mirror of
https://github.com/donnemartin/interactive-coding-challenges.git
synced 2024-03-22 13:11:13 +08:00
Add graph shortest path unweighted challenge
This commit is contained in:
Donne Martin
parent
d352f56ecb
commit
3837b5a8cc
|
|
@ -0,0 +1,215 @@
|
|||
{
|
||||
"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: Find the shortest path between two nodes in a graph.\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",
|
||||
"* Is the graph directed?\n",
|
||||
" * Yes\n",
|
||||
"* Is the graph weighted?\n",
|
||||
" * No\n",
|
||||
"* Can we assume we already have Graph and Node classes?\n",
|
||||
" * Yes\n",
|
||||
"* Are the inputs two Nodes?\n",
|
||||
" * Yes\n",
|
||||
"* Is the output a list of Node keys that make up the shortest path?\n",
|
||||
" * Yes\n",
|
||||
"* If there is no path, should we return None?\n",
|
||||
" * Yes\n",
|
||||
"* Can we assume this is a connected graph?\n",
|
||||
" * Yes\n",
|
||||
"* Can we assume the inputs are valid?\n",
|
||||
" * Yes\n",
|
||||
"* Can we assume this fits memory?\n",
|
||||
" * Yes"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"## Test Cases\n",
|
||||
"\n",
|
||||
"Input:\n",
|
||||
"* `add_edge(source, destination, weight)`\n",
|
||||
"\n",
|
||||
"```\n",
|
||||
"graph.add_edge(0, 1)\n",
|
||||
"graph.add_edge(0, 4)\n",
|
||||
"graph.add_edge(0, 5)\n",
|
||||
"graph.add_edge(1, 3)\n",
|
||||
"graph.add_edge(1, 4)\n",
|
||||
"graph.add_edge(2, 1)\n",
|
||||
"graph.add_edge(3, 2)\n",
|
||||
"graph.add_edge(3, 4)\n",
|
||||
"```\n",
|
||||
"\n",
|
||||
"Result:\n",
|
||||
"* search_path(start=0, end=2) -> [0, 1, 3, 2]\n",
|
||||
"* search_path(start=0, end=0) -> [0]\n",
|
||||
"* search_path(start=4, end=5) -> None"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"## Algorithm\n",
|
||||
"\n",
|
||||
"Refer to the [Solution Notebook](http://nbviewer.ipython.org/github/donnemartin/interactive-coding-challenges/blob/master/graphs_trees/graph_path_exists/path_exists_solution.ipynb). 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": true
|
||||
},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"%run ../graph/graph.py\n",
|
||||
"%load ../graph/graph.py"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"class GraphShortestPath(Graph):\n",
|
||||
"\n",
|
||||
" def shortest_path(self, source_key, dest_key):\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_shortest_path.py\n",
|
||||
"from nose.tools import assert_equal\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"class TestShortestPath(object):\n",
|
||||
"\n",
|
||||
" def test_shortest_path(self):\n",
|
||||
" nodes = []\n",
|
||||
" graph = GraphShortestPath()\n",
|
||||
" for id in range(0, 6):\n",
|
||||
" nodes.append(graph.add_node(id))\n",
|
||||
" graph.add_edge(0, 1)\n",
|
||||
" graph.add_edge(0, 4)\n",
|
||||
" graph.add_edge(0, 5)\n",
|
||||
" graph.add_edge(1, 3)\n",
|
||||
" graph.add_edge(1, 4)\n",
|
||||
" graph.add_edge(2, 1)\n",
|
||||
" graph.add_edge(3, 2)\n",
|
||||
" graph.add_edge(3, 4)\n",
|
||||
"\n",
|
||||
" assert_equal(graph.shortest_path(nodes[0].key, nodes[2].key), [0, 1, 3, 2])\n",
|
||||
" assert_equal(graph.shortest_path(nodes[0].key, nodes[0].key), [0])\n",
|
||||
" assert_equal(graph.shortest_path(nodes[4].key, nodes[5].key), None)\n",
|
||||
"\n",
|
||||
" print('Success: test_shortest_path')\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"def main():\n",
|
||||
" test = TestShortestPath()\n",
|
||||
" test.test_shortest_path()\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"if __name__ == '__main__':\n",
|
||||
" main()"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"## Solution Notebook\n",
|
||||
"\n",
|
||||
