hs-course/lesson-01/main.py

from auditorium import Show
import math
from auditorium.show import Context
from markdown.core import markdown
import numpy as np
import matplotlib.pyplot as plt

show = Show('My Show')


@show.slide
def presentation(ctx):
    """
    Welcome to Mathematical Foundation of Algorithms

    Marcelo Fornet

    * Email: [mfornet94@gmail.com](mailto:mfornet94@gmail.com)
    * Telegram: [@mnaeraxr](https://t.me/mnaeraxr)
    """


@show.slide
def score_system(ctx):
    """
    # Score
    - Maximum score: 180 points
    - Maximum points to accumulate: 200
    - Final Grade: $\\frac{min(P, 180)}{180} \cdot 100$
    """


@show.slide
def number_representation(ctx: Context):
    """
    # Decimal system
    """

    with ctx.fragment(ctx):
        ctx.markdown("How do we represent number in base 10?")

    with ctx.fragment(ctx):
        ctx.markdown(
            "$$2021 = 2 \cdot 10^3 + 0 \cdot 10^2 + 2 \cdot 10^1 + 1 \cdot 10^0$$")


def int_to_base(number, base):
    assert base <= 36
    digits = []
    while number > 0:
        dig = number % base

        if base > 10:
            dig = str(dig) if dig < 10 else chr(97 + dig - 10)

        digits.append(dig)
        number //= base

    if len(digits) == 0:
        digits.append(0)
    return list(reversed(digits))


@number_representation.slide
def dynamic_base_10(ctx: Context):
    """
    # Decimal system
    """

    number = ctx.text_input("2021")
    try:
        number = int(number)
        assert number >= 0

        digits = int_to_base(number, 10)

        n = len(digits)

        # Uncomment if fix latex issue
        # output = ' + '.join(f"{d} \cdot 10^{n-p-1}" for (p, d)
        #                     in enumerate(reversed(digits)) if d > 0)
        # output = f'$${output}$$'

        output = ' + '.join(f"{d} * {10**(n-p-1)}" for (p, d)
                            in enumerate(digits) if d > 0)

        if output == '':
            output = '0'
    except Exception as e:
        output = f"{number} is not a valid number"
    ctx.markdown(output)


@number_representation.slide
def number_representation_poll_1(ctx: Context):
    """
    # Decimal system
    """

    ctx.markdown("Can we represent all integer numbers using decimal system?")

    with ctx.fragment(ctx):
        with ctx.columns(2) as cl:
            with ctx.fragment('highlight-green'):
                ctx.markdown('Yes')
            cl.tab()
            ctx.markdown('No')


@number_representation.slide
def number_representation_poll_2(ctx: Context):
    """
    # Decimal system
    """
    ctx.markdown("Can we represent every number in a unique way?")
    with ctx.fragment(ctx):
        with ctx.columns(2) as cl:
            with ctx.fragment('highlight-green'):
                ctx.markdown('Yes')
            cl.tab()
            ctx.markdown('No')


@ show.slide
def number_to_list_of_digits(ctx):
    """
    # Practice exercise

    1. Convert a python integer to its decimal representation.

    https://ideone.com/Ekmuzk
    """


@ show.slide
def list_of_digits_to_number(ctx):
    """
    # Practice exercise

    2. Convert a number in decimal representation to python integer.

    https://ideone.com/CkX1rd
    """


@ show.slide
def what_is_base2(ctx):
    """
    # Base 2
    """

    number = ctx.text_input("5")
    try:
        number = int(number)
        assert number >= 0

        digits = int_to_base(number, 2)

        n = len(digits)

        # Uncomment if fix latex issue
        # output = ' + '.join(f"{d} \cdot 10^{n-p-1}" for (p, d)
        #                     in enumerate(reversed(digits)) if d > 0)
        # output = f'$${output}$$'

        output_2 = ' + '.join(f"{2**(n-p-1)}" for (p, d)
                              in enumerate(digits) if d > 0)

        if output_2 == '':
            output_2 = '0'

        output_1 = bin(number)
    except Exception as e:
        output_1 = f"{number} is not a valid number"
        output_2 = ""

    ctx.markdown(output_1)
    ctx.markdown(output_2)


@show.slide
def what_is_base_b(ctx):
    """
    # Base b

    $$v = \sum_i d_i \cdot b^i$$
    """


@what_is_base_b.slide
def what_is_base_b_2(ctx):
    """
    # Base b
    """
    number = 3**10
    base = ctx.text_input("10")
    try:
        base = int(base)
        assert 2 <= base <= 36
        digits = int_to_base(number, base)
        output = ''.join(str(x) for x in digits)
    except Exception as e:
        print(e)
        output = str(e)
    ctx.markdown(str(number))
    ctx.markdown(output)


@ show.slide
def fibonacci_base(ctx: Context):
    """
    # Fibonacci base
    """


