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import numpy as np
def calculate_q(k):
    '''
    Use a numerical root finder to determine q from the equation
    q = exp(k*(q-1)).
    '''
    from scipy.optimize import root
    return root(lambda q: q - np.exp(k * (q - 1)), 0).x[0]
    
import matplotlib.pyplot as plt 

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import matplotlib
matplotlib.use('TkAgg')
from pylab import *
import networkx as nx
import numpy.random as rd

n = 15 #number of nodes
k = 3 # number of connections per node, to make (will increase as edges are added from each node)

def initialize():

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import matplotlib
matplotlib.use('TkAgg')
from pylab import *
import networkx as nx
import random as rd

n = 30 # number of nodes
#k = 4 # number of neighbors of each node

def initialize():

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#pull version

import matplotlib
matplotlib.use('TkAgg')
from pylab import *
import networkx as nx
import random as rd
import numpy as np

def initialize():

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import numpy as np
import random as rd
import matplotlib.pyplot as plt

class TrafficSimulation():
    
    def __init__(self, road_length, density, max_velocity, prob_slow, repetitions):
        self.road_length = road_length
        self.density = density
        self.max_velocity = max_velocity

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import numpy as np
import random as rd

class TrafficSimulation():
    
    def __init__(self, road_length, density, max_velocity, prob_slow):
        self.road_length = road_length
        self.density = density
        self.max_velocity = max_velocity
        self.prob_slow = prob_slow

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import matplotlib
matplotlib.use('TkAgg')

import pylab as PL
import random as RD
import scipy as SP
import numpy as np

RD.seed()

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# Simple CA simulator in Python
#
# *** Hosts & Pathogens ***
#
# Copyright 2008-2012 Hiroki Sayama
# sayama@binghamton.edu

# Modified to run with Python 3

import matplotlib

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#Exercise 11.3

import matplotlib
import fractions
from fractions import *
matplotlib.use('TkAgg')
from pylab import *

n = 100 # size of space: n x n
p = 0.1 # probability of initially panicky individuals

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import random
from random import randint, choice
import numpy as np
import itertools

random.seed(1)

class Passenger():
    
    def __init__(self, desired_floor = 0, current_floor = 0):