# Project 3: Map-based Routing Application

## Setting Up the Graph for the Map

Welcome to Project 3, where we will apply the principles of graph theory and algorithms to develop a map-based routing application. This project will integrate the concepts we've explored, particularly Dijkstra's algorithm, to calculate the shortest path between two points on a map. This kind of application has practical real-world uses, akin to the functionality seen in GPS navigation systems.

In this project, we will create a simplified version of a routing application. We'll construct a graph representing a map, where intersections and pathways are nodes and edges, respectively. The edges will have weights corresponding to distances or travel times. Our task will be to find the shortest path between two nodes using Dijkstra's algorithm.

The first step in our project is to set up a graph representing our map. We'll define a class for the graph and initialize it with nodes and edges.

**Graph Structure:**

We'll start by defining a class `Graph`

that will hold our map data. Each node in the graph will represent a location (like an intersection), and each edge will represent a pathway or road between these locations, with a weight indicating the distance or time to travel that edge.

**Example Code:**

`class Graph:`

def __init__(self):

self.nodes = set()

self.edges = defaultdict(list)

self.distances = {}

def add_node(self, value):

self.nodes.add(value)

def add_edge(self, from_node, to_node, distance):

self.edges[from_node].append(to_node)

self.distances[(from_node, to_node)] = distance

# Example Usage

graph = Graph()

graph.add_node("A")

graph.add_node("B")

graph.add_node("C")

graph.add_edge("A", "B", 1)

graph.add_edge("B", "C", 2)

graph.add_edge("A", "C", 4)

In this setup, we have nodes 'A', 'B', and 'C', with edges connecting them and corresponding distances.

## Setting Up the Graph for the Map

Welcome to Project 3, where we will apply the principles of graph theory and algorithms to develop a map-based routing application. This project will integrate the concepts we've explored, particularly Dijkstra's algorithm, to calculate the shortest path between two points on a map. This kind of application has practical real-world uses, akin to the functionality seen in GPS navigation systems.

In this project, we will create a simplified version of a routing application. We'll construct a graph representing a map, where intersections and pathways are nodes and edges, respectively. The edges will have weights corresponding to distances or travel times. Our task will be to find the shortest path between two nodes using Dijkstra's algorithm.

The first step in our project is to set up a graph representing our map. We'll define a class for the graph and initialize it with nodes and edges.

**Graph Structure:**

We'll start by defining a class `Graph`

that will hold our map data. Each node in the graph will represent a location (like an intersection), and each edge will represent a pathway or road between these locations, with a weight indicating the distance or time to travel that edge.

**Example Code:**

`class Graph:`

def __init__(self):

self.nodes = set()

self.edges = defaultdict(list)

self.distances = {}

def add_node(self, value):

self.nodes.add(value)

def add_edge(self, from_node, to_node, distance):

self.edges[from_node].append(to_node)

self.distances[(from_node, to_node)] = distance

# Example Usage

graph = Graph()

graph.add_node("A")

graph.add_node("B")

graph.add_node("C")

graph.add_edge("A", "B", 1)

graph.add_edge("B", "C", 2)

graph.add_edge("A", "C", 4)

In this setup, we have nodes 'A', 'B', and 'C', with edges connecting them and corresponding distances.

## Setting Up the Graph for the Map

Welcome to Project 3, where we will apply the principles of graph theory and algorithms to develop a map-based routing application. This project will integrate the concepts we've explored, particularly Dijkstra's algorithm, to calculate the shortest path between two points on a map. This kind of application has practical real-world uses, akin to the functionality seen in GPS navigation systems.

In this project, we will create a simplified version of a routing application. We'll construct a graph representing a map, where intersections and pathways are nodes and edges, respectively. The edges will have weights corresponding to distances or travel times. Our task will be to find the shortest path between two nodes using Dijkstra's algorithm.

The first step in our project is to set up a graph representing our map. We'll define a class for the graph and initialize it with nodes and edges.

**Graph Structure:**

We'll start by defining a class `Graph`

that will hold our map data. Each node in the graph will represent a location (like an intersection), and each edge will represent a pathway or road between these locations, with a weight indicating the distance or time to travel that edge.

**Example Code:**

`class Graph:`

def __init__(self):

self.nodes = set()

self.edges = defaultdict(list)

self.distances = {}

def add_node(self, value):

self.nodes.add(value)

def add_edge(self, from_node, to_node, distance):

self.edges[from_node].append(to_node)

self.distances[(from_node, to_node)] = distance

# Example Usage

graph = Graph()

graph.add_node("A")

graph.add_node("B")

graph.add_node("C")

graph.add_edge("A", "B", 1)

graph.add_edge("B", "C", 2)

graph.add_edge("A", "C", 4)

In this setup, we have nodes 'A', 'B', and 'C', with edges connecting them and corresponding distances.

## Setting Up the Graph for the Map

**Graph Structure:**

`Graph`

that will hold our map data. Each node in the graph will represent a location (like an intersection), and each edge will represent a pathway or road between these locations, with a weight indicating the distance or time to travel that edge.

**Example Code:**

`class Graph:`

def __init__(self):

self.nodes = set()

self.edges = defaultdict(list)

self.distances = {}

def add_node(self, value):

self.nodes.add(value)

def add_edge(self, from_node, to_node, distance):

self.edges[from_node].append(to_node)

self.distances[(from_node, to_node)] = distance

# Example Usage

graph = Graph()

graph.add_node("A")

graph.add_node("B")

graph.add_node("C")

graph.add_edge("A", "B", 1)

graph.add_edge("B", "C", 2)

graph.add_edge("A", "C", 4)