Beecrowd #1414 - Copa do Mundo

bee-1414.ipynb

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  "cells": [
    {
      "cell_type": "markdown",
      "source": [
        "# Resolvendo problema [#1414 - Copa do Mundo](https://resources.beecrowd.com/repository/UOJ_1414.html)"
      ],
      "metadata": {
        "id": "ljyNT49b7qhG"
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    },
    {
      "cell_type": "markdown",
      "source": [
        "## Inicia SymPy"
      ],
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      "source": [
        "from sympy import *\n",
        "\n",
        "init_printing()"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Variáveis\n",
        "\n",
        "- `p`: Total de pontos\n",
        "- `n`: Número de jogos\n",
        "- `v`: Número de vitórias\n",
        "- `e`: Número de empates"
      ],
      "metadata": {
        "id": "XtbJWGy32-UV"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "p, n, v, e = symbols('p n v e')"
      ],
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        "id": "f7a7NAyc2-s6"
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      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Relações"
      ],
      "metadata": {
        "id": "qeRje0K76Z15"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Relação entre o número de jogos, vitórias e empates"
      ],
      "metadata": {
        "id": "CJTdiVqR3xQf"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "equacao_jogos = Eq(n, v + e)\n",
        "equacao_jogos"
      ],
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          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "n = e + v"
            ],
            "text/latex": "$\\displaystyle n = e + v$"
          },
          "metadata": {},
          "execution_count": 3
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Relação da pontuação"
      ],
      "metadata": {
        "id": "4VOhKq5V3364"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "equacao_pontos = Eq(p, 3 * v + 2 * e)\n",
        "equacao_pontos"
      ],
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        "id": "R7lRqS-q37Qo",
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      "execution_count": 4,
      "outputs": [
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          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "p = 2⋅e + 3⋅v"
            ],
            "text/latex": "$\\displaystyle p = 2 e + 3 v$"
          },
          "metadata": {},
          "execution_count": 4
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Resolvendo exemplos"
      ],
      "metadata": {
        "id": "MgeOvs-37Kmi"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Exemplo 1"
      ],
      "metadata": {
        "id": "1dXnsugJ7kVf"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "solve([\n",
        "    equacao_jogos,\n",
        "    equacao_pontos,\n",
        "    Eq(n, 3),\n",
        "    Eq(p, 9),\n",
        "])[e]"
      ],
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        "id": "ndNjM5MQ7NXK",
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      "execution_count": 5,
      "outputs": [
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          "data": {
            "text/plain": [
              "0"
            ],
            "text/latex": "$\\displaystyle 0$"
          },
          "metadata": {},
          "execution_count": 5
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Exemplo 2"
      ],
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        "id": "bB7wm54N7m7O"
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    },
    {
      "cell_type": "code",
      "source": [
        "solve([\n",
        "    equacao_jogos,\n",
        "    equacao_pontos,\n",
        "    Eq(n, 3),\n",
        "    Eq(p, 7),\n",
        "])[e]"
      ],
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      "execution_count": 6,
      "outputs": [
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          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "2"
            ],
            "text/latex": "$\\displaystyle 2$"
          },
          "metadata": {},
          "execution_count": 6
        }
      ]
    }
  ]
}