#!/usr/bin/python
# -*- coding: utf-8 -*-
#
# Pyromaths
# Un programme en Python qui permet de créer des fiches d'exercices types de
# mathématiques niveau collège ainsi que leur corrigé en LaTeX.
# Copyright (C) 2006 -- Jérôme Ortais (jerome.ortais@pyromaths.org)
#
# This program is free software; you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation; either version 2 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program; if not, write to the Free Software
# Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
#

import random
import math

#===============================================================================
# Fractions partage
#===============================================================================


def dimensions_rectangle():
    taille_max = 8
    while True:
        (l, h) = (random.randrange(4, taille_max), random.randrange(4,
                  taille_max))
        div_t = diviseurs(l * h)
        if len(div_t) > 3:
            break
    if l < h:
        (l, h) = (h, l)
    return (l, h)


def numerateur_denominateur(l, h, cas):
    """

    @param l: largeur
    @param h: longueur
    @param cas:
        - nid: numerateur < denominateur
        - un: numerateur = denominateur
        - nsd: numerateur > denominateur
    @type cas: string
    """

    ldiv = diviseurs(l * h)
    if cas == "un":
        d = random.randrange(3, l * h)
    else:
        while True:
            d = ldiv[random.randrange(len(ldiv) - 1)]
            if d > 2:
                break
    if cas == "un":
        n = d
    elif cas == "nid":
        n = random.randrange(1, d)
    else:
        n = random.randrange(d + 1, d * 2)
    return (n, d)


def trace_rectangle(exo, cor, l, h, cas):
    exo.append("\\psgrid[gridcolor=Olive,subgriddiv=0,gridlabels=0pt]")
    cor.append("\\psgrid[gridcolor=Olive,subgriddiv=0,gridlabels=0pt]")
    exo.append("\\psframe[linewidth=1.5\\pslinewidth,linecolor=Maroon](0,0)(%s,%s)"% (l, h))
    cor.append("\\psframe[linewidth=1.5\\pslinewidth,linecolor=Maroon](0,0)(%s,%s)"% (l, h))
    if cas == "nsd":
        cor.append("\\psframe[linewidth=1.5\\pslinewidth,linecolor=Maroon](%s,0)(%s,%s)" %
                (l + 1, 2 * l + 1, h))

def trace_rectangle_quiz(quiz, l, h):
    quiz_rectangle = ("$$\\picture(%s,%s){" % (l*30+10, h*30+10))
    for i in range(h+1):
        quiz_rectangle += ("(5,%s){\\line(%s,0)}" % (i*30+5, l*30))
    for i in range(l+1):
        quiz_rectangle += ("(%s,5){\\line(0,%s)}" % (i*30+5, h*30))
    return quiz_rectangle + "}$$"

def fractions_partage_corrige(l, h, n, d):
    div_l = diviseurs(l)
    div_h = diviseurs(h)
    div_d = diviseurs(d)
    (lc, hc) = (l, h)
    if n == d:
        (lc, hc) = (l, h)
    elif div_l.count(d):
        lc = l // d
    elif div_h.count(d):
        hc = h // d
    else:
        for i in range(len(div_d) - 1):
            if div_l.count(div_d[i + 1]) and div_h.count(d // div_d[i + 1]):
                (lc, hc) = (l // div_d[i + 1], (h * div_d[i + 1]) // d)
                break
    return (lc, hc)


def trace_partage(cor, l, h, lc, hc, cas):
    if lc < l:
        cor.append("\\multips(%s,0)(%s,0){%s}{\\psline[linecolor=Maroon](0,0)(0,%s)}" %
                 (lc, lc, l // lc - 1, h))
        if cas == "nsd":
            cor.append("\\rput(%s,0){\\multips(%s,0)(%s,0){%s}{\\psline[linecolor=Maroon](0,0)(0,%s)}}" %
                     (l + 1, lc, lc, l // lc - 1, h))
    if hc < h:
        cor.append("\\multips(0,%s)(0,%s){%s}{\\psline[linecolor=Maroon](0,0)(%s,0)}" %
                 (hc, hc, h // hc - 1, l))
        if cas == "nsd":
            cor.append("\\rput(%s,0){\\multips(0,%s)(0,%s){%s}{\\psline[linecolor=Maroon](0,0)(%s,0)}}" %
                     (l + 1, hc, hc, h // hc - 1, l))


