quick review: https://excalidraw.com/#json=yHsjyn_at8jhO5O_-nNez,tKSX3kQ7fyfgVbTr0UYyKg

bfs

BFS: for graph traversal

• take graph, start_vertex

• make a visited list or set to keep track of visited nodes

• make a queue list to keep track of the nodes orders

• put the start node in queue

• while the queue is not empty run the following:

• let n = front node of the queue i.e. 1st element in queue

• pop the front node from the queue

• check if n is in visited list or not

• if no then add n into visited list and print n

• let neighbors = neighbors nodes of n

• for each neighbor of n do:

• if the neighbor is not in visited list add them in queue list so that they we can pop it and visit it

• done

BFS: for graph traversal

• take graph, start_vertex

• make a visited list or set to keep track of visited nodes

• make a queue list to keep track of the nodes orders

• put the start node in visited

• put the start node in queue

• while the queue is not empty run the following:

• let n = front node of the queue i.e. 1st element in queue

• pop the front node from the queue

• check if n is in visited list or not

• if no then add n into visited list and print n

• let neighbors = neighbors nodes of n

• for each neighbor of n do:

• if the neighbor is not in visited list add them in queue list so that they we can pop it and visit it

• and add the neighbor in visited list also

• done

recursive_best-first_search

Recursive-Best-First Search (BFS) algorithm to find the optimal path from a given source node to a target node in a graph.

Theory:

• The Best-First Search algorithm is a heuristic-based search algorithm that explores the graph by always selecting the node that appears to be closest to the target based on the heuristic function (the H_dist dictionary in this case).
• The algorithm continues to explore the graph until it finds the target node or exhausts all possible paths.

Here's a detailed explanation of the code:

1. Imports:

from queue import PriorityQueue: This line imports the PriorityQueue class from the queue module, which is used to maintain the priority queue during the search.

---

2. Heuristic Distances (H_dist):

This dictionary stores the heuristic distances (estimated costs) for each node in the graph. The heuristic distance is used to guide the search towards the target node.

---

3. Graph Representation (Graph_nodes):

This dictionary represents the graph, where each key is a node, and the value is a list of its neighboring nodes and their corresponding costs.

---

4. Recursive Best-First Search (recursive_best_first_search):

This function implements the recursive version of the Best-First Search algorithm.

• Parameters:

  • graph: The graph representation.
  • current_node: The current node being explored.
  • target: The target node to be reached.
  • visited: A set of visited nodes to avoid revisiting them.
  • current_cost: The current cost of the path from the source to the current node.
  • parent: A dictionary to keep track of the parent of each node in the path.

---

6. Base case:

If the current node is the target node, the function reconstructs the optimal path, prints it, and the total cost, and returns True.

---

7. Recursive case:

• The function adds the current node to the visited set.
• It retrieves the list of neighbors for the current node from the graph.
• The neighbors are sorted based on the sum of the current cost, the cost to reach the neighbor, and the heuristic distance to the target.
• The function recursively explores each unvisited neighbor, updating the parent dictionary and the total cost.
• If the recursive call returns True, the function returns True to indicate that the target has been found.
• If the recursive call returns False, the function backtracks by removing the neighbor from the parent dictionary.
• The function returns False if the target node is not found.

---

8. Best-First Search (best_first_search):

This function is the entry point for the Best-First Search algorithm.

• Parameters:

  • graph: The graph representation.
  • source: The source node.
  • target: The target node.
• The function initializes the visited set and the parent dictionary, with the source node as the root.
• It calls the recursive_best_first_search function with the initial parameters and starts the search.

---

6. Execution:

• The code calls the best_first_search function with the Graph_nodes graph, the source node 'S', and the target node 'G'.

for more details: https://zzzcode.ai/python/code-explain?id=c418ff37-1572-416b-8a4d-19993106c1f4

calculations:,

Start state: S

• From 'S' we can go to 'A' and 'g'

• For S -> A: f(n) => g(n) + h(n) => 1 + 3 => 4

• For S -> g: f(n) => g(n) + h(n) => 10 + 0 => 10

• We see that the path with less f(n) is S -> A

• So hold S -> g , and let h1 = 10

• From 'A' we can go to 'B' and 'C'

• For S -> A -> B: f(n) = g(n) + h(n) => 3 + 4 => 7

• For S -> A -> C: f(n) = g(n) + h(n) => 2 + 2 => 4

• By comparing both f(n), we see that the path S -> A -> C has less f(n)

• So, hold S -> A -> B, and let h2 = 7

• From 'C' we can go to 'D' and 'g':

• For S -> A -> C -> D: f(n) = g(n) + h(n) => 5 + 6 => 11

• For S -> A -> C -> g: f(n) = g(n) + h(n) => 6 + 0 => 6

• By comparing both f(n), we see that the path S -> A -> C -> g has less f(n)

• So, hold S -> A -> C -> D, let h3 = 11

• we have reached our final destination node or goal node

• so let x = f(n) for S -> A -> C -> g

• we check whether any holded f(n) is less than x

• therefore,

h1 < x => 10 < 6 => false

h2 < x => 7 < 6 => false

h3 < x => 11 < 6 => false

• Therefore, the optimal path is S -> A -> C -> g and the path cost is 6