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Add grid path challenge
This commit is contained in:
Donne Martin
parent
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commit
460406097d
0
recursion_dynamic/grid_path/__init__.py
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0
recursion_dynamic/grid_path/__init__.py
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212
recursion_dynamic/grid_path/grid_path_challenge.ipynb
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212
recursion_dynamic/grid_path/grid_path_challenge.ipynb
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@ -0,0 +1,212 @@
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{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"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)."
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Challenge Notebook"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Problem: Implement an algorithm to have a robot move from the upper left corner to the bottom right corner of a grid.\n",
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"\n",
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"* [Constraints](#Constraints)\n",
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"* [Test Cases](#Test-Cases)\n",
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"* [Algorithm](#Algorithm)\n",
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"* [Code](#Code)\n",
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"* [Unit Test](#Unit-Test)\n",
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"* [Solution Notebook](#Solution-Notebook)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Constraints\n",
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"\n",
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"* Are there restrictions to how the robot moves?\n",
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" * The robot can only move right and down\n",
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"* Are some cells off limits?\n",
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" * Yes\n",
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"* Is this a rectangular grid? i.e. the grid is not jagged?\n",
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" * Yes\n",
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"* Will there always be a valid way for the robot to get to the bottom right?\n",
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" * No, return None\n",
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"* Can we assume the inputs are valid?\n",
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" * No\n",
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"* Can we assume this fits memory?\n",
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" * Yes"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Test Cases\n",
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"\n",
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"<pre>\n",
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"o = valid cell\n",
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"x = invalid cell\n",
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"\n",
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" 0 1 2 3\n",
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"0 o o o o\n",
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"1 o x o o\n",
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"2 o o x o\n",
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"3 x o o o\n",
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"4 o o x o\n",
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"5 o o o x\n",
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"6 o x o x\n",
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"7 o x o o\n",
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"</pre>\n",
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"\n",
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"* General case\n",
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"\n",
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"```\n",
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"expected = [(0, 0), (1, 0), (2, 0),\n",
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" (2, 1), (3, 1), (4, 1),\n",
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" (5, 1), (5, 2), (6, 2), \n",
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" (7, 2), (7, 3)]\n",
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"```\n",
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"\n",
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"* No valid path: In above example, row 7 col 2 is also invalid -> None\n",
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"* None input -> None\n",
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"* Empty matrix -> None"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Algorithm\n",
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"\n",
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"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."
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Code"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"class Grid(object):\n",
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"\n",
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" def find_path(self, matrix):\n",
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" # TODO: Implement me\n",
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" pass"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Unit Test"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"**The following unit test is expected to fail until you solve the challenge.**"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"# %load test_grid_path.py\n",
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"from nose.tools import assert_equal\n",
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"\n",
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"\n",
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"class TestGridPath(object):\n",
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"\n",
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" def test_grid_path(self):\n",
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" grid = Grid()\n",
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" assert_equal(grid.find_path(None), None)\n",
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" assert_equal(grid.find_path([[]]), None)\n",
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" max_rows = 8\n",
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" max_cols = 4\n",
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" matrix = [[1] * max_cols for _ in range(max_rows)]\n",
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" matrix[1][1] = 0\n",
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" matrix[2][2] = 0\n",
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" matrix[3][0] = 0\n",
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" matrix[4][2] = 0\n",
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" matrix[5][3] = 0\n",
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" matrix[6][1] = 0\n",
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" matrix[6][3] = 0\n",
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" matrix[7][1] = 0\n",
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" result = grid.find_path(matrix)\n",
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" expected = [(0, 0), (1, 0), (2, 0),\n",
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" (2, 1), (3, 1), (4, 1),\n",
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" (5, 1), (5, 2), (6, 2), \n",
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" (7, 2), (7, 3)]\n",
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" assert_equal(result, expected)\n",
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" matrix[7][2] = 0\n",
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" result = grid.find_path(matrix)\n",
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" assert_equal(result, None)\n",
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" print('Success: test_grid_path')\n",
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"\n",
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"\n",
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"def main():\n",
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" test = TestGridPath()\n",
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" test.test_grid_path()\n",
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"\n",
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"\n",
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"if __name__ == '__main__':\n",
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" main()"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Solution Notebook\n",
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"\n",
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"Review the [Solution Notebook]() for a discussion on algorithms and code solutions."
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]
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.5.0"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 0
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}
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276
recursion_dynamic/grid_path/grid_path_solution.ipynb
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276
recursion_dynamic/grid_path/grid_path_solution.ipynb
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@ -0,0 +1,276 @@
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{
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"cells": [
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{
|
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"cell_type": "markdown",
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"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)."