def coloriage(cor, n, d, l, h, lc, hc):
    if n == d:
        cor.append("\\psframe[fillstyle=solid](0,0)(%s,%s)" %
                 (l, h))
    else:
        (x, y, nfig) = (0, 0, 0)
        for i in range(n):
            if nfig:
                cor.append("\\rput(%s,0){\\psframe[fillstyle=solid](%s,%s)(%s,%s)}" %
                         (nfig, x, y, x + lc, y + hc))
            else:
                cor.append("\\psframe[fillstyle=solid](%s,%s)(%s,%s)" %
                         (x, y, x + lc, y + hc))
            if x + lc < l:
                x = x + lc
            elif y + hc < h:
                (x, y) = (0, y + hc)
            else:
                (x, y, nfig) = (0, 0, l + 1)


def diviseurs(n):
    l = []
    for i in range(1, int(math.sqrt(n)) + 1):
        if not n % i:
            l.append(i)
            if i != n // i:
                l.append(n // i)
    l.sort()
    return l


def FractionPartage():
    exo = ["\\exercice", '\\begin{multicols}{2}', '\\begin{enumerate}']
    cor = ["\\exercice*", '\\begin{multicols}{2}', '\\begin{enumerate}']
    quiz = [u"numerical"]
    
    lcas = ["nid", "un", "nsd", "nid", "nsd"]
    for i in range(4):
        cas = lcas.pop(random.randrange(len(lcas)))
        if cas == "nsd":
            while True:
                (l, h) = dimensions_rectangle()
                if l < 8:
                    break
        else:
            (l, h) = dimensions_rectangle()
        (n, d) = numerateur_denominateur(l, h, cas)
        (lc, hc) = fractions_partage_corrige(l, h, n, d)

        exo.append(_(u"\\item Colorer $\\frac{%s}{%s}$ de ce rectangle.\\par") %
                 (n, d))
        cor.append(_(u"\\item Colorer $\\frac{%s}{%s}$ de ce rectangle.\\par") %
                 (n, d))
        exo.append("\\psset{unit=4mm}")
        cor.append("\\psset{unit=4mm}")
        exo.append("\\begin{pspicture}(16,%s)" % h)
        cor.append("\\begin{pspicture}(16,%s)" % h)
        (lc, hc) = fractions_partage_corrige(l, h, n, d)
        coloriage(cor, n, d, l, h, lc, hc)
        trace_rectangle(exo, cor, l, h, cas)
        trace_partage(cor, l, h, lc, hc, cas)
        exo.append("\\end{pspicture}")
        cor.append("\\end{pspicture}")
        if i == 1:
            exo.append("\\columnbreak")
            cor.append("\\columnbreak")
        quiz.append([_(u'Fraction d\'un rectangle'),
                       (_(u"Répond:\n La fraction $$\\frac{%s}{%s}$$ du rectangle d'en bas, a _____ unités.\n ") % (n, d))+
                       trace_rectangle_quiz(quiz, l, h),
                       (l*h*n/d)])
        

    exo.append('\\end{enumerate}')
    exo.append('\\end{multicols}')
    cor.append('\\end{enumerate}')
    cor.append('\\end{multicols}')
    return (exo, cor, quiz)

#===============================================================================
# Fractions et abscisses
#===============================================================================


def valeurs_abscisses():
    origine = random.randrange(3, 11)
    nb_divisions = (
        6,
        8,
        9,
        10,
        12,
        14,
        15,
        16,
        18,
        20,
        )
    div = nb_divisions[random.randrange(len(nb_divisions))]
    nb_subd = diviseurs(div)
    subd = nb_subd[random.randrange(len(nb_subd) - 2) + 1]
    while subd < 3:
        subd = nb_subd[random.randrange(len(nb_subd) - 2) + 1]
    nb_grad = 58  #nb de graduations sur la demi-droite graduée
    lpts = [0 for i in range(7)]  #liste des places des points à trouver/placer sur la 1/2 droite graduée
    lpts[4] = random.randrange(1, nb_grad // div + 1) * div
    for i in range(2):
        a = random.randrange(1, nb_grad)
        while lpts.count(a):
            a = random.randrange(1, nb_grad)
        lpts[i] = a
    for i in range(2):
        a = random.randrange(1, (nb_grad * subd) // div)
        while lpts.count((a * div) // subd):
            a = random.randrange(1, (nb_grad * subd) // div)
        lpts[i + 2] = (a * div) // subd
    for i in range(2):
        a = random.randrange(1, (nb_grad * subd) // div)
        while lpts.count((a * div) // subd):
            a = random.randrange(1, (nb_grad * subd) // div)
        lpts[i + 5] = (a * div) // subd