"Review the [Solution Notebook](http://nbviewer.ipython.org/github/donnemartin/interactive-coding-challenges/blob/master/graphs_trees/graph_path_exists/path_exists_solution.ipynb) 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": "3.4.3"
|
||||
}
|
||||
},
|
||||
"nbformat": 4,
|
||||
"nbformat_minor": 0
|
||||
}
|
||||
|
|
@ -0,0 +1,274 @@
|
|||
{
|
||||
"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: Find the shortest path between two nodes in a graph.\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",
|
||||
"* Is the graph directed?\n",
|
||||
" * Yes\n",
|
||||
"* Is the graph weighted?\n",
|
||||
" * No\n",
|
||||
"* Can we assume we already have Graph and Node classes?\n",
|
||||
" * Yes\n",
|
||||
"* Are the inputs two Nodes?\n",
|
||||
" * Yes\n",
|
||||
"* Is the output a list of Node keys that make up the shortest path?\n",
|
||||
" * Yes\n",
|
||||
"* If there is no path, should we return None?\n",
|
||||
" * Yes\n",
|
||||
"* Can we assume this is a connected graph?\n",
|
||||
" * Yes\n",
|
||||
"* Can we assume the inputs are valid?\n",
|
||||
" * Yes\n",
|
||||
"* Can we assume this fits memory?\n",
|
||||
" * Yes"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"## Test Cases\n",
|
||||
"\n",
|
||||
"Input:\n",
|
||||
"* `add_edge(source, destination, weight)`\n",
|
||||
"\n",
|
||||
"```\n",
|
||||
"graph.add_edge(0, 1)\n",
|
||||
"graph.add_edge(0, 4)\n",
|
||||
"graph.add_edge(0, 5)\n",
|
||||
"graph.add_edge(1, 3)\n",
|
||||
"graph.add_edge(1, 4)\n",
|
||||
"graph.add_edge(2, 1)\n",
|
||||
"graph.add_edge(3, 2)\n",
|
||||
"graph.add_edge(3, 4)\n",
|
||||
"```\n",
|
||||
"\n",
|
||||
"Result:\n",
|
||||
"* search_path(start=0, end=2) -> [0, 1, 3, 2]\n",
|
||||
"* search_path(start=0, end=0) -> [0]\n",
|
||||
"* search_path(start=4, end=5) -> None"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"## Algorithm\n",
|
||||
"\n",
|
||||
"To determine the shorted path in an unweighted graph, we can use breadth-first search keeping track of the previous nodes ids for each node. Previous nodes ids can be a dictionary of key: current node id and value: previous node id.\n",
|
||||
"\n",
|
||||
"* If the start node is the end node, return True\n",
|
||||
"* Add the start node to the queue and mark it as visited\n",
|
||||
" * Update the previous node ids, the previous node id of the start node is None\n",
|
||||
"* While the queue is not empty\n",
|
||||
" * Dequeue a node and visit it\n",
|
||||
" * If the node is the end node, return the previous nodes\n",
|
||||
" * Set the previous node to the current node\n",
|
||||
" * Iterate through each adjacent node\n",
|
||||
" * If the node has not been visited, add it to the queue and mark it as visited\n",
|
||||
" * Update the previous node ids\n",
|
||||
"* Return None\n",
|
||||
"\n",
|
||||
"Walk the previous node ids backwards to get the path.\n",
|
||||
"\n",
|
||||
"Complexity:\n",
|
||||
"* Time: O(V + E), where V = number of vertices and E = number of edges\n",
|
||||
"* Space: O(V + E)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"## Code"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 1,
|
||||
"metadata": {
|
||||
"collapsed": true
|
||||
},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"%run ../graph/graph.py"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 2,
|
||||
"metadata": {
|
||||
"collapsed": true
|
||||
},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"from collections import deque\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"class GraphShortestPath(Graph):\n",
|
||||
"\n",
|
||||
" def shortest_path(self, source_key, dest_key):\n",
|
||||
" if source_key is None or dest_key is None:\n",
|
||||
" return None\n",
|
||||
" if source_key is dest_key:\n",
|
||||
" return [source_key]\n",
|
||||
" prev_node_keys = self._shortest_path(source_key, dest_key)\n",
|
||||
" if prev_node_keys is None:\n",
