#! /usr/bin/python
# -*- coding: utf-8 -*-

import copy as CO
import bisect as BI
import math as MA
import matplotlib.pyplot as PLT
'''
dice game
copyright 2018 Marc Dechico
this one add matplotlib for visualizing the distri
'''

class CountingValueError(ValueError):
    pass

def arangements_ie( n, l ):
    """ arrangements_ie ( n,( k1, k2, k3,...) )
    Return the number of possible arrangements of n elements
    with k1, k2,.... elements being indistinguishable.
    """
    a= MA.factorial( n )
    K=0
    for k in l:
        K += k
        if K > n:
            raise CountingValueError ("Can't have k indistinguishable objects taken from n objects if k > n")
        a= a / MA.factorial( k )
    return a
def result(result):
    print "gain\t\tresult"
    for r in result:
        pass


def storegain(trialgain,trialproba):
    #print "### trial gain:",trialgain,"|proba:",trialproba*100,"%"
    global tp
    global gains
    gains.append([trialgain,trialproba])
    tp+=trialproba
    i = BI.bisect_right(totwin,trialgain) -1
    totproba [i] += trialproba

def trial(t):
    global g_no
    global g_N
    trialproba = 0.0
    trialgain = 0.0
    for i  in range (g_no):
        k=t[i]
        if k!=0:
            p = gamewin[i][0]
            gain = gamewin[i][1]
            trialgain += gain * k
            proba=MA.pow(p,k)
            if trialproba == 0:
                trialproba= proba
            else:
               trialproba*= proba
            #print "-- outcome:",i,"|k:",k,"|p:",p,"|totgain:", gain * k
    trialproba*=arangements_ie(g_N,t)

    storegain(trialgain, trialproba)


def callback ( t):

    #print t
    #print "."
    global cpt
    cpt+=1
    trial(t)

def rec_gen ( co , t ,s ):
    '''
    N: number of experiment still  available
    co: current outcome (position in t )
    t : list of occurence number for each outcome
    '''

    for i in xrange ( 0,g_N-s+1 ):
        t[ co ] = i
        ss=s+i
        if ss == g_N :
             callback ( t )
             continue

        if  co > 0 :
            t2 = CO.copy ( t )
            rec_gen ( co-1 , t2,ss )

    del(t)
    return

def gen ( no , N ):
    '''
    no: number outcome
    N : Number of subsequent experiment (trial of N experiment)
    t : contain the number of occurence for each outcomes
    '''
    global g_no  # number of outcome
    g_no = no
    global g_N  # number of experiment
    g_N = N
    print "===", g_no,g_N
    t = [ 0 ] * no
    rec_gen ( no-1 , t,0 )

def plot1(totwin,totproba):

    PLT.title("distri")
    PLT.xlabel("win")
    PLT.ylabel("proba")

    PLT.plot(totwin,totproba)

    PLT.grid(True)
    PLT.show()






if __name__ == "__main__":

    # number of expiriment (how many time I throw the dices)
    N = 100

    #list of outcomes  (proba, gain)
    gamewin = [ [1.0/6, 200], [2.0/6, 10], [3.0/6, 0] ]

    # game expectation E(X)
    gameexpect= 0
    for g in gamewin:
        gameexpect += g[ 0 ] * g[ 1 ]
    print "Game expectation = ", gameexpect
    # game variance var(X)=E(X²)-E²(X)
    gamevar = 0
    for g in gamewin:
        gamevar +=  MA.pow( g[ 1 ], 2 ) * g[ 0 ]
    gamevar -= MA.pow( gameexpect , 2 )
    print "Game variance = ", gamevar
    print "Game Standard Error =", MA.sqrt(gamevar)

    # maxwin after N experiments
    maxwin = 200 * N

    print "Maxwin after N throws:", maxwin
    print "Expectation after  N throws:", gameexpect * N

    # to have the total gains  we get after N experiments  well distributed in
    #  the result  list [(gains,proba), .... ]
    totwin = range( 0, int(maxwin), int(maxwin/500))
    totproba = [0.0] * len( totwin )

    cpt = 0
    tp=0
    gains=[]
    gen( len(gamewin),N )
    print "cpt",cpt,"tp",tp
    result = zip( totproba, totwin )

    # verifying that the calculus are corrects:
    # total probability for all final gains = 1
    print "verify the sum of all probabilty = 1:",sum(totproba)

    # game expectation E(Xn) after N throws
    totgameexpect= 0
    for g in result:
        totgameexpect += g[ 0 ] * g[ 1 ]
    print "Game expectation after N throws= ", totgameexpect
    # game variance after N throws var(Xn)=E(Xn²)-E²(Xn)
    totgamevar = 0
    for g in result:
        totgamevar +=  MA.pow( g[ 1 ], 2 ) * g[ 0 ]
    totgamevar -= MA.pow( totgameexpect , 2 )
    print "Game variance N throws = ", totgamevar
    print "Game Standard Error N throws =", MA.sqrt(totgamevar)

    # have
    plot1(totwin,totproba)