    #npts=noms_pts(7)

    npts = ['A', 'B', 'C', 'D', 'E', 'F', 'G']
    lnum = list(range(7))  #liste des numérateurs
    lnum[0] = origine * div + lpts[0]
    lnum[1] = origine * div + lpts[1]
    lnum[2] = origine * subd + (lpts[2] * subd) // div
    lnum[3] = origine * subd + (lpts[3] * subd) // div
    lnum[4] = random.randrange(3, div)
    while diviseurs(div).count(lnum[4]):
        lnum[4] = random.randrange(3, div)
    lnum[5] = origine * div + lpts[5]
    lnum[6] = origine * div + lpts[6]
    return (origine, div, subd, lpts, npts, lnum)


def noms_pts(nb):  # renvoie nb noms de points
    (listenb, listepts) = ([], [])
    for i in range(26):
        listenb.append(i + 65)
    for i in range(nb):
        listepts.append(chr(listenb.pop(random.randrange(26 - i))))
    listepts.sort()
    return listepts


def unites_fractions(exo, cor, quiz, origine, div, subd):
    postf = _(u'ièmes')
    lch = [
        _(u'cinqu'),
        _(u'six'),
        _(u'sept'),
        _(u'huit'),
        _(u'neuv'),
        _(u'dix'),
        _(u'onz'),
        _(u'douz'),
        _(u'treiz'),
        _(u'quatorz'),
        _(u'quinz'),
        _(u'seiz'),
        _(u'dix-sept'),
        _(u'dix-huit'),
        _(u'dix-neuv'),
        _(u'vingt'),
        ]
    lfr = dict([(i + 5, lch[i] + postf) for i in range(len(lch))])
    lfr[2] = _(u'demis')
    lfr[3] = _(u'tiers')
    lfr[4] = _(u'quarts')
    exo.append(_(u'\\item 1 unité = \\ldots %s') % lfr[div])
    exo.append(_(u'\\item 1 unité = \\ldots~%s') % lfr[subd])
    exo.append(_(u'\\item %s unités = \\ldots~%s') % (origine,
             lfr[div]))
    exo.append(_(u'\\item %s unités = \\ldots~%s') % (origine,
             lfr[subd]))
    cor.append(_(u'\\item 1 unité = %s %s') % (div, lfr[div]))
    cor.append(_(u'\\item 1 unité = %s %s') % (subd, lfr[subd]))
    cor.append(_(u'\\item %s unités = %s %s') % (origine,
             origine * div, lfr[div]))
    cor.append(_(u'\\item %s unités = %s %s') % (origine,
             origine * subd, lfr[subd]))
    quiz_unites_fractions = [u'cloze']
    quiz_nom = _(u"Fractions dans la droite 1: unité à la fraction")
    quiz_exo_cor = _(u"Répond:<br/>\n")
    quiz_exo_cor += u'<table border=\"0\" cellspacing=\"0\" cellpadding=\"0\">\n'
    quiz_exo_cor += u'<tbody><tr><td>\n'
    quiz_exo_cor += (_(u"$$a)\\,$$ 1 unité sont {1:NUMERICAL:=%s} %s<br/>\n") % (div, lfr[div]))
    quiz_exo_cor += (_(u"$$b)\\,$$ 1 unité sont {1:NUMERICAL:=%s} %s\n") % (subd, lfr[subd]))
    quiz_exo_cor += u"</td><td>\n"
    quiz_exo_cor += (_(u"$$c)\\,$$ %s unités sont {1:NUMERICAL:=%s} %s<br/>\n") %
                       (origine, origine * div, lfr[div]))
    quiz_exo_cor += (_(u"$$d)\\,$$ %s unités sont {1:NUMERICAL:=%s} %s\n") %
                       (origine, origine * subd, lfr[subd]))
    quiz_exo_cor += u"</td></tr></tbody></table>"
    quiz_unites_fractions.append([quiz_nom, quiz_exo_cor, ""])
    return quiz_unites_fractions


