This code implements the **Breadth-First Search (BFS)** algorithm to traverse...

June 28, 2025 at 08:21 AM

graph={"A":["B","C"],"B":["D","E","F"],"C":["G","E","I"],"D":["J"],"E":["K"],"F":["L"],"G":["M"],"H":["N"],"I":["O"],"J":[],"K":[],"L":[],"M":[],"N":[],"O":[]} def bfs(graph,start): open=[start] close=[] while open: node=open.pop(0) if node not in close: close.append(node) neighbour=graph[node] for i in neighbour: open.append(i) return close print(bfs(graph,"A"))

This code implements the Breadth-First Search (BFS) algorithm to traverse a graph. It takes a graph represented as an adjacency list (stored in the dictionary graph) and a starting node (start), and returns the BFS traversal order of the graph's nodes.

Here is the step-by-step explanation of the code:

  1. Graph Representation: The dictionary graph defines a directed graph as an adjacency list. For example, the key "A" corresponds to a list of its neighbors ["B", "C"]. Similarly, other nodes (e.g., "B", "C", etc.) have their own neighbors defined, while some nodes (e.g., "J", "K", etc.) are terminal nodes with no neighbors.

  2. BFS Function:

    • The function bfs(graph, start) accepts the graph and a starting node.
    • It initializes:
      • open, a queue (list) containing the node to process, starting with the "start" node.
      • close, a list storing the nodes that have already been visited.
    • The while open loop continues as long as there are nodes to process in the open queue.
    • The first node in open is removed using pop(0), and if it has not already been visited (not in close), it is added to the close list.
    • Then, all neighbors of the current node (from graph[node]) are appended to the open queue to be visited later.
    • This repeats until the open queue is empty, at which point every reachable node has been visited in BFS order.
  3. Return Statement: After the traversal, the list close contains the order of nodes visited in BFS.

  4. Execution & Output: The graph traversal starts from node "A" (bfs(graph, "A")). The BFS traversal visits nodes level by level in the graph. The returned result is the order in which the nodes are visited.

Output Explanation: The traversal for this graph from node "A" proceeds as follows:

  • Start with open = ["A"], close = [].
  • Visit node "A". Add its neