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Add grid path challenge

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Donne Martin 2017-03-28 05:07:25 -04:00
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recursion_dynamic/grid_path/__init__.py Normal file
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recursion_dynamic/grid_path/grid_path_challenge.ipynb Normal file
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This notebook was prepared by [Donne Martin](https://github.com/donnemartin). Source and license info is on [GitHub](https://github.com/donnemartin/interactive-coding-challenges)."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Challenge Notebook"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Problem: Implement an algorithm to have a robot move from the upper left corner to the bottom right corner of a grid.\n",
"\n",
"* [Constraints](#Constraints)\n",
"* [Test Cases](#Test-Cases)\n",
"* [Algorithm](#Algorithm)\n",
"* [Code](#Code)\n",
"* [Unit Test](#Unit-Test)\n",
"* [Solution Notebook](#Solution-Notebook)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Constraints\n",
"\n",
"* Are there restrictions to how the robot moves?\n",
" * The robot can only move right and down\n",
"* Are some cells off limits?\n",
" * Yes\n",
"* Is this a rectangular grid? i.e. the grid is not jagged?\n",
" * Yes\n",
"* Will there always be a valid way for the robot to get to the bottom right?\n",
" * No, return None\n",
"* Can we assume the inputs are valid?\n",
" * No\n",
"* Can we assume this fits memory?\n",
" * Yes"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Test Cases\n",
"\n",
"<pre>\n",
"o = valid cell\n",
"x = invalid cell\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",
"</pre>\n",
"\n",
"* General case\n",
"\n",
"```\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",
"```\n",
"\n",
"* No valid path: In above example, row 7 col 2 is also invalid -> None\n",
"* None input -> None\n",
"* Empty matrix -> None"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Algorithm\n",
"\n",
"Refer to the [Solution Notebook](). If you are stuck and need a hint, the solution notebook's algorithm discussion might be a good place to start."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Code"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"class Grid(object):\n",
"\n",
" def find_path(self, matrix):\n",
" # TODO: Implement me\n",
" pass"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Unit Test"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**The following unit test is expected to fail until you solve the challenge.**"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"# %load test_grid_path.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('Success: test_grid_path')\n",
"\n",
"\n",
"def main():\n",
" test = TestGridPath()\n",
" test.test_grid_path()\n",
"\n",
"\n",
"if __name__ == '__main__':\n",
" main()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Solution Notebook\n",
"\n",
"Review the [Solution Notebook]() for a discussion on algorithms and code solutions."
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.5.0"
}
},
"nbformat": 4,
"nbformat_minor": 0
}

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recursion_dynamic/grid_path/grid_path_solution.ipynb Normal file
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This notebook was prepared by [Donne Martin](https://github.com/donnemartin). Source and license info is on [GitHub](https://github.com/donnemartin/interactive-coding-challenges)."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Solution Notebook"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Problem: Implement an algorithm to have a robot move from the upper left corner to the bottom right corner of a grid.\n",
"\n",
"* [Constraints](#Constraints)\n",
"* [Test Cases](#Test-Cases)\n",
"* [Algorithm](#Algorithm)\n",
"* [Code](#Code)\n",
"* [Unit Test](#Unit-Test)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Constraints\n",
"\n",
"* Are there restrictions to how the robot moves?\n",
" * The robot can only move right and down\n",
"* Are some cells invalid (off limits)?\n",
" * Yes\n",
"* Can we assume the starting and ending cells are valid cells?\n",
" * Yes\n",
"* Is this a rectangular grid? i.e. the grid is not jagged?\n",
" * Yes\n",
"* Will there always be a valid way for the robot to get to the bottom right?\n",
" * No, return None\n",
"* Can we assume the inputs are valid?\n",
" * No\n",
"* Can we assume this fits memory?\n",
" * Yes"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Test Cases\n",
"\n",
"<pre>\n",
"o = valid cell\n",
"x = invalid cell\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",
"</pre>\n",
"\n",
"* General case\n",
"\n",
"```\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",
"```\n",
"\n",
"* No valid path, say row 7, col 2 is invalid\n",
"* None input\n",
"* Empty matrix"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Algorithm\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": [
"## Code"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"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": [
"## Unit Test"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Overwriting test_grid_path.py\n"
]
}
],
"source": [
"%%writefile test_grid_path.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('Success: test_grid_path')\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": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Success: test_grid_path\n"
]
}
],
"source": [
"%run -i test_grid_path.py"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.5.0"
}
},
"nbformat": 4,
"nbformat_minor": 0
}

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recursion_dynamic/grid_path/test_grid_path.py Normal file
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from nose.tools import assert_equal
class TestGridPath(object):
def test_grid_path(self):
grid = Grid()
assert_equal(grid.find_path(None), None)
assert_equal(grid.find_path([[]]), None)
max_rows = 8
max_cols = 4
matrix = [[1] * max_cols for _ in range(max_rows)]
matrix[1][1] = 0
matrix[2][2] = 0
matrix[3][0] = 0
matrix[4][2] = 0
matrix[5][3] = 0
matrix[6][1] = 0
matrix[6][3] = 0
matrix[7][1] = 0
result = grid.find_path(matrix)
expected = [(0, 0), (1, 0), (2, 0),
(2, 1), (3, 1), (4, 1),
(5, 1), (5, 2), (6, 2),
(7, 2), (7, 3)]
assert_equal(result, expected)
matrix[7][2] = 0
result = grid.find_path(matrix)
assert_equal(result, None)
print('Success: test_grid_path')
def main():
test = TestGridPath()
test.test_grid_path()
if __name__ == '__main__':
main()