def trace_demi_droite(exo, cor, origine, div, subd, lpts, npts, lnum):
    exo.append("\\psline[arrowscale=2,linecolor=Maroon]{->}(0,0)(18,0)")
    exo.append("\\rput(2mm,0){%")
    exo.append("\\multips(0,0)(3 mm,0){58}{\\psline[linecolor=Maroon](0,-.1)(0,.1)}")
    exo.append("\\multips(0,0)(%s mm,0){%s}{\\psline[linecolor=Maroon](0,-.2)(0,.2)}" %
             (div * 3, 58 // div + 1))
    cor.append("\\psline[arrowscale=2,linecolor=Maroon]{->}(0,0)(18,0)")
    cor.append("\\rput(2mm,0){%")
    cor.append("\\multips(0,0)(3 mm,0){58}{\\psline[linecolor=Maroon](0,-.1)(0,.1)}")
    cor.append("\\multips(0,0)(%s mm,0){%s}{\\psline[linecolor=Maroon](0,-.2)(0,.2)}" %
             (div * 3, 58 // div + 1))
    for i in range(58 // div + 1):
        exo.append("\\rput[t](%s mm,-3mm){\\centering %s}" % ((i * div) *
                 3, origine + i))
        cor.append("\\rput[t](%s mm,-3mm){\\centering %s}" % ((i * div) *
                 3, origine + i))
    for i in range(2):
        exo.append("\\rput[t](%s mm,4mm){\\centering $%s$}" % (lpts[i +
                 5] * 3 + .1, npts[i + 5]))
    for i in range(7):
        cor.append("\\rput[t](%s mm,4mm){\\centering $%s$}" % (lpts[i] *
                 3 + .1, npts[i]))
    exo.append("}")
    cor.append("}")


def ecrit_abscisses(exo, cor, origine, div, subd, lpts, lnum):
    exo.append("\\item $\\left(\\cfrac{%s}{%s}\\right)$" % (lnum[0], div))
    exo.append("\\item $\\left(\\cfrac{%s}{%s}\\right)$" % (lnum[1], div))
    exo.append("\\item $\\left(\\cfrac{%s}{%s}\\right)$" % (lnum[2], subd))
    exo.append("\\item $\\left(\\cfrac{%s}{%s}\\right)$" % (lnum[3], subd))
    exo.append("\\item $\\left(\\cfrac{%s}{%s}\\right)$" % (origine *
             lnum[4] + (lpts[4] // div) * lnum[4], lnum[4]))
    cor.append("\\item $\\left(\\cfrac{%s}{%s}\\right)$" % (lnum[0], div))
    cor.append("\\item $\\left(\\cfrac{%s}{%s}\\right)$" % (lnum[1], div))
    cor.append("\\item $\\left(\\cfrac{%s}{%s}\\right)$" % (lnum[2], subd))
    cor.append("\\item $\\left(\\cfrac{%s}{%s}\\right)$" % (lnum[3], subd))
    cor.append("\\item $\\left(\\cfrac{%s}{%s}\\right)$" % (origine *
             lnum[4] + (lpts[4] // div) * lnum[4], lnum[4]))

