mirror of
https://github.com/donnemartin/interactive-coding-challenges.git
synced 2024-03-22 13:11:13 +08:00
391 lines
11 KiB
Python
391 lines
11 KiB
Python
{
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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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"# 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 a graph.\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)"
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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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"* Is the graph directed?\n",
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" * Implement both\n",
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"* Do the edges have weights?\n",
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" * Yes\n",
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"* Can the graph have cycles?\n",
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" * Yes\n",
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"* If we try to add a node that already exists, do we just do nothing?\n",
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" * Yes\n",
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"* If we try to delete a node that doesn't exist, do we just do nothing?\n",
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" * Yes\n",
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"* Can we assume the inputs are valid?\n",
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" * Yes\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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"Input:\n",
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"* `add_edge(source, destination, weight)`\n",
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"\n",
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"```\n",
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"graph.add_edge(0, 1, 5)\n",
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"graph.add_edge(0, 5, 2)\n",
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"graph.add_edge(1, 2, 3)\n",
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"graph.add_edge(2, 3, 4)\n",
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"graph.add_edge(3, 4, 5)\n",
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"graph.add_edge(3, 5, 6)\n",
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"graph.add_edge(4, 0, 7)\n",
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"graph.add_edge(5, 4, 8)\n",
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"graph.add_edge(5, 2, 9)\n",
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"```\n",
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"\n",
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"Result:\n",
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"* `source` and `destination` nodes within `graph` are connected with specified `weight`.\n",
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"\n",
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"Note: \n",
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"* The Graph class will be used as a building block for more complex graph 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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"## Algorithm\n",
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"\n",
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"### Node\n",
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"\n",
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"Node will keep track of its:\n",
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"* id\n",
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"* visit state\n",
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"* incoming edge count (useful for algorithms such as topological sort)\n",
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"* adjacent nodes and edge weights\n",
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"\n",
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"#### add_neighhbor\n",
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"\n",
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"* If the neighbor doesn't already exist as an adjacent node\n",
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" * Update the adjancet nodes and edge weights\n",
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" * Increment the neighbor's incoming edge count\n",
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"\n",
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"Complexity:\n",
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"* Time: O(1)\n",
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"* Space: O(1)\n",
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"\n",
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"#### remove_neighhbor\n",
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"\n",
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"* If the neighbor exists as an adjacent node\n",
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" * Decrement the neighbor's incoming edge count\n",
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" * Remove the neighbor as an adjacent node\n",
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"\n",
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"Complexity:\n",
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"* Time: O(1)\n",
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"* Space: O(1)\n",
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"\n",
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"### Graph\n",
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"\n",
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"Graph will keep track of its:\n",
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"* nodes\n",
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"\n",
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"#### add_node\n",
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"\n",
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"* If node already exists, return it\n",
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"* Create a node with the given id\n",
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"* Add the newly created node to the collection of nodes\n",
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"\n",
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"Complexity:\n",
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"* Time: O(1)\n",
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"* Space: O(1)\n",
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"\n",
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"#### add_edge\n",
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"\n",
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"* If the source node is not in the collection of nodes, add it\n",
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"* If the dest node is not in the collection of nodes, add it\n",
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"* Add a connection from the source node to the dest node with the given edge weight\n",
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"\n",
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"#### add_undirected_edge\n",
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"\n",
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"* Call add_edge\n",
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"* Also add a connection from the dest node to the source node with the given edge weight\n",
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"\n",
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"Complexity:\n",
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"* Time: O(1)\n",
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"* Space: O(1)"
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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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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Overwriting graph.py\n"
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]
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}
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],
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"source": [
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"%%writefile graph.py\n",
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"from enum import Enum # Python 2 users: Run pip install enum34\n",
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"\n",
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"\n",
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"class State(Enum):\n",
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" unvisited = 0\n",
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" visiting = 1\n",
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" visited = 2\n",
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"\n",
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"\n",
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"class Node:\n",
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"\n",
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" def __init__(self, key):\n",
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" self.key = key\n",
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" self.visit_state = State.unvisited\n",
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" self.incoming_edges = 0\n",
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" self.adj_nodes = {} # Key = key, val = Node\n",
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" self.adj_weights = {} # Key = key, val = weight\n",
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"\n",
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" def __repr__(self):\n",
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" return str(self.key)\n",
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"\n",
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" def __lt__(self, other):\n",
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" return self.key < other.key\n",
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"\n",
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" def add_neighbor(self, neighbor, weight=0):\n",
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" if neighbor is None or weight is None:\n",
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" raise TypeError('neighbor or weight cannot be None')\n",
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" neighbor.incoming_edges += 1\n",
