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interactive-coding-challenges/graphs_trees/graph/graph_solution.ipynb

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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 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",
" * Implement both\n",
"* Do the edges have weights?\n",
" * Yes\n",
"* Can the graph have cycles?\n",
" * Yes\n",
"* If we try to add a node that already exists, do we just do nothing?\n",
" * Yes\n",
"* If we try to delete a node that doesn't exist, do we just do nothing?\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, 5)\n",
"graph.add_edge(0, 5, 2)\n",
"graph.add_edge(1, 2, 3)\n",
"graph.add_edge(2, 3, 4)\n",
"graph.add_edge(3, 4, 5)\n",
"graph.add_edge(3, 5, 6)\n",
"graph.add_edge(4, 0, 7)\n",
"graph.add_edge(5, 4, 8)\n",
"graph.add_edge(5, 2, 9)\n",
"```\n",
"\n",
"Result:\n",
"* `source` and `destination` nodes within `graph` are connected with specified `weight`.\n",
"\n",
"Note: \n",
"* The Graph class will be used as a building block for more complex graph challenges."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Algorithm\n",
"\n",
"### Node\n",
"\n",
"Node will keep track of its:\n",
"* id\n",
"* visit state\n",
"* incoming edge count (useful for algorithms such as topological sort)\n",
"* adjacent nodes and edge weights\n",
"\n",
"#### add_neighbor\n",
"\n",
"* If the neighbor doesn't already exist as an adjacent node\n",
" * Update the adjacent nodes and edge weights\n",
" * Increment the neighbor's incoming edge count\n",
"\n",
"Complexity:\n",
"* Time: O(1)\n",
"* Space: O(1)\n",
"\n",
"#### remove_neighbor\n",
"\n",
"* If the neighbor exists as an adjacent node\n",
" * Decrement the neighbor's incoming edge count\n",
" * Remove the neighbor as an adjacent node\n",
"\n",
"Complexity:\n",
"* Time: O(1)\n",
"* Space: O(1)\n",
"\n",
"### Graph\n",
"\n",
"Graph will keep track of its:\n",
"* nodes\n",
"\n",
"#### add_node\n",
"\n",
"* If node already exists, return it\n",
"* Create a node with the given id\n",
"* Add the newly created node to the collection of nodes\n",
"\n",
"Complexity:\n",
"* Time: O(1)\n",
"* Space: O(1)\n",
"\n",
"#### add_edge\n",
"\n",
"* If the source node is not in the collection of nodes, add it\n",
"* If the dest node is not in the collection of nodes, add it\n",
"* Add a connection from the source node to the dest node with the given edge weight\n",
"\n",
"#### add_undirected_edge\n",
"\n",
"* Call add_edge\n",
"* Also add a connection from the dest node to the source node with the given edge weight\n",
"\n",
"Complexity:\n",
"* Time: O(1)\n",
"* Space: O(1)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Code"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Overwriting graph.py\n"
]
}
],
"source": [
"%%writefile graph.py\n",
"from enum import Enum # Python 2 users: Run pip install enum34\n",
"\n",
"\n",
"class State(Enum):\n",
"\n",
" unvisited = 0\n",
" visiting = 1\n",
" visited = 2\n",
"\n",
"\n",
"class Node:\n",
"\n",
" def __init__(self, key):\n",
" self.key = key\n",
" self.visit_state = State.unvisited\n",
" self.incoming_edges = 0\n",
" self.adj_nodes = {} # Key = key, val = Node\n",
" self.adj_weights = {} # Key = key, val = weight\n",
"\n",
" def __repr__(self):\n",
" return str(self.key)\n",
"\n",
" def __lt__(self, other):\n",
" return self.key < other.key\n",
"\n",
" def add_neighbor(self, neighbor, weight=0):\n",
" if neighbor is None or weight is None:\n",
" raise TypeError('neighbor or weight cannot be None')\n",
" neighbor.incoming_edges += 1\n",
" self.adj_weights[neighbor.key] = weight\n",
" self.adj_nodes[neighbor.key] = neighbor\n",
"\n",
" def remove_neighbor(self, neighbor):\n",
" if neighbor is None:\n",
" raise TypeError('neighbor cannot be None')\n",
" if neighbor.key not in self.adj_nodes:\n",
" raise KeyError('neighbor not found')\n",
" neighbor.incoming_edges -= 1\n",
" del self.adj_weights[neighbor.key]\n",
" del self.adj_nodes[neighbor.key]\n",
"\n",
"\n",
"class Graph:\n",
"\n",
" def __init__(self):\n",
" self.nodes = {} # Key = key, val = Node\n",
"\n",
