ChimeClicker

chimeclicker.py

# coding: utf-8

# In[107]:

import numpy as np
import matplotlib.pyplot as plt
get_ipython().magic('matplotlib inline')


# In[108]:

n_max = 10**1
cost_0 = 100


# In[109]:

def cost_from_level(level, cost_0, previous = None):
    if level == 0:
        return cost_0
    if previous:
        return previous + 0.1 * cost_0 * level
    return cost_from_level(level-1, cost_0) + 0.1 * cost_0 * level
    
def cost_stable(level, cost_0):
    return cost_0 * (1 + 0.05 * level*(level-1))


# In[110]:

levels = np.linspace(1, n_max, n_max, dtype = 'i')
c1 = [cost_from_level(0, cost_0, 0)]
for i in range(1, n_max):
    c1.append(cost_from_level(i, cost_0, c1[-1]))
c2 = [cost_stable(i, cost_0) for i in levels]
diff = [c2[i-1] - c1[i-1] for i in levels]

plt.figure(figsize=(16,6))

plt.plot(levels, c1, "b-")
plt.plot(levels, c2, "r*")
plt.plot(levels, diff, "r-")

plt.show()

print(max(diff))


# In[111]:

def cum_cost_stable(level_to, level_from, cost_0):
    n = level_from
    m = level_to
    return cost_0 * (m - n + 1 + 1/60 * (m*(m+1)*(m+2) - n*n*n + n))


# In[112]:

levels = np.linspace(1, n_max, n_max, dtype = 'i')
cc1 = [cost_0]
for i in range(1, n_max):
    cc1.append(cc1[-1] + c1[i])

cc2 = [cum_cost_stable(i, 0, cost_0) for i in range(n_max)]
diff = [i - j for (i,j) in zip(cc1,cc2)]

plt.figure(figsize=(16,6))

plt.plot(levels, cc1, "b-")
plt.plot(levels, cc2, "r*")
plt.plot(levels, diff, "r-")

plt.show()

print(max(diff))


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