{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "CItwGnEDMlCR"
      },
      "source": [
        "#  **Pauta Auxiliar 3: Recursión y Diagramas de Estado**\n",
        "\n",
        "### Profesores: Nelson Baloian, Benjamín Bustos, Sebastian Ferrada, Patricio Poblete\n",
        "### Auxiliares: Sebastián Acuña, Valentina Aravena, Vicente Olivares, Ricardo Valdivia"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "B5CogT3yCCg2"
      },
      "source": [
        "## P1. Triángulo de Pascal"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2HN4N7BFi4Nh"
      },
      "source": [
        "La idea del ejercicio es usar como caso recursivo lo siguiente:\n",
        "\\begin{equation*}\n",
        "\\binom{n}{k} = \\binom{n-1}{k-1} + \\binom{n−1}{k}\n",
        "\\end{equation*}\n",
        "hasta llegar a los casos base:\n",
        "\\begin{equation*}\n",
        "\\binom{n}{n} = \\binom{n}{0} = 1\n",
        "\\end{equation*}"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "b3zjjeq0Cq5q"
      },
      "outputs": [],
      "source": [
        "# calcula la combinatoria de n sobre k\n",
        "# n, k enteros no negativos, n >= k\n",
        "# Ejemplo: combinatoria(5, 2) devuelve 10\n",
        "\n",
        "def combinatoria(n, k):\n",
        "  # Casos base (n = k y n = 0)\n",
        "  if n==k or k==0:\n",
        "    return 1\n",
        "\n",
        "  # Casos recursivos\n",
        "  else:\n",
        "    # Las variables comb1 y comb2 representan las combinatorias en las que se separa\n",
        "    comb1 = combinatoria(n-1, k-1)\n",
        "    comb2 = combinatoria(n-1, k)\n",
        "    return comb1 + comb2\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "40rOHXgzDX3X",
        "outputId": "04ca7917-6cec-4146-d916-3994af86520c"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Todo funciona!!\n",
            "Estrellita dorada para ti\n"
          ]
        }
      ],
      "source": [
        "assert combinatoria(5,2) == 10\n",
        "assert combinatoria(10,6) == 210\n",
        "assert combinatoria(4,4) == 1\n",
        "assert combinatoria(5,0) == 1\n",
        "assert combinatoria(0,0) == 1\n",
        "assert combinatoria(101,2) == 5050\n",
        "print(\"Todo funciona!!\")\n",
        "print(\"Estrellita dorada para ti\")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "d84QBFB2DQTr"
      },
      "source": [
        "## P2. Un juego con monedas"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vKZg6LJbZVzl"
      },
      "source": [
        "Alicia y Roberto, son dos niños que les encanta jugar con monedas. Un día Alicia llega a la casa de Roberto con un nuevo juego que acaba de inventar. Usando una moneda no cargada (es decir, P(sello) = P(cara) = 1/2), se lanza la moneda al aire una cantidad indeterminada de veces, hasta que se cumpla alguna de las siguientes situaciones:\n",
        "\n",
        "• Si sale de corrido cara, cara, sello. Alicia gana el juego.\n",
        "\n",
        "• Si sale de corrido cara, sello, sello. Roberto gana el juego.\n",
        "\n",
        "Roberto cree que este juego no es justo, por esto te pide ayuda a ti, su amigo/a computín. ¿Puedes ayudar a Roberto a decidir si es justo o no el juego?"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "N6X680FaZafl"
      },
      "source": [
        "### Diagrama de Estado del problema\n",
        "![Monedas_color.jpg](data:image/jpeg;base64,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)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "QchL71PTZcGy"
      },
      "outputs": [],
      "source": [
        "import random\n",
        "def lanzarMoneda():\n",
        "  if (random.random() < 0.5):\n",
        "    return True\n",
        "  return False\n",
        "\n",
        "def juegoConMonedas():\n",
        "  estado = \"Morado\"\n",
        "  while(estado!=\"Naranja\" and estado!=\"Azul\"):\n",
        "    if lanzarMoneda(): # Salio Cara\n",
        "      if estado==\"Morado\":\n",
        "        estado=\"Verde\"\n",
        "      elif estado==\"Verde\":\n",
        "        estado=\"Amarillo\"\n",
        "      elif estado==\"Amarillo\":\n",
        "        estado=\"Amarillo\"\n",
        "      else:\n",
        "        estado=\"Verde\"\n",
        "    else: # Salio Sello\n",
        "      if estado==\"Morado\":\n",
        "        estado=\"Morado\"\n",
        "      elif estado==\"Verde\":\n",
        "        estado=\"Gris\"\n",
        "      elif estado==\"Amarillo\":\n",
        "        estado=\"Naranja\"\n",
        "      else:\n",
        "        estado=\"Azul\"\n",
        "  if estado==\"Naranja\":\n",
        "    return False\n",
