(20)])

canvas

plt.imshow(canvas)

canvas[5,10] = 1

canvas

plt.imshow(canvas)

image.shape

plt.imshow(image)