The shortest path problem is a fundamental problem in graph theory, where the goal is to find the shortest path between two nodes in a graph.
In the context of robotics and computer vision, the shortest path can represent the optimal route that a robot or camera should take to reach a target location while avoiding obstacles. This is crucial for path planning and navigation tasks.
To find the shortest path, we can use algorithms such as Dijkstra's algorithm or A* algorithm. These algorithms explore the graph to determine the shortest path based on the weights of the edges.
Here's an example of Python code that finds the shortest path between two nodes in a graph using Dijkstra's algorithm:
PYTHON
1if __name__ == '__main__':
2 # Python code for finding the shortest path
3 from collections import defaultdict, deque
4
5 class Graph:
6 def __init__(self):
7 self.adj_list = defaultdict(list)
8
9 def add_edge(self, source, destination, weight):
10 self.adj_list[source].append((destination, weight))
11
12 def shortest_path(self, start, end):
13 distances = {vertex: float('inf') for vertex in self.adj_list}
14 distances[start] = 0
15 previous_vertices = {}
16 queue = deque([start])
17
18 while queue:
19 current_vertex = queue.popleft()
20
21 for neighbor, edge_weight in self.adj_list[current_vertex]:
22 weight = distances[current_vertex] + edge_weight
23
24 if weight < distances[neighbor]:
25 distances[neighbor] = weight
26 previous_vertices[neighbor] = current_vertex
27 queue.append(neighbor)
28
29 path = []
30 current_vertex = end
31
32 while current_vertex != start:
33 path.append(current_vertex)
34 current_vertex = previous_vertices[current_vertex]
35
36 path.append(start)
37 path.reverse()
38
39 return path
40
41 # Create a graph
42 g = Graph()
43
44 # Add edges to the graph
45 g.add_edge('A', 'B', 5)
46 g.add_edge('A', 'C', 3)
47 g.add_edge('B', 'D', 2)
48 g.add_edge('C', 'D', 1)
49 g.add_edge('C', 'E', 6)
50 g.add_edge('D', 'E', 4)
51 g.add_edge('D', 'F', 8)
52 g.add_edge('E', 'F', 5)
53
54 # Find the shortest path between two nodes
55 shortest_path = g.shortest_path('A', 'F')
56
57 print('Shortest Path:')
58 print(' -> '.join(shortest_path))
xxxxxxxxxx
58
print(' -> '.join(shortest_path))
if __name__ == '__main__':
# Python code for finding the shortest path
from collections import defaultdict, deque
class Graph:
def __init__(self):
self.adj_list = defaultdict(list)
def add_edge(self, source, destination, weight):
self.adj_list[source].append((destination, weight))
def shortest_path(self, start, end):
distances = {vertex: float('inf') for vertex in self.adj_list}
distances[start] = 0
previous_vertices = {}
queue = deque([start])
while queue:
current_vertex = queue.popleft()
for neighbor, edge_weight in self.adj_list[current_vertex]:
weight = distances[current_vertex] + edge_weight
if weight < distances[neighbor]:
distances[neighbor] = weight
previous_vertices[neighbor] = current_vertex
queue.append(neighbor)
path = []
OUTPUT
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