mdlAufgabengeneratoren/aufgabengenerator_formulas_fraction_new.py

import random
import operator
import re
from math import gcd, lcm
import xml.etree.ElementTree as ET
from collections import Counter

# Define operators and their corresponding functions
ops = {
    '+': operator.add,
    '-': operator.sub,
    '*': operator.mul,
    '/': operator.truediv
}

# Konstanten
# Anzahl der zu generierenden Fragen.
NUM_QUESTIONS = 5
# Algebraische Struktur der Aufgaben
STRUCTURE = "(+)-((+)-(+))"
# Gleiche Nenner erlauben
SAME_ALLOWED = True
# Größter Zähler
MAX_NUMERATOR = 10
# Größter Nenner
MAX_DENOMINATOR = 8
# Größter erlaubter gemeinsamer Nenner
MAX_COMMON_DENOMINATOR = 100
# Dateiname für Ausgabe
FILENAME = 'formulas_new_quiz.xml'

def parse_expression(expression):
    """Parse an algebraic expression and determine the required number of numbers"""
    op_count = 0

    # Count operators in parentheses
    paren_count = 1
    max_depth = 0

    for i, char in enumerate(expression):
        # if char == '(':
        #     paren_count += 1
        # elif char == ')':
        #     paren_count -= 1
        #
        #     # Update max depth when a closed parenthesis is encountered
        #     max_depth = max(max_depth, paren_count)

        if char in ops.keys():
            op_count += 1

    return max_depth + op_count + 1

# Anzahl der benötigten Brüche
NUM_FRACTIONS = parse_expression(STRUCTURE)


# Platzhalter hinzufügen
def add_placeholders(expression):
    placeholder_counter = 0  # Zähler für die Platzhalter

    def placeholder_generator():
        nonlocal placeholder_counter
        placeholder = f'n{placeholder_counter}'
        placeholder_counter += 1
        return placeholder

    output = []  # Ausgabe als Liste zum späteren Zusammensetzen
    need_placeholder = True  # Flag, um zu tracken, ob ein Platzhalter hinzugefügt werden soll

    for char in expression:
        if char in '+-*/':  # Operator gefunden
            if need_placeholder:  # Wenn wir einen Platzhalter brauchen
                output.append(placeholder_generator())
            output.append(char)  # Fügen Sie den Operator hinzu
            need_placeholder = True  # Nach einem Operator müssen wir wieder einen Platzhalter hinzufügen
        elif char == '(':  # Eine neue Sub-Expression beginnt
            output.append(char)  # Fügen Sie die öffnende Klammer hinzu
            need_placeholder = True
        elif char == ')':  # Eine Sub-Expression endet
            if need_placeholder:  # Wenn wir einen Platzhalter brauchen
                output.append(placeholder_generator())
            output.append(char)  # Fügen Sie die schließende Klammer hinzu
            need_placeholder = False  # Nach einer schließenden Klammer erwarten wir keine Platzhalter mehr
        else:  # Bei anderen Zeichen
            if need_placeholder:  # Wenn wir einen Platzhalter brauchen
                output.append(placeholder_generator())
            output.append(char)  # Fügen Sie das Zeichen hinzu
            need_placeholder = False  # Nach einem Platzhalter sollten wir keinen weiteren setzen

    # Platzhalter am Beginn hinzufügen
    if output and not (output[0] == f'n{0}' or output[0] == '('):
        result = [placeholder_generator()] + output
    else:
        result = output
    # Platzhalter am Ende hinzufügen, wenn nötig
    if output[-1] in '+-*/':
        result = result + [placeholder_generator()]
    else:
        pass

    # Zusammensetzen des finalen Ausdrucks
    final_expression = ''.join(result).strip()
    print(final_expression)
    return final_expression


# Algebraische Struktur mit Platzhaltern
STRUCTURE_PH = add_placeholders(STRUCTURE)

def calculate(expression, numbers):
    """Calculate the result of the expression using n[0], n[1], ..."""
    # numbers = [random.randint(1, 10) for _ in range(num)]
    print(numbers)
    # Replace placeholders with actual number values
    for i, num in enumerate(numbers):
        placeholder = f'n{i}'
        expression = re.sub(rf'\{placeholder}\s*([+-/*])', rf'{num} \1', expression)
        expression = re.sub(rf'({placeholder})\s*', rf'{num}', expression)

    print(expression)
    # Evaluate the result
    return eval(expression)

def gen_calculate_string(expression :str, liststring :str):
    # Replace placeholders with actual number values
    for i in range(NUM_FRACTIONS):
        placeholder = f'n{i}'
        expression = re.sub(rf'\{placeholder}\s*([+-/*])', rf'{liststring}[{i}] \1', expression)
        expression = re.sub(rf'({placeholder})\s*', rf'{liststring}[{i}]', expression)

    print(expression)
    # Return the changed expression
    return expression

def gen_latex_calculate_string(expression :str, liststring: str):
    # Replace placeholders with actual number values
    for i in range(NUM_FRACTIONS):
        placeholder = f'n{i}'
        replacement = liststring[i]
        print(replacement)
        expression = re.sub(rf'\{placeholder}\s*([+-/*])', replacement, expression)
        expression = re.sub(rf'({placeholder})\s*', replacement, expression)