        "  else:\n",
        "    return True\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "background_save": true
        },
        "id": "9HerMoqjcQsW",
        "outputId": "83bf4c66-46ba-41e9-e16e-f7ff6fbf407c"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Alicia:  666676262\n",
            "Roberto:  333323738\n"
          ]
        }
      ],
      "source": [
        "n = 1000000000\n",
        "A = 0\n",
        "R = 0\n",
        "while(n > 0):\n",
        "  n -= 1\n",
        "  if juegoConMonedas():\n",
        "    R += 1\n",
        "  else:\n",
        "    A += 1\n",
        "\n",
        "print(\"Alicia: \",A)\n",
        "print(\"Roberto: \",R)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vsYm5N-5Cs5K"
      },
      "source": [
        "## P3. Factores Primos"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "AG-zJlKOY4yO"
      },
      "source": [
        "Como se menciona en el enunciado de la pregunta, los números enteros positivos se pueden representar separándolo en sus factores primos. En particular, nos interesa que se puede ir separando factor por factor. Por ejemplo:\n",
        "\n",
        "\\begin{align*}\n",
        "90 &= 2 * 45 \\\\\n",
        "&= 2 * 3 * 15 \\\\\n",
        "&= 2 * 3 * 3 * 5\n",
        "\\end{align*}\n",
        "\n",
        "Podemos aprovechar lo anterior para la recursión de nuestra función, esta funcionaría de la siguiente manera:\n",
        "\n",
        "\n",
        "*   Si n es primo, retorna **str(n)**.\n",
        "*   En caso contrario, se busca el factor primo *p* más pequeño y se retorna **str(p) + \"*\" + factorPrimo(n//p)**.\n",
        "\n",
        "\n",
        "Siguiendo el ejemplo de arriba, la función para n = 90 funcionaría de la siguiente manera:\n",
        "\n",
        "\\begin{align*}\n",
        "factoresPrimos(90) &= 2 * factoresPrimos(45)\\\\\n",
        "&= 2 * 3 * factoresPrimos(15) \\\\\n",
        "&= 2 * 3 * 3 * factoresPrimos(5)\\\\\n",
        "&= 2 * 3 * 3 * 5\n",
        "\\end{align*}\n",
        "\n",
        "Ahora, ¿cómo determinamos si n es primo o cual es su factor primo más pequeño?\n",
        "\n",
        "\n",
        "Primero tenemos que tener en cuenta que el divisor d más pequeño distinto de 1 de un número entero positivo n siempre es primo. Esto se puede demostrar por contradicción: Si d no fuera primo se podría descomponer en dos factores que serían divisores de n y menores que d, contradiciendo que d es el divisor más pequeño de n.\n",
        "\n",
        "(Demostración no necesaria para el curso, solo para que decir que todavía nos acordamos de cómo demostrar 😀)\n",
        "\n",
        "\n",
        "Teniendo lo anterior en cuenta, podemos buscar el número más pequeño que divida a n. Si no encontramos uno, n es primo.\n",
        "\n",
        "Pero no es necesario probar con todos los enteros desde 2 hasta $n-1$, con llegar hasta $\\sqrt{n}$ basta. Esto se debe a que si existiese un divisor $d_1$ de n mayor que $\\sqrt{n}$, también debe existir un divisor $d_2$ menor a $\\sqrt{n}$, tal que $d_1*d_2=n$. Por esa razón no es necesario buscar divisores superiores a $\\sqrt{n}$.\n",
        "\n",
        "El siguiente código representa al texto anterior:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "gbBBSYk8DQDf"
      },
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "\n",
        "def factoresPrimos(n):\n",
        "    limite = int(np.sqrt(n))\n",
        "    div = 2\n",
        "\n",
        "    # div aumenta hasta que sea divisor de n o hasta que el divisor sea mayor que sqrt(n)\n",
        "    while n % div != 0 and div <= limite:\n",
        "        div += 1\n",
        "\n",
        "    # Caso base\n",
        "    # Si div es mayor que limite, n es primo\n",
        "    if div > limite:\n",
        "        return str(n)\n",
        "    # Llamada recursiva\n",
        "    else:\n",
        "        return str(div)+\"*\"+factoresPrimos(n//div)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "gKMktVXQ4VoA",
        "outputId": "96a4a96b-7807-46b8-ac81-0e638e7b484d"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Todo de maravilla\n"
          ]
        }
      ],
      "source": [
        "assert factoresPrimos(2) == \"2\"\n",
        "assert factoresPrimos(23) == \"23\"\n",
        "assert factoresPrimos(10) == \"2*5\"\n",
        "assert factoresPrimos(90) == \"2*3*3*5\"\n",
        "print(\"Todo de maravilla\")"
      ]
    }
  ],
  "metadata": {
    "colab": {
      "provenance": []
    },
    "kernelspec": {
      "display_name": "Python 3",
      "name": "python3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}