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"source": [
"# Data Science Academy - Python Fundamentos - Capítulo 7\n",
"\n",
"## Download: http://github.com/dsacademybr"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Missão: Implementar um algoritmo para mover um robô do canto superior esquerdo para o canto inferior direito de uma grade."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Nível de Dificuldade: Médio"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Premissas\n",
"\n",
"* Existem restrições de como o robô se move?\n",
" * O robô só pode se mover para a direita e para baixo\n",
"* Algumas células são inválidas (fora dos limites)?\n",
" * Sim\n",
"* Podemos supor que as células inicial e final são células válidas?\n",
" * Sim\n",
"* Isso é uma grade retangular? ou seja, a grade não é irregular?\n",
" * Sim\n",
"* Haverá sempre uma maneira válida para o robô chegar ao canto inferior direito?\n",
" * Não, retorno None\n",
"* Podemos assumir que as entradas são válidas?\n",
" * Não\n",
"* Podemos supor que isso se encaixa na memória?\n",
" * Sim"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Teste Cases\n",
"\n",
"\n",
"o = célula válida\n",
"x = célula inválida\n",
"\n",
" 0 1 2 3\n",
"0 o o o o\n",
"1 o x o o\n",
"2 o o x o\n",
"3 x o o o\n",
"4 o o x o\n",
"5 o o o x\n",
"6 o x o x\n",
"7 o x o o\n",
"\n",
"\n",
"* Caso geral\n",
"\n",
"```\n",
"Saída esperada = [(0, 0), (1, 0), (2, 0),\n",
" (2, 1), (3, 1), (4, 1),\n",
" (5, 1), (5, 2), (6, 2), \n",
" (7, 2), (7, 3)]\n",
"```\n",
"\n",
"* Nenhum caminho válido, por exemplo, linha 7, col 2 é inválido\n",
"* Nenhuma entrada\n",
"* Matriz vazia"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Algoritmo\n",
"\n",
"To get to row r and column c [r, c], we will need to have gone:\n",
"\n",
"* Right from [r, c-1] if this is a valid cell - [Path 1] \n",
"* Down from [r-1, c] if this is a valid cell - [Path 2]\n",
"\n",
"If we look at [Path 1], to get to [r, c-1], we will need to have gone:\n",
"\n",
"* Right from [r, c-2] if this is a valid cell\n",
"* Down from [r-1, c-1] if this is a valid cell\n",
"\n",
"Continue this process until we reach the start cell or until we find that there is no path.\n",
"\n",
"Base case:\n",
"\n",
"* If the input row or col are < 0, or if [row, col] is not a valid cell\n",
" * Return False\n",
"\n",
"Recursive case:\n",
"\n",
"We'll memoize the solution to improve performance.\n",
"\n",
"* Use the memo to see if we've already processed the current cell\n",
"* If any of the following is True, append the current cell to the path and set our result to True:\n",
" * We are at the start cell\n",
" * We get a True result from a recursive call on:\n",
" * [row, col-1]\n",
" * [row-1, col]\n",
"* Update the memo\n",
"* Return the result\n",
"\n",
"Complexity:\n",
"* Time: O(row * col)\n",
"* Space: O(row * col) for the recursion depth"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Solução"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": true
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"outputs": [],
"source": [
"class Grid(object):\n",
"\n",
" def find_path(self, matrix):\n",
" if matrix is None or not matrix:\n",
" return None\n",
" cache = {}\n",
" path = []\n",
" if self._find_path(matrix, len(matrix) - 1, \n",
" len(matrix[0]) - 1, cache, path):\n",
" return path\n",
" else:\n",
" return None\n",
"\n",
" def _find_path(self, matrix, row, col, cache, path):\n",
" if row < 0 or col < 0 or not matrix[row][col]:\n",
" return False\n",
" cell = (row, col)\n",
" if cell in cache:\n",
" return cache[cell]\n",
" cache[cell] = (row == 0 and col == 0 or\n",
" self._find_path(matrix, row, col - 1, cache, path) or\n",
" self._find_path(matrix, row - 1, col, cache, path))\n",
" if cache[cell]:\n",
" path.append(cell)\n",
" return cache[cell]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Teste da Solução"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Writing missao3.py\n"
]
}
],
"source": [
"%%writefile missao3.py\n",
"from nose.tools import assert_equal\n",
"\n",
"\n",
"class TestGridPath(object):\n",
"\n",
" def test_grid_path(self):\n",
" grid = Grid()\n",
" assert_equal(grid.find_path(None), None)\n",
" assert_equal(grid.find_path([[]]), None)\n",
" max_rows = 8\n",
" max_cols = 4\n",
" matrix = [[1] * max_cols for _ in range(max_rows)]\n",
" matrix[1][1] = 0\n",
" matrix[2][2] = 0\n",
" matrix[3][0] = 0\n",
" matrix[4][2] = 0\n",
" matrix[5][3] = 0\n",
" matrix[6][1] = 0\n",
" matrix[6][3] = 0\n",
" matrix[7][1] = 0\n",
" result = grid.find_path(matrix)\n",
" expected = [(0, 0), (1, 0), (2, 0),\n",
" (2, 1), (3, 1), (4, 1),\n",
" (5, 1), (5, 2), (6, 2), \n",
" (7, 2), (7, 3)]\n",
" assert_equal(result, expected)\n",
" matrix[7][2] = 0\n",
" result = grid.find_path(matrix)\n",
" assert_equal(result, None)\n",
" print('Sua solução foi executada com sucesso! Parabéns!')\n",
"\n",
"\n",
"def main():\n",
" test = TestGridPath()\n",
" test.test_grid_path()\n",
"\n",
"\n",
"if __name__ == '__main__':\n",
" main()"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Sua solução foi executada com sucesso! Parabéns!\n"
]
}
],
"source": [
"%run -i missao3.py"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Fim"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Obrigado - Data Science Academy - facebook.com/dsacademybr"
]
}
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