    # Klammern anpassen
    expression = re.sub(rf'\(', u'\\\\left(', expression)
    expression = re.sub(rf'\)', u'\\\\right)', expression)
    # print(expression)
    # Return the changed expression
    return expression

def create_html_table_for_fracture_input(rows: list):
    table_rows = []
    # Tabellenzeilen festlegen
    for i, row in enumerate(rows):
        if (i % 2) == 0:
            table_row = "<tr style='border-bottom: 1px solid black;'>"
        else:
            table_row = "<tr>"

        for cell in row:
            table_row += f"<td style='padding: 5px;'>{cell}</td>"

        table_row += "</tr>"
        table_rows.append(table_row)

    # Tabelle zusammenbauen
    table_html = f"<table style='border-collapse: collapse; display: inline-table;'>\n" + "\n".join(table_rows) + "</table>"

    return table_html


def create_formula_question(ex_number: int):
    numerators = []
    denominators = []
    for i in range(NUM_FRACTIONS):
        n = random.randint(1, MAX_NUMERATOR)
        d = random.randint(2, MAX_DENOMINATOR)
        numerators.append(n)
        denominators.append(d)

    # Müssen Nenner unterschiedlich sein?
    if not SAME_ALLOWED:
        # Sicherstellen, dass die Nenner unterschiedlich sind
        same_denominators = [k for k,v in Counter(denominators).items() if v>1]
        while len(same_denominators) > 1:
            new_denom = random.randint(2, MAX_DENOMINATOR)
            try:
                index = denominators.index(same_denominators[0])
                denominators[index] = new_denom
            except ValueError:
                pass
            # denominators.replace(same_denominators[0], new_denom)
            same_denominators = [k for k,v in Counter(denominators).items() if v>1]
    else:
        # keine Änderung / Ersetzung nötig
        pass
    # [DEBUG]
    print(numerators)
    print(denominators)
    # [DEBUG]

    # Hauptnenner bestimmen
    *denoms_integers, = denominators
    common_denominator = lcm(*denoms_integers)
    cd = common_denominator

    fractions = []
    for i in range(NUM_FRACTIONS):
        fraction = {"n": numerators[i], "d": denominators[i]}
        fractions.append(fraction)
    # [DEBUG]
    print(fractions)
    # [DEBUG]

    expanded_numerators = [frac["n"] * cd // frac["d"] for frac in fractions]

    expanded_fractions = []
    for i in range(NUM_FRACTIONS):
        fraction = {"n": expanded_numerators[i], "d": cd}
        expanded_fractions.append(fraction)
    # [DEBUG]
    print(expanded_fractions)
    # [DEBUG]

    result_numerator = calculate(STRUCTURE_PH, expanded_numerators)
    # [DEBUG]
    print(result_numerator)
    print(cd)
    # [DEBUG]

    gcd_result = gcd(result_numerator, cd)
    if gcd_result > 1:
        print("kürzbar")
        shortable = True
        shortened_numerator = result_numerator // gcd_result
        shortened_denominator = common_denominator // gcd_result
    else:
        shortable = False

    # Start der Aufgabe
    question = ET.Element('question', attrib={'type': 'formulas'})

    # Name der Aufgabe
    has_plus = '+' in STRUCTURE
    has_minus = '-' in STRUCTURE
    has_mult = '*' in STRUCTURE
    has_div = '/' in STRUCTURE

    if has_plus and has_minus:
        expression_type = "Addition/Subtraktion" + f" ({STRUCTURE})"
        exercise_text = "Berechne den Term"
    elif has_plus:
        expression_type = "Addition" + f" ({STRUCTURE})"
        exercise_text = "Addiere die Brüche"
    elif has_minus:
        expression_type = "Subtraktion" + f" ({STRUCTURE})"
        exercise_text = "Subtrahiere die Brüche"
    else:
        expression_type = "Rechnung" + f" ({STRUCTURE})"
        exercise_text = "Berechne den Term"
    name_elem = ET.SubElement(question, 'name')
    text_elem = ET.SubElement(name_elem, 'text')
    text_elem.text = f'{expression_type} von {NUM_FRACTIONS} ungleichnamigen Brüchen {ex_number}'