" def add_node(self, key):\n",
" if key is None:\n",
" raise TypeError('key cannot be None')\n",
" if key not in self.nodes:\n",
" self.nodes[key] = Node(key)\n",
" return self.nodes[key]\n",
"\n",
" def add_edge(self, source_key, dest_key, weight=0):\n",
" if source_key is None or dest_key is None:\n",
" raise KeyError('Invalid key')\n",
" if source_key not in self.nodes:\n",
" self.add_node(source_key)\n",
" if dest_key not in self.nodes:\n",
" self.add_node(dest_key)\n",
" self.nodes[source_key].add_neighbor(self.nodes[dest_key], weight)\n",
"\n",
" def add_undirected_edge(self, src_key, dst_key, weight=0):\n",
" if src_key is None or dst_key is None:\n",
" raise TypeError('key cannot be None')\n",
" self.add_edge(src_key, dst_key, weight)\n",
" self.add_edge(dst_key, src_key, weight)"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"%run graph.py"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Unit Test"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Overwriting test_graph.py\n"
]
}
],
"source": [
"%%writefile test_graph.py\n",
"import unittest\n",
"\n",
"\n",
"class TestGraph(unittest.TestCase):\n",
"\n",
" def create_graph(self):\n",
" graph = Graph()\n",
" for key in range(0, 6):\n",
" graph.add_node(key)\n",
" return graph\n",
"\n",
" def test_graph(self):\n",
" graph = self.create_graph()\n",
" graph.add_edge(0, 1, weight=5)\n",
" graph.add_edge(0, 5, weight=2)\n",
" graph.add_edge(1, 2, weight=3)\n",
" graph.add_edge(2, 3, weight=4)\n",
" graph.add_edge(3, 4, weight=5)\n",
" graph.add_edge(3, 5, weight=6)\n",
" graph.add_edge(4, 0, weight=7)\n",
" graph.add_edge(5, 4, weight=8)\n",
" graph.add_edge(5, 2, weight=9)\n",
"\n",
" self.assertEqual(graph.nodes[0].adj_weights[graph.nodes[1].key], 5)\n",
" self.assertEqual(graph.nodes[0].adj_weights[graph.nodes[5].key], 2)\n",
" self.assertEqual(graph.nodes[1].adj_weights[graph.nodes[2].key], 3)\n",
" self.assertEqual(graph.nodes[2].adj_weights[graph.nodes[3].key], 4)\n",
" self.assertEqual(graph.nodes[3].adj_weights[graph.nodes[4].key], 5)\n",
" self.assertEqual(graph.nodes[3].adj_weights[graph.nodes[5].key], 6)\n",
" self.assertEqual(graph.nodes[4].adj_weights[graph.nodes[0].key], 7)\n",
" self.assertEqual(graph.nodes[5].adj_weights[graph.nodes[4].key], 8)\n",
" self.assertEqual(graph.nodes[5].adj_weights[graph.nodes[2].key], 9)\n",
"\n",
" self.assertEqual(graph.nodes[0].incoming_edges, 1)\n",
" self.assertEqual(graph.nodes[1].incoming_edges, 1)\n",
" self.assertEqual(graph.nodes[2].incoming_edges, 2)\n",
" self.assertEqual(graph.nodes[3].incoming_edges, 1)\n",
" self.assertEqual(graph.nodes[4].incoming_edges, 2)\n",
" self.assertEqual(graph.nodes[5].incoming_edges, 2)\n",
"\n",
" graph.nodes[0].remove_neighbor(graph.nodes[1])\n",
" self.assertEqual(graph.nodes[1].incoming_edges, 0)\n",
" graph.nodes[3].remove_neighbor(graph.nodes[4])\n",
" self.assertEqual(graph.nodes[4].incoming_edges, 1)\n",
"\n",
" self.assertEqual(graph.nodes[0] < graph.nodes[1], True)\n",
"\n",
" print('Success: test_graph')\n",
"\n",
" def test_graph_undirected(self):\n",
" graph = self.create_graph()\n",
" graph.add_undirected_edge(0, 1, weight=5)\n",
" graph.add_undirected_edge(0, 5, weight=2)\n",
" graph.add_undirected_edge(1, 2, weight=3)\n",
"\n",
" self.assertEqual(graph.nodes[0].adj_weights[graph.nodes[1].key], 5)\n",
" self.assertEqual(graph.nodes[1].adj_weights[graph.nodes[0].key], 5)\n",
" self.assertEqual(graph.nodes[0].adj_weights[graph.nodes[5].key], 2)\n",
" self.assertEqual(graph.nodes[5].adj_weights[graph.nodes[0].key], 2)\n",
" self.assertEqual(graph.nodes[1].adj_weights[graph.nodes[2].key], 3)\n",
" self.assertEqual(graph.nodes[2].adj_weights[graph.nodes[1].key], 3)\n",
"\n",
" print('Success: test_graph_undirected')\n",
"\n",
"\n",
"def main():\n",
" test = TestGraph()\n",
" test.test_graph()\n",
" test.test_graph_undirected()\n",
"\n",
"\n",
"if __name__ == '__main__':\n",
" main()"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Success: test_graph\n",
"Success: test_graph_undirected\n"
]
}
],
"source": [
"%run -i test_graph.py"
]
}
],
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