@fibonacci_base.slide
def fibonacci_sequence(ctx: Context):
    """
    # Fibonacci sequence
    """
    with ctx.fragment(ctx):
        ctx.markdown("$$F_1 = 1$$")
        ctx.markdown("$$F_2 = 2$$")
        ctx.markdown("$$F_n = F_{n-1} + F_{n-2}$$")

    L = [1, 2]

    while len(L) < 10:
        L.append(L[-1] + L[-2])

    with ctx.fragment(ctx):
        ctx.markdown(', '.join(map(str, L)))


@ fibonacci_base.slide
def fibonacci_base_description(ctx: Context):
    """
    # Fibonacci base

    $$v = \sum_{1 <= i} d_i \cdot F_i $$

    $$d_i \in (0, 1)$$
    """


@ fibonacci_base.slide
def fibonacci_base_example(ctx: Context):
    """
    # Fibonacci base
    """
    value = str(ctx.text_input("1100101"))
    n = len(value)
    L = [1, 2]
    while len(L) < n:
        L.append(L[-1] + L[-2])

    output_number = 0
    output_sum = ""

    R = []

    for i, d in enumerate(value):
        if d == '1':
            output_number += L[n - i - 1]
            R.append(L[n - i - 1])

    output_sum = ' + '.join(map(str, R))

    ctx.markdown(str(output_number))
    ctx.markdown(output_sum)


@fibonacci_base.slide
def fibonacci_base_poll_1(ctx: Context):
    """
    # Fibonacci base
    """

    ctx.markdown(
        "Can we represent all integer numbers using fibonacci base?")

    with ctx.fragment(ctx):
        with ctx.columns(2) as cl:
            with ctx.fragment('highlight-green'):
                ctx.markdown('Yes')
            cl.tab()
            ctx.markdown('No')


@fibonacci_base.slide
def fibonacci_base_poll_2(ctx: Context):
    """
    # Fibonacci base
    """
    ctx.markdown("Can we represent every number in a unique way?")
    with ctx.fragment(ctx):
        with ctx.columns(2) as cl:
            ctx.markdown('Yes')
            cl.tab()
            with ctx.fragment('highlight-red'):
                ctx.markdown('No')

# Make a break


@ show.slide
def computer_representation(ctx: Context):
    """
    ### Representation in the computer
    """

    with ctx.fragment(ctx):
        ctx.markdown("Binary")

    with ctx.fragment(ctx):
        ctx.markdown("Bytes")

    with ctx.fragment(ctx):
        ctx.markdown("C++ Demo")


@ show.slide
def base_16_64_application(ctx):
    """
    ### Application of higher base

    * Hexadecimal
    * Base64
    """

    with ctx.fragment(ctx):
        ctx.markdown("Demo")


@ show.slide
def decimal_number_in_base_10(ctx):
    """
    Decimal number

    $$\sum_{-\infty \lt i \lt \infty} d_i \cdot 10^{i}$$
    """


@ show.slide
def decimal_number_in_computer(ctx):
    """
    Single precision floating point format
    """

    with ctx.fragment(ctx):
        ctx.markdown("Wikipedia")

    with ctx.fragment(ctx):
        ctx.markdown("C++ Demo")

    # Some precision issues with catastrophic cancelation (substraction)
    # Compare numbers directly with each other
    # a / b == c (not always the same)

    # Case where the two numbers have same representation
    # but a == b (is false) This is with nan
    # and different representation but a == b (is true) this is 0 and -0


@ show.slide
def homework(ctx):
    """
    Homework
    """


@homework.slide
def task_1(ctx):
    """
    `*`

    Code that convert from any base to any other base

    Hint: Try converting to python number first
    """


@homework.slide
def task_2(ctx):
    """
    `*`

    Code that convert from base 2 to base 16 without converting to python number
    """


@homework.slide
def task_3(ctx):
    """
    `***`

    On fibonacci base, if we forbid consecutive 1, prove that every number is represented uniquely

    [Share LaTeX example]
    """
    # > Proof that fibonacci base without non-consecutive 1 is unique
    #   > Hint 1: Try using induction
    #   > Hint 2: Assume all numbers less than F_n


@homework.slide
def task_4(ctx):
    """
    `**`

    Make a program that converts from a number to fibonacci base
    """


@homework.slide
def task_5(ctx):
    """
    `***`

    There are $n$ books. Each of them can be painted in one of $k$ different colors.

    1. How many different ways can the books be painted.
    2. Make a program that prints all different possible ways.
    """


@ show.slide
def bye(ctx):
    """
    Mathematical Foundation of Algorithms

    Marcelo Fornet

    * Email: [mfornet94@gmail.com](mailto:mfornet94@gmail.com)
    * Telegram: [@mnaeraxr](https://t.me/mnaeraxr)
    """