    # Allgemeiner Aufgabentext
    questiontext_elem = ET.SubElement(question, 'questiontext', attrib={'format': 'html'})
    text_elem = ET.SubElement(questiontext_elem, 'text')
    if shortable:
        text_elem.text = f"<![CDATA[ <p>{exercise_text} und kürze das Ergebnis so weit wie möglich.</p>" + "<p>{#A} </p> ]]>"
    else:
        text_elem.text = f"<![CDATA[ <p>{exercise_text}.</p>"+"<p>{#A} </p> ]]>"

    # Allgemeines Feedback
    generalfeedback_elem = ET.SubElement(question, 'generalfeedback', attrib={'format': 'html'})
    text_elem = ET.SubElement(generalfeedback_elem, 'text')
    text_elem.text = ' '

    # Grundlegende Bewertungsinformationen
    ET.SubElement(question, 'defaultgrade').text = '1.0000000'
    ET.SubElement(question, 'penalty').text = '0.3333333'
    ET.SubElement(question, 'hidden').text = '0'
    ET.SubElement(question, 'idnumber').text = ' '

    # Feedback für korrekte und inkorrekte Antworten
    correctfeedback_elem = ET.SubElement(question, 'correctfeedback', attrib={'format': 'html'})
    text_elem = ET.SubElement(correctfeedback_elem, 'text')
    text_elem.text = '''<![CDATA[ <p>Die Antwort ist richtig.</p> ]]> '''

    partiallycorrectfeedback_elem = ET.SubElement(question, 'partiallycorrectfeedback', attrib={'format': 'html'})
    text_elem = ET.SubElement(partiallycorrectfeedback_elem, 'text')
    text_elem.text = '''<![CDATA[ <p>Die Antwort ist teilweise richtig.</p> ]]> '''

    incorrectfeedback_elem = ET.SubElement(question, 'incorrectfeedback', attrib={'format': 'html'})
    text_elem = ET.SubElement(incorrectfeedback_elem, 'text')
    text_elem.text = '''<![CDATA[ <p>Die Antwort ist falsch.</p> ]]>'''

    ET.SubElement(question, 'shownumcorrect')

    varsrandom_elem = ET.SubElement(question, 'varsrandom')
    text_elem = ET.SubElement(varsrandom_elem, 'text')
    text_elem.text = f' '

    # Globale Variablen definieren
    varsglobal_elem = ET.SubElement(question, 'varsglobal')
    text_elem = ET.SubElement(varsglobal_elem, 'text')
    numerators_string = ",".join([str(n) for n in numerators])
    denominators_string = ",".join([str(d) for d in denominators])
    text_elem.text = f'n = [{numerators_string}];\n d = [{denominators_string}];'

    # Durchnummerierung der Antworten
    answernumbering_elem = ET.SubElement(question, 'answernumbering')
    text_elem = ET.SubElement(answernumbering_elem, 'text')
    text_elem.text = 'ABCD'

    # Antworten definieren
    answers_elem = ET.SubElement(question, 'answers')

    # Indizes für die Antworten
    partindex_elem = ET.SubElement(answers_elem, 'partindex')
    ET.SubElement(partindex_elem, 'text').text = '0'
    placeholder_elem = ET.SubElement(answers_elem, 'placeholder')
    ET.SubElement(placeholder_elem, 'text').text = '#A'

    # Punktzahl auf Teilaufgabe
    answermark_elem = ET.SubElement(answers_elem, 'answermark')
    if shortable:
        ET.SubElement(answermark_elem, 'text').text = '2'
    else:
        ET.SubElement(answermark_elem, 'text').text = '1'

    # Antworttyp
    answertype_elem = ET.SubElement(answers_elem, 'answertype')
    ET.SubElement(answertype_elem, 'text').text = '0'
    numbox_elem = ET.SubElement(answers_elem, 'numbox')
    ET.SubElement(numbox_elem, 'text').text = '2'


    # Berechnungsvariablen
    # common divisor
    cdtext = ""
    for i in range(NUM_FRACTIONS):
        if i == 0:
            pass
        elif i == 1:
            cdtext += f"cd{i} = lcm(d[{i}],d[{i-1}]);"
        else:
            cdtext += f"cd{i} = lcm(cd{i-1}, d[{i}]);"
    cdtext += f"cd = cd{NUM_FRACTIONS-1};"