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" self.adj_weights[neighbor.key] = weight\n",
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" self.adj_nodes[neighbor.key] = neighbor\n",
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"\n",
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" def remove_neighbor(self, neighbor):\n",
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" if neighbor is None:\n",
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" raise TypeError('neighbor cannot be None')\n",
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" if neighbor.key not in self.adj_nodes:\n",
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" raise KeyError('neighbor not found')\n",
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" neighbor.incoming_edges -= 1\n",
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" del self.adj_weights[neighbor.key]\n",
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" del self.adj_nodes[neighbor.key]\n",
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"\n",
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"\n",
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"class Graph:\n",
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"\n",
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" def __init__(self):\n",
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" self.nodes = {} # Key = key, val = Node\n",
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"\n",
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" def add_node(self, key):\n",
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" if key is None:\n",
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" raise TypeError('key cannot be None')\n",
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" if key not in self.nodes:\n",
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" self.nodes[key] = Node(key)\n",
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" return self.nodes[key]\n",
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"\n",
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" def add_edge(self, source_key, dest_key, weight=0):\n",
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" if source_key is None or dest_key is None:\n",
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" raise KeyError('Invalid key')\n",
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" if source_key not in self.nodes:\n",
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" self.add_node(source_key)\n",
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" if dest_key not in self.nodes:\n",
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" self.add_node(dest_key)\n",
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" self.nodes[source_key].add_neighbor(self.nodes[dest_key], weight)\n",
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"\n",
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" def add_undirected_edge(self, src_key, dst_key, weight=0):\n",
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" if src_key is None or dst_key is None:\n",
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" raise TypeError('key cannot be None')\n",
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" self.add_edge(src_key, dst_key, weight)\n",
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" self.add_edge(dst_key, src_key, weight)"
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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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"source": [
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"%run graph.py"
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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": 3,
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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_graph.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_graph.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 TestGraph(object):\n",
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"\n",
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" def create_graph(self):\n",
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" graph = Graph()\n",
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" for key in range(0, 6):\n",
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" graph.add_node(key)\n",
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" return graph\n",
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"\n",
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" def test_graph(self):\n",
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" graph = self.create_graph()\n",
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" graph.add_edge(0, 1, weight=5)\n",
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" graph.add_edge(0, 5, weight=2)\n",
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" graph.add_edge(1, 2, weight=3)\n",
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" graph.add_edge(2, 3, weight=4)\n",
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" graph.add_edge(3, 4, weight=5)\n",
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" graph.add_edge(3, 5, weight=6)\n",
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" graph.add_edge(4, 0, weight=7)\n",
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" graph.add_edge(5, 4, weight=8)\n",
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" graph.add_edge(5, 2, weight=9)\n",
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"\n",
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" assert_equal(graph.nodes[0].adj_weights[graph.nodes[1].key], 5)\n",
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" assert_equal(graph.nodes[0].adj_weights[graph.nodes[5].key], 2)\n",
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" assert_equal(graph.nodes[1].adj_weights[graph.nodes[2].key], 3)\n",
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" assert_equal(graph.nodes[2].adj_weights[graph.nodes[3].key], 4)\n",
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" assert_equal(graph.nodes[3].adj_weights[graph.nodes[4].key], 5)\n",
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" assert_equal(graph.nodes[3].adj_weights[graph.nodes[5].key], 6)\n",
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" assert_equal(graph.nodes[4].adj_weights[graph.nodes[0].key], 7)\n",
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" assert_equal(graph.nodes[5].adj_weights[graph.nodes[4].key], 8)\n",
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" assert_equal(graph.nodes[5].adj_weights[graph.nodes[2].key], 9)\n",
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"\n",
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" assert_equal(graph.nodes[0].incoming_edges, 1)\n",
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" assert_equal(graph.nodes[1].incoming_edges, 1)\n",
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" assert_equal(graph.nodes[2].incoming_edges, 2)\n",
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" assert_equal(graph.nodes[3].incoming_edges, 1)\n",
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" assert_equal(graph.nodes[4].incoming_edges, 2)\n",
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" assert_equal(graph.nodes[5].incoming_edges, 2)\n",
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"\n",
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" graph.nodes[0].remove_neighbor(graph.nodes[1])\n",
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" assert_equal(graph.nodes[1].incoming_edges, 0)\n",
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" graph.nodes[3].remove_neighbor(graph.nodes[4])\n",
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" assert_equal(graph.nodes[4].incoming_edges, 1)\n",
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"\n",
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" assert_equal(graph.nodes[0] < graph.nodes[1], True)\n",
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"\n",
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" print('Success: test_graph')\n",
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"\n",
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" def test_graph_undirected(self):\n",
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" graph = self.create_graph()\n",
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" graph.add_undirected_edge(0, 1, weight=5)\n",
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" graph.add_undirected_edge(0, 5, weight=2)\n",
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" graph.add_undirected_edge(1, 2, weight=3)\n",
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"\n",
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" assert_equal(graph.nodes[0].adj_weights[graph.nodes[1].key], 5)\n",
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" assert_equal(graph.nodes[1].adj_weights[graph.nodes[0].key], 5)\n",
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" assert_equal(graph.nodes[0].adj_weights[graph.nodes[5].key], 2)\n",
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" assert_equal(graph.nodes[5].adj_weights[graph.nodes[0].key], 2)\n",
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" assert_equal(graph.nodes[1].adj_weights[graph.nodes[2].key], 3)\n",
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" assert_equal(graph.nodes[2].adj_weights[graph.nodes[1].key], 3)\n",
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"\n",
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" print('Success: test_graph_undirected')\n",
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"\n",
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"\n",
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"def main():\n",
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" test = TestGraph()\n",
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" test.test_graph()\n",
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" test.test_graph_undirected()\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": 4,
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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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"Success: test_graph\n",
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"Success: test_graph_undirected\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_graph.py"
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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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