def ecrit_abscisses_quiz(quiz, origine, div, subd, lpts, npts, lnum):
    quiz_ecrit = [u'cloze']
    eje_abscisses = "$$\\fs2\\picture(585,100){"
    eje_abscisses += "(0,50){\line(585,0)}"   # Recta
    for i in range(58):
        eje_abscisses += "(%s,45){\\line(0,10)}" % (i*10+5) # Marcas pequeñas de la recta
    for i in range(58 // div + 1):
        eje_abscisses += "(%s,40){\\line(0,20)}" % (i*10*div+5)   # Marcas grandes de la recta
        eje_abscisses += "(%s,25){%s}" % ((i*10*div+2), origine + i)  # Número de las marcas grandes
    for i in range(5):
        eje_abscisses += "(%s,60){%s}" % ((lpts[i]*10+1), npts[i])    # Letras en la recta
    eje_abscisses += "}$$"
    quiz_nom = _(u"Fractions dans la droite 2: localisation")
    quiz_exo_cor = _(u"Compte les parties de la demi-droite d'en bas et indique que fraction est chaque lettre:<br/>\n")
    quiz_exo_cor += u'<table style=\"width: 650px;\" border=\"0\" cellspacing=\"0\" cellpadding=\"0\">\n'
    quiz_exo_cor += u'<tbody><tr><td>\n'
    quiz_order = []
    for i in range(5):
        quiz_abscisses_cor = ""
        for x in range(5):
            if x == i:
                quiz_abscisses_cor += (u"~=" + npts[x])
            else:
                quiz_abscisses_cor += (u"~" + npts[x])
        if i < 2:
            quiz_order.append(_(u"{1:MULTICHOICE:%s} est $$\\frac{%s}{%s}$$</td><td>\n") %
                                (quiz_abscisses_cor, lnum[i], div))
        elif i < 4:
            quiz_order.append(_(u"{1:MULTICHOICE:%s} est $$\\frac{%s}{%s}$$</td><td>\n") %
                                (quiz_abscisses_cor, lnum[i], subd))
        else:
            quiz_order.append(_(u"{1:MULTICHOICE:%s} est $$\\frac{%s}{%s}$$</td><td>\n") %
                                (quiz_abscisses_cor, origine * lnum[4] + (lpts[4] // div) * lnum[4], lnum[4]))
    random.shuffle(quiz_order)
    quiz_exo_cor += "".join(quiz_order) 
    quiz_exo_cor += u"</td></tr></tbody></table><br/>\n"
    quiz_exo_cor += eje_abscisses
    quiz_ecrit.append([quiz_nom, quiz_exo_cor, ""])
    return quiz_ecrit

def trouve_abscisses(exo, cor, div, subd, lnum):
    exo.append(_("\\item $F~\\left(\\cfrac{\\ldots}{%s}\\right)$)") % div)
    exo.append(_("\\item $F~\\left(\\cfrac{\\ldots}{%s}\\right)$)") % subd)
    exo.append(_("\\item $G~\\left(\\cfrac{\\ldots}{%s}\\right)$)") % div)
    exo.append(_("\\item $G~\\left(\\cfrac{\\ldots}{%s}\\right)$)") % subd)
    cor.append("\\item $F~\\left(\\cfrac{%s}{%s}\\right)$" % (lnum[5], div))
    cor.append("\\item $F~\\left(\\cfrac{%s}{%s}\\right)$" % ((lnum[5] *
             subd) // div, subd))
    cor.append("\\item $G~\\left(\\cfrac{%s}{%s}\\right)$" % (lnum[6], div))
    cor.append("\\item $G~\\left(\\cfrac{%s}{%s}\\right)$" % ((lnum[6] *
             subd) // div, subd))


def trouve_abscisses_quiz(quiz, origine, div, subd, lpts, npts, lnum):
    quiz_trouve = [u'cloze']
    eje_abscisses = "$$\\fs2\\picture(585,100){"
    eje_abscisses += "(0,50){\line(585,0)}"   # Recta
    for i in range(58):
        eje_abscisses += "(%s,45){\\line(0,10)}" % (i*10+5) # Marcas pequeñas de la recta
    for i in range(58 // div + 1):
        eje_abscisses += "(%s,40){\\line(0,20)}" % (i*10*div+5)   # Marcas grandes de la recta
        eje_abscisses += "(%s,25){%s}" % ((i*10*div+2), origine + i)  # Número de las marcas grandes
    for i in range(2):
        eje_abscisses += "(%s,60){%s}" % ((lpts[i+5]*10+1), npts[i+5])    # Letras en la recta
    eje_abscisses += "}$$"
    quiz_nom = _(u"Fractions dans la droite 3: compléter")
    quiz_exo_cor = _(u"Selon sa lettre dans la demi-droite, complète le numérateur des fractions :<br/><br/>\n")
    quiz_exo_cor += (u"$$a)\\, \\text{ Si } F = \\frac{?}{%s} \\; ? =$$ {1:NUMERICAL:=%s}"
                       % (div, lnum[5]))
    quiz_exo_cor += (u"$$\\hspace{20} b)\\, \\text{ Si } F = \\frac{?}{%s} \\; ? =$$ {1:NUMERICAL:=%s}<br/><br/>\n"
                       % (subd, (lnum[5] *subd) // div))
    quiz_exo_cor += (u"$$c)\\, \\text{ Si } G = \\frac{?}{%s} \\; ? =$$ {1:NUMERICAL:=%s}"
                       % (div, lnum[6]))
    quiz_exo_cor += (u"$$\\hspace{20} d)\\, \\text{ Si } G = \\frac{?}{%s} \\; ? =$$ {1:NUMERICAL:=%s}<br/>\n"
                       % (subd, (lnum[6] *subd) // div))
    quiz_exo_cor += eje_abscisses
    quiz_trouve.append([quiz_nom, quiz_exo_cor, ""])
    return quiz_trouve
    