    # expansions
    extext = "e = ["
    for i in range(NUM_FRACTIONS):
        extext += f"cd / d[{i}],"
    extext = extext[:-1]
    extext += "];"

    # expanded_numerators
    entext = "ens = ["
    for i in range(NUM_FRACTIONS):
        entext += f"n[{i}]*e[{i}],"
    entext = entext[:-1]
    entext += "];"

    # result numerator
    resnum = "resnum = " + gen_calculate_string(STRUCTURE_PH, "ens") + ";"

    # gcd of result numerator and result (common) denominator
    resgcd = "resgcd = gcd(resnum, cd);"

    # shortened result numerator
    sresnum = "sresnum = resnum / resgcd;"

    # shortened result denominator
    sresden = "sresden = cd / resgcd;"

    vars1_elem = ET.SubElement(answers_elem, 'vars1')
    if shortable:
        vars1_elem_text = f"<![CDATA[{cdtext}\n {extext}\n {entext}\n {resnum}\n {resgcd}\n {sresnum}\n {sresden}]]>"
    else:
        vars1_elem_text = f"<![CDATA[{cdtext}\n {extext}\n {entext}\n {resnum}]]>"
    ET.SubElement(vars1_elem, 'text').text = vars1_elem_text

    # Antwort
    answer_elem = ET.SubElement(answers_elem, 'answer')
    if shortable:
        answer_text = '[resnum, cd, sresnum, sresden]'
    else:
        answer_text = '[resnum, cd]'
    ET.SubElement(answer_elem, 'text').text = answer_text

    answernotunique_elem = ET.SubElement(answers_elem, 'answernotunique')
    ET.SubElement(answernotunique_elem, 'text').text = '0'

    vars2_elem = ET.SubElement(answers_elem, 'vars2')
    if shortable:
        vars2_elem_text = "<![CDATA[ ga = _0 == resnum && _1 == cd;\n gb = (_0 / _1) == (resnum / cd);\n gsa = _2 == sresnum && _3 == sresden;\n gsb = (_2 / _3) == (sresnum / sresden); ]]>"
    else:
        vars2_elem_text = "<![CDATA[ ga = _0 == resnum && _1 == cd; gb = (_0 / _1) == (resnum / cd); ]]>"
    ET.SubElement(vars2_elem, 'text').text = vars2_elem_text

    correctness_elem = ET.SubElement(answers_elem, 'correctness')
    if shortable:
        ET.SubElement(correctness_elem, 'text').text = '0.25*ga + 0.25*gb + 0.25*gsa + 0.25*gsb'
    else:
        ET.SubElement(correctness_elem, 'text').text = '0.5*ga + 0.5*gb'

    unitpenalty_elem = ET.SubElement(answers_elem, 'unitpenalty')
    ET.SubElement(unitpenalty_elem, 'text').text = '1'

    postunit_elem = ET.SubElement(answers_elem, 'postunit')
    ET.SubElement(postunit_elem, 'text').text = ' '

    ruleid_elem = ET.SubElement(answers_elem, 'ruleid')
    ET.SubElement(ruleid_elem, 'text').text = '1'

    otherrule_elem = ET.SubElement(answers_elem, 'otherrule')
    ET.SubElement(otherrule_elem, 'text').text = ' '

    # Unterfragen-Text
    subqtext_elem = ET.SubElement(answers_elem, 'subqtext', attrib={'format': 'html'})

    fractions_latex_strings = []
    for i in range(NUM_FRACTIONS):
        l_str = "\\\\frac{{"+ f"n[{i}]" +"}}{{"+ f"d[{i}]" +"}}"
        fractions_latex_strings.append(l_str)
    latex_calculation = gen_latex_calculate_string(STRUCTURE_PH, fractions_latex_strings)


    sub_q_t_begin = "<![CDATA[ <p>Berechne:</p>"
    sub_q_t_math = "<p>\\(\\Large \\displaystyle " + f"{latex_calculation}" + "=\\)</p>"
    rows_list = [
        ["Zähler:", "{_0}"],
        ["Nenner:", "{_1}"]
    ]

    sub_q_t_input = '<div style="display: inline-table"> ='
    if shortable:

        sub_q_t_input += create_html_table_for_fracture_input(rows_list)

        rows_list_s = [["Gekürzter Zähler:", "{_2}"],
                       ["Gekürzter Nenner:", "{_3}"]]
        sub_q_t_input += " = "
        sub_q_t_input += create_html_table_for_fracture_input(rows_list_s)

    else:
        sub_q_t_input += create_html_table_for_fracture_input(rows_list)
    sub_q_t_input += '</div>'
    sub_q_t_end = "]]>"

    sub_question_text = sub_q_t_begin + sub_q_t_math + sub_q_t_input + sub_q_t_end
    ET.SubElement(subqtext_elem, 'text').text = sub_question_text

    expanded_fractions_latex_strings = []
    for i in range(NUM_FRACTIONS):
        l_str = "\\\\frac{{"+ f"ens[{i}]" +"}}{{"+ f"cd" +"}}"
        expanded_fractions_latex_strings.append(l_str)
    expanded_latex_calculation = gen_latex_calculate_string(STRUCTURE_PH, expanded_fractions_latex_strings)

    # Lösungshinweis
    feedback_elem = ET.SubElement(answers_elem, 'feedback', attrib={'format': 'html'})
    if shortable:
        feedback_text = '''<![CDATA[ <h4>Lösungshinweis</h4>
                           <p>Die korrekte Lösung ist:</p>
                           <p>\\(\\displaystyle''' + f"{latex_calculation}" +" = " + f"{expanded_latex_calculation}" + ''' = \\frac{{resnum}}{{cd}} = \\frac{{sresnum}}{{sresden}} \\) </p> ]]>'''
    else:
        feedback_text = '''<![CDATA[ <h4>Lösungshinweis</h4>
                           <p>Die korrekte Lösung ist:</p>
                           <p>\\( \\displaystyle ''' + f"{latex_calculation}" +" = " + f"{expanded_latex_calculation}" + ''' = \\frac{{resnum}}{{cd}} \\) </p> ]]>'''
    ET.SubElement(feedback_elem, 'text').text = feedback_text

    # correctfeedback

    correctfeedback_elem = ET.SubElement(answers_elem, 'correctfeedback', attrib={'format': 'html'})
    correctfeedback_text = '''<![CDATA[ <p>Richtig!</p>]]>'''
    ET.SubElement(correctfeedback_elem, 'text').text = correctfeedback_text

    # partially correct feedback

    pcorrectfeedback_elem = ET.SubElement(answers_elem, 'partiallycorrectfeedback', attrib={'format': 'html'})
    pcorrectfeedback_text = '''<![CDATA[ <p>Teilweise richtig.</p>]]>'''
    ET.SubElement(pcorrectfeedback_elem, 'text').text = pcorrectfeedback_text

    # incorrect feedback
    incorrectfeedback_elem = ET.SubElement(answers_elem, 'incorrectfeedback', attrib={'format': 'html'})
    incorrectfeedback_text = '''<![CDATA[ <p>Leider nicht richtig.</p>]]>'''
    ET.SubElement(incorrectfeedback_elem, 'text').text = incorrectfeedback_text

    return question


def generate_questions(num_questions):
    """
    Generiert eine Liste von Aufgaben.

    Args:
        num_questions (int): Die Anzahl der zu generierenden Fragen.

    Returns:
        list: Eine Liste von Frage-Elementen.
    """
    questions = []
    for i in range(num_questions):
        # Hier können Sie die Funktionsdefinition für die Erzeugung einer Aufgabe hinzufügen
        questions.append(create_formula_question(i))

    return questions

def create_quiz(questions):
    """
    Erstellt das gesamte Quiz-Element.

    Args:
        questions (list): Eine Liste von Frage-Elementen.

    Returns:
        Element: Das gesamte Quiz -Element.
    """
    quiz = ET.Element('quiz')
    for q in questions:
        quiz.append(q)
    return quiz

def save_to_file(xml_element, filename):
    """
    Speichert das XML-Dokument in eine Datei.

    Args:
        xml_element (Element): Das XML-Element, zu speichern.
        filename (str): Der Name der Zieldatei.

    Returns:
        None
    """
    tree = ET.ElementTree(xml_element)
    ET.indent(tree, space="\t", level=0)
    with open(filename, 'wb') as f:
        tree.write(f, encoding='utf_8', xml_declaration=True)

    return

def replace_vars2(xml_file):
    # XML-Datei lesen
    with open(xml_file, 'r') as f:
        text = f.read()

    text = text.replace("&amp;","&")
    text = text.replace("&lt;","<")
    text = text.replace("&gt;",">")

    with open(xml_file, 'w') as f:
        f.write(text)


# Hauptprogramm
if __name__ == "__main__":

    questions = generate_questions(NUM_QUESTIONS)
    quiz = create_quiz(questions)

    save_to_file(quiz, FILENAME)
    replace_vars2(FILENAME)

    print("Moodle-XMLDatei erfolgreich erstellt.")