|
||||
" return None\n",
|
||||
" else:\n",
|
||||
" path_ids = [dest_key]\n",
|
||||
" prev_node_key = prev_node_keys[dest_key]\n",
|
||||
" while prev_node_key is not None:\n",
|
||||
" path_ids.append(prev_node_key)\n",
|
||||
" prev_node_key = prev_node_keys[prev_node_key]\n",
|
||||
" return path_ids[::-1]\n",
|
||||
"\n",
|
||||
" def _shortest_path(self, source_key, dest_key):\n",
|
||||
" queue = deque()\n",
|
||||
" queue.append(self.nodes[source_key])\n",
|
||||
" prev_node_keys = {source_key: None}\n",
|
||||
" self.nodes[source_key].visit_state = State.visited\n",
|
||||
" while queue:\n",
|
||||
" node = queue.popleft()\n",
|
||||
" if node.key is dest_key:\n",
|
||||
" return prev_node_keys\n",
|
||||
" prev_node = node\n",
|
||||
" for adj_node in node.adj_nodes.values():\n",
|
||||
" if adj_node.visit_state == State.unvisited:\n",
|
||||
" queue.append(adj_node)\n",
|
||||
" prev_node_keys[adj_node.key] = prev_node.key\n",
|
||||
" adj_node.visit_state = State.visited\n",
|
||||
" return None"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"## Unit Test"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 3,
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"Overwriting test_shortest_path.py\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"%%writefile test_shortest_path.py\n",
|
||||
"from nose.tools import assert_equal\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"class TestShortestPath(object):\n",
|
||||
"\n",
|
||||
" def test_shortest_path(self):\n",
|
||||
" nodes = []\n",
|
||||
" graph = GraphShortestPath()\n",
|
||||
" for id in range(0, 6):\n",
|
||||
" nodes.append(graph.add_node(id))\n",
|
||||
" graph.add_edge(0, 1)\n",
|
||||
" graph.add_edge(0, 4)\n",
|
||||
" graph.add_edge(0, 5)\n",
|
||||
" graph.add_edge(1, 3)\n",
|
||||
" graph.add_edge(1, 4)\n",
|
||||
" graph.add_edge(2, 1)\n",
|
||||
" graph.add_edge(3, 2)\n",
|
||||
" graph.add_edge(3, 4)\n",
|
||||
"\n",
|
||||
" assert_equal(graph.shortest_path(nodes[0].key, nodes[2].key), [0, 1, 3, 2])\n",
|
||||
" assert_equal(graph.shortest_path(nodes[0].key, nodes[0].key), [0])\n",
|
||||
" assert_equal(graph.shortest_path(nodes[4].key, nodes[5].key), None)\n",
|
||||
"\n",
|
||||
" print('Success: test_shortest_path')\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"def main():\n",
|
||||
" test = TestShortestPath()\n",
|
||||
" test.test_shortest_path()\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"if __name__ == '__main__':\n",
|
||||
" main()"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 4,
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"Success: test_shortest_path\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"%run -i test_shortest_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
|
||||
}
|
||||
|
|
@ -0,0 +1,33 @@
|
|||
from nose.tools import assert_equal
|
||||
|
||||
|
||||
class TestShortestPath(object):
|
||||
|
||||
def test_shortest_path(self):
|
||||
nodes = []
|
||||
graph = GraphShortestPath()
|
||||
for id in range(0, 6):
|
||||
nodes.append(graph.add_node(id))
|
||||
graph.add_edge(0, 1)
|
||||
graph.add_edge(0, 4)
|
||||
graph.add_edge(0, 5)
|
||||
graph.add_edge(1, 3)
|
||||
graph.add_edge(1, 4)
|
||||
graph.add_edge(2, 1)
|
||||
graph.add_edge(3, 2)
|
||||
graph.add_edge(3, 4)
|
||||
|
||||
assert_equal(graph.shortest_path(nodes[0].key, nodes[2].key), [0, 1, 3, 2])
|
||||
assert_equal(graph.shortest_path(nodes[0].key, nodes[0].key), [0])
|
||||
assert_equal(graph.shortest_path(nodes[4].key, nodes[5].key), None)
|
||||
|
||||
print('Success: test_shortest_path')
|
||||
|
||||
|
||||
def main():
|
||||
test = TestShortestPath()
|
||||
test.test_shortest_path()
|
||||
|
||||
|
||||
if __name__ == '__main__':
|
||||
main()
|
||||
Loading…
Reference in New Issue
Block a user