To develop a code to find the shortest route from the source to the destination point using Dijkstra's shortest path algorithm.
Dijkstra's Algorithm finds the shortest path between a given node (which is called the "source node") and all other nodes in a graph. This algorithm uses the weights of the edges to find the path that minimizes the total distance (weight) between the source node and all other nodes.
Identify a location in the google map:
Select a specific number of nodes with distance
Import required packages.
Include each node and its distance separately in the dictionary data structure.
End of program.
%matplotlib inline
import matplotlib.pyplot as plt
import random
import math
import sys
from collections import defaultdict, deque, Counter
from itertools import combinations
import heapq
class Problem(object):
"""The abstract class for a formal problem. A new domain subclasses this,
overriding `actions` and `results`, and perhaps other methods.
The default heuristic is 0 and the default action cost is 1 for all states.
When yiou create an instance of a subclass, specify `initial`, and `goal` states
(or give an `is_goal` method) and perhaps other keyword args for the subclass."""
def __init__(self, initial=None, goal=None, **kwds):
self.__dict__.update(initial=initial, goal=goal, **kwds)
def actions(self, state):
raise NotImplementedError
def result(self, state, action):
raise NotImplementedError
def is_goal(self, state):
return state == self.goal
def action_cost(self, s, a, s1):
return 1
def __str__(self):
return '{0}({1}, {2})'.format(
type(self).__name__, self.initial, self.goal)
class Node:
"A Node in a search tree."
def __init__(self, state, parent=None, action=None, path_cost=0):
self.__dict__.update(state=state, parent=parent, action=action, path_cost=path_cost)
def __str__(self):
return '<{0}>'.format(self.state)
def __len__(self):
return 0 if self.parent is None else (1 + len(self.parent))
def __lt__(self, other):
return self.path_cost < other.path_cost
failure = Node('failure', path_cost=math.inf) # Indicates an algorithm couldn't find a solution.
cutoff = Node('cutoff', path_cost=math.inf) # Indicates iterative deepening search was cut off.
def expand(problem, node):
"Expand a node, generating the children nodes."
s = node.state
for action in problem.actions(s):
s1 = problem.result(s, action)
cost = node.path_cost + problem.action_cost(s, action, s1)
yield Node(s1, node, action, cost)
def path_actions(node):
"The sequence of actions to get to this node."
if node.parent is None:
return []
return path_actions(node.parent) + [node.action]
def path_states(node):
"The sequence of states to get to this node."
if node in (cutoff, failure, None):
return []
return path_states(node.parent) + [node.state]
class PriorityQueue:
"""A queue in which the item with minimum f(item) is always popped first."""
def __init__(self, items=(), key=lambda x: x):
self.key = key
self.items = [] # a heap of (score, item) pairs
for item in items:
self.add(item)
def add(self, item):
"""Add item to the queuez."""
pair = (self.key(item), item)
heapq.heappush(self.items, pair)
def pop(self):
"""Pop and return the item with min f(item) value."""
return heapq.heappop(self.items)[1]
def top(self): return self.items[0][1]
def __len__(self): return len(self.items)
def best_first_search(problem, f):
"Search nodes with minimum f(node) value first."
node = Node(problem.initial)
frontier = PriorityQueue([node], key=f)
reached = {problem.initial: node}
while frontier:
node = frontier.pop()
if problem.is_goal(node.state):
return node
for child in expand(problem,node):
s = child.state
if s not in reached or child.path_cost < reached[s].path_cost:
reached[s] = child
frontier.add(child)
return failure
def g(n):
return n.path_cost
cost = 1
return cost
class RouteProblem(Problem):
"""A problem to find a route between locations on a `Map`.
Create a problem with RouteProblem(start, goal, map=Map(...)}).
States are the vertexes in the Map graph; actions are destination states."""
def actions(self, state):
"""The places neighboring `state`."""
return self.map.neighbors[state]
def result(self, state, action):
"""Go to the `action` place, if the map says that is possible."""
return action if action in self.map.neighbors[state] else state
def action_cost(self, s, action, s1):
"""The distance (cost) to go from s to s1."""
return self.map.distances[s, s1]
def h(self, node):
"Straight-line distance between state and the goal."
locs = self.map.locations
return straight_line_distance(locs[node.state], locs[self.goal])
class Map:
"""A map of places in a 2D world: a graph with vertexes and links between them.
In `Map(links, locations)`, `links` can be either [(v1, v2)...] pairs,
or a {(v1, v2): distance...} dict. Optional `locations` can be {v1: (x, y)}
If `directed=False` then for every (v1, v2) link, we add a (v2, v1) link."""
def __init__(self, links, locations=None, directed=False):
if not hasattr(links, 'items'): # Distances are 1 by default
links = {link: 1 for link in links}
if not directed:
for (v1, v2) in list(links):
links[v2, v1] = links[v1, v2]
self.distances = links
self.neighbors = multimap(links)
self.locations = locations or defaultdict(lambda: (0, 0))
def multimap(pairs) -> dict:
"Given (key, val) pairs, make a dict of {key: [val,...]}."
result = defaultdict(list)
for key, val in pairs:
result[key].append(val)
return result
House_nearby_locations = Map(
{('Avadi', 'Pudur'): 7,('Pudur', 'Kallikupam'): 1,('Kallikupam' , 'Korattur'): 3,('Kallikupam' , 'Kolathur'): 5,('Korattur' , 'Villivakkam'): 3,
('Kolathur' , 'Villivakkam'): 2,('Korattur' , 'Mogappair'): 3,('Villivakkam' , 'Ayanavaram'): 3,('Mogappair' , 'Anna Nagar'): 4,('Anna Nagar' , 'Ayanavaram'): 3,
('Kolathur' , 'Perambur'): 2,('Perambur' , 'Ayanavaram'): 2,('Mogappair' , 'Koyambedu'): 3,('Koyambedu' , 'Chetpet'): 5,('Ayanavaram' , 'Chetpet'): 3,('Perambur' , 'Vyasarpadi'): 3,
('Vyasarpadi' , 'Tondiarpet'): 3,('Tondiarpet' , 'Royapuram'): 2,('Koyambedu' , 'T. Nagar'): 5,('T. Nagar' , 'Alwarpet'): 2,('Alwarpet' , 'Marina Beach'): 4,('Marina Beach' , 'Chetpet'): 5})
r0 = RouteProblem('Pudur', 'Mogappair', map=House_nearby_locations)
r1 = RouteProblem('Avadi', 'Kolathur', map=House_nearby_locations)
r2 = RouteProblem('Anna Nagar', 'T. Nagar', map=House_nearby_locations)
r3 = RouteProblem('Ayanavaram', 'Alwarpet', map=House_nearby_locations)
r4 = RouteProblem('Villivakkam', 'Royapuram', map=House_nearby_locations)
goal_state_path=best_first_search(r4,g)
print("GoalStateWithPath:{0}".format(goal_state_path))
path_states(goal_state_path)
print("Total Distance={0} Kilometers".format(goal_state_path.path_cost))
Dijkstra’s Algorithm is an algorithm for finding the shortest paths between nodes in a graph. For a given source node in the graph, the algorithm finds the shortest path between that node and every other node.
Thus a code was developed to find the shortest route from the source to the destination point using Dijkstra's shortest path algorithm.
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