        
def QuestionsAbscisses():
    exo = ["\\exercice"]
    cor = ["\\exercice*"]
    quiz = []
    (origine, div, subd, lpts, npts, lnum) = valeurs_abscisses()
    exo.append("\\begin{enumerate}")
    exo.append(_(u"\\item Compléter :"))
    exo.append("\\begin{multicols}{2}")
    exo.append("\\begin{enumerate}")
    cor.append("\\begin{enumerate}")
    cor.append(_(u"\\item Compléter :"))
    cor.append("\\begin{multicols}{2}")
    cor.append("\\begin{enumerate}")
    quiz.append(unites_fractions(exo, cor, quiz, origine, div, subd))
    exo.append("\\end{enumerate}")
    exo.append("\\end{multicols}")
    exo.append(_(u"\\item Sur la demi-droite ci-dessous, placer les points d'abscisse donnée :"))
    exo.append("\\begin{multicols}{5}")
    exo.append("\\begin{enumerate}")
    exo.append("\\renewcommand{\\theenumii}{\\Alph{enumii}}")
    exo.append("\\renewcommand{\\labelenumii}{$\\theenumii$}")
    cor.append("\\end{enumerate}")
    cor.append("\\end{multicols}")
    cor.append(_(u"\\item Sur la demi-droite ci-dessous, placer les points d'abscisse donnée :"))
    cor.append("\\begin{multicols}{5}")
    cor.append("\\begin{enumerate}")
    cor.append("\\renewcommand{\\theenumii}{\\Alph{enumii}}")
    cor.append("\\renewcommand{\\labelenumii}{$\\theenumii$}")
    ecrit_abscisses(exo, cor, origine, div, subd, lpts, lnum)
    quiz.append(ecrit_abscisses_quiz(quiz, origine, div, subd, lpts, npts, lnum))
    exo.append("\\end{enumerate}")
    exo.append("\\end{multicols}")
    exo.append(_(u"\\item Compléter les abscisses des points suivants :"))
    exo.append("\\begin{multicols}{4}")
    exo.append("\\begin{enumerate}")
    cor.append("\\end{enumerate}")
    cor.append("\\end{multicols}")
    cor.append(_(u"\\item Compléter les abscisses des points suivants :"))
    cor.append("\\begin{multicols}{4}")
    cor.append("\\begin{enumerate}")
    trouve_abscisses(exo, cor, div, subd, lnum)
    quiz.append(trouve_abscisses_quiz(quiz, origine, div, subd, lpts, npts, lnum))
    exo.append("\\end{enumerate}")
    exo.append("\\end{multicols}")
    exo.append("\\end{enumerate}")
    exo.append("\\begin{pspicture}(0,-.5)(18,.5)")
    cor.append("\\end{enumerate}")
    cor.append("\\end{multicols}")
    cor.append("\\end{enumerate}")
    cor.append("\\begin{pspicture}(0,-.5)(18,.5)")
    trace_demi_droite(exo, cor, origine, div, subd, lpts, npts, lnum)
    exo.append("\\end{pspicture}")
    cor.append("\\end{pspicture}")
    return (exo, cor, quiz)