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Solution Notebook"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
|
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"## Problem: Implement an algorithm to have a robot move from the upper left corner to the bottom right corner of a grid.\n",
|
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"\n",
|
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"* [Constraints](#Constraints)\n",
|
||||
"* [Test Cases](#Test-Cases)\n",
|
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"* [Algorithm](#Algorithm)\n",
|
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"* [Code](#Code)\n",
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"* [Unit Test](#Unit-Test)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
|
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"## Constraints\n",
|
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"\n",
|
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"* Are there restrictions to how the robot moves?\n",
|
||||
" * The robot can only move right and down\n",
|
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"* Are some cells invalid (off limits)?\n",
|
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" * Yes\n",
|
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"* Can we assume the starting and ending cells are valid cells?\n",
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" * Yes\n",
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"* 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"
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||||
]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Test Cases\n",
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"\n",
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"<pre>\n",
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"o = valid cell\n",
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"x = invalid cell\n",
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"\n",
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" 0 1 2 3\n",
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"0 o o o o\n",
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"1 o x o o\n",
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"2 o o x o\n",
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"3 x o o o\n",
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"4 o o x o\n",
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"5 o o o x\n",
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"6 o x o x\n",
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"7 o x o o\n",
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"</pre>\n",
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"\n",
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"* General case\n",
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"\n",
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"```\n",
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"expected = [(0, 0), (1, 0), (2, 0),\n",
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" (2, 1), (3, 1), (4, 1),\n",
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" (5, 1), (5, 2), (6, 2), \n",
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" (7, 2), (7, 3)]\n",
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"```\n",
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"\n",
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"* No valid path, say row 7, col 2 is invalid\n",
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"* None input\n",
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"* Empty matrix"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Algorithm\n",
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"\n",
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"To get to row r and column c [r, c], we will need to have gone:\n",
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"\n",
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"* Right from [r, c-1] if this is a valid cell - [Path 1] \n",
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"* Down from [r-1, c] if this is a valid cell - [Path 2]\n",
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"\n",
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"If we look at [Path 1], to get to [r, c-1], we will need to have gone:\n",
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"\n",
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"* Right from [r, c-2] if this is a valid cell\n",
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"* Down from [r-1, c-1] if this is a valid cell\n",
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"\n",
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"Continue this process until we reach the start cell or until we find that there is no path.\n",
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"\n",
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"Base case:\n",
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"\n",
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"* If the input row or col are < 0, or if [row, col] is not a valid cell\n",
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" * Return False\n",
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"\n",
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"Recursive case:\n",
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"\n",
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"We'll memoize the solution to improve performance.\n",
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"\n",
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"* Use the memo to see if we've already processed the current cell\n",
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"* If any of the following is True, append the current cell to the path and set our result to True:\n",
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" * We are at the start cell\n",
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" * We get a True result from a recursive call on:\n",
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" * [row, col-1]\n",
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" * [row-1, col]\n",
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"* Update the memo\n",
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"* Return the result\n",
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"\n",
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"Complexity:\n",
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"* Time: O(row * col)\n",
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"* Space: O(row * col) for the recursion depth"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Code"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 1,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"class Grid(object):\n",
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"\n",
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" def find_path(self, matrix):\n",
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" if matrix is None or not matrix:\n",
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" return None\n",
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" cache = {}\n",
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" path = []\n",
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" if self._find_path(matrix, len(matrix) - 1, \n",
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" len(matrix[0]) - 1, cache, path):\n",
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" return path\n",
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" else:\n",
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" return None\n",
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"\n",
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" def _find_path(self, matrix, row, col, cache, path):\n",
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" if row < 0 or col < 0 or not matrix[row][col]:\n",
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" return False\n",
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" cell = (row, col)\n",
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" if cell in cache:\n",
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" return cache[cell]\n",
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" cache[cell] = (row == 0 and col == 0 or\n",
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" self._find_path(matrix, row, col - 1, cache, path) or\n",
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" self._find_path(matrix, row - 1, col, cache, path))\n",
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" if cache[cell]:\n",
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" path.append(cell)\n",
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" return cache[cell]"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Unit Test"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Overwriting test_grid_path.py\n"
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]
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}
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],
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"source": [
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"%%writefile test_grid_path.py\n",
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"from nose.tools import assert_equal\n",
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"\n",
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"\n",
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"class TestGridPath(object):\n",
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"\n",
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" def test_grid_path(self):\n",
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" grid = Grid()\n",
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" assert_equal(grid.find_path(None), None)\n",
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" assert_equal(grid.find_path([[]]), None)\n",
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" max_rows = 8\n",
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" max_cols = 4\n",
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" matrix = [[1] * max_cols for _ in range(max_rows)]\n",
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" matrix[1][1] = 0\n",
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" matrix[2][2] = 0\n",
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" matrix[3][0] = 0\n",
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" matrix[4][2] = 0\n",
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" matrix[5][3] = 0\n",
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" matrix[6][1] = 0\n",
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" matrix[6][3] = 0\n",
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" matrix[7][1] = 0\n",
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" result = grid.find_path(matrix)\n",
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" expected = [(0, 0), (1, 0), (2, 0),\n",
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" (2, 1), (3, 1), (4, 1),\n",
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" (5, 1), (5, 2), (6, 2), \n",
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" (7, 2), (7, 3)]\n",
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" assert_equal(result, expected)\n",
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" matrix[7][2] = 0\n",
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" result = grid.find_path(matrix)\n",
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" assert_equal(result, None)\n",
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" print('Success: test_grid_path')\n",
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"\n",
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"\n",
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"def main():\n",
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" test = TestGridPath()\n",
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" test.test_grid_path()\n",
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"\n",
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"\n",
|
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"if __name__ == '__main__':\n",
|
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" main()"
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]
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},
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{
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"cell_type": "code",
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||||
"execution_count": 3,
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
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"output_type": "stream",
|
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"text": [
|
||||
"Success: test_grid_path\n"
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]
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}
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],
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"source": [
|
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"%run -i test_grid_path.py"
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]
|
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}
|
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],
|
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"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
|
||||
}
|
||||
39
recursion_dynamic/grid_path/test_grid_path.py
Normal file
39
recursion_dynamic/grid_path/test_grid_path.py
Normal file
|
|
@ -0,0 +1,39 @@
|
|||
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()
|
||||
Loading…
Reference in New Issue
Block a user