import random
import math
import csv
#Graphs imports
import matplotlib.pyplot as plt
import numpy as npy


def singleQueue(alpha, beta, time=480):
    """
    >>> random.seed(57)
    >>> singleQueue(10, 3, 480)
    3
    >>> random.seed(101)
    >>> singleQueue(5, 3, 480)
    6
    >>> random.seed(101)
    >>> singleQueue(5, 3)
    6
    >>> random.seed(935)
    >>> singleQueue(10, 9, 280)
    10
    >>> type(singleQueue(10, 9, 280))
    <class 'int'>
    """
    #Sets the initial variables to correct starting point.
    c = 0
    ta = 0
    ts = 0
    Q = 1
    maxQ = 0

    #Used to loop the first clause of the alogrithim until c < simTime is no.
    while c < time:
        #Asks if ta < ts to allow the code to follow the correct path.
        if ta < ts:
            #The code will go down the 'left path' updating all information and variables.
            ts = ts - ta
            c = c + ta
            Q = Q + 1
            #Used to update the max length of the queue.
            if Q >maxQ:
                maxQ = Q
            #Update a random time for the next customer arrival.
            ta = nextTime(alpha)
        else:
            #Similair to the 'if' statement, however goes down the 'right path'.
            ta = ta - ts
            c = c + ts
            Q = Q - 1
            #Update the time to be served.
            ts = nextTime(beta)
        #To fulfill the final conditions of Q = 0?
        while Q == 0:
            c = c + ta
            Q = Q + 1
            if Q > maxQ:
                maxQ = Q
            ta = nextTime(alpha)
    return maxQ



def doubleQueue(alpha, beta, time=480):
    ta = 0
    ts1 = 0
    ts2 = 0
    c = 0
    maxQ = 0
    Q = 1
    while c < time:
        if ta < ts1 and ta < ts2:
            ts = ts - ta
            ts2 = ts2 - ta
            c = c + ta
            Q = Q + 1
            if Q > maxQ:
                maxQ = Q
            ta = nextTime(alpha)
        else:
            if ts1 < ts2:
                ta = ta - ts1
                ts2 = ts2 - ts1
                c = c + ts1
                Q = Q - 1
                ts1 = nextTime(beta)
            else:
                ta = ta - ts2
                ts1 = ts1 - ts2
                c = c + ts1
                Q = Q - 1
                ts2 = nextTime(beta)
        while Q == 0:
            c = c + ta
            Q = Q + 1
            if Q > maxQ:
                maxQ = Q
            ta = nextTime(alpha)
    return maxQ

#3b:

#Plot points on a graph
#Assign graph parameters
plt.title('The relationship between the introduction of a second teller and maximum queue times')
plt.ylabel('Max Queue length')
plt.xlabel('Alpha / Beta values')
#Declare required vars
alphavars = npy.arange(1.1,10,0.1)
betavars = npy.arange(1,0,-0.1)
b = 1
plotpoints =[]

for a in alphavars:
        maxQ_value = 0
        for i in range(100):
            maxQ_value += singleQueue(a,b)
        plotpoints.append(maxQ_value / 100)
        b = b-0.1
plt.plot(alphavars,plotpoints,label ="Unaltered Queue")

for a in alphavars:
        maxQ_value = 0
        for i in range(100):
            maxQ_value += doubleQueue(a,b)
        plotpoints.append(maxQ_value / 100)
        b = b-0.1
plt.plot(alphavars,plotpoints,label ="Double Queue")