import numpy as np
from numpy import arange
from mpl_toolkits.mplot3d.axes3d import Axes3D
import matplotlib.pyplot as plt
def map2(fn, A, B):
"""Map fn to corresponding elements of 2D arrays A and B."""
return[list(map(fn, Arow, Brow)) for (Arow, Brow) in zip(A, B)]
def score(A, B):
"""Compute the outcome of the race for player A, given A and B to be speeds of the cars."""
assert 10 <= A <= 100 and 10 <= B <= 100 # you can't get too slow or too fast
trackA = 100  B
trackB = 100  A
tA = trackA/A
tB = trackB/B
return tB  tA
## Graph the space of possible scores for A
speeds = arange(10, 101)
A, B = np.meshgrid(speeds, speeds)
fig = plt.figure(figsize=(10, 10))
ax = fig.add_subplot(1, 1, 1, projection='3d')
ax.set_xlabel('Speed of A')
ax.set_ylabel('Speed of B')
ax.set_zlabel('Race Score for A')
ax.plot_surface(A, B, map2(score, A, B));
fig.show()
## Maximum score for A
print("Max score for A:", max([score(A, B), A, B] for A in speeds for B in speeds))
## If player B gets to respond with a speed choice, with full knowledge of A's choice, what
## speed should A choose to maximize the score?
print("Max score for A if B responds:",
max(min([score(A, B), A, B] for B in speeds) for A in speeds))
## What if B chooses a speed first, and then A responds?
print("Max score for A if A responds:",
min(max([score(A, B), A, B] for A in speeds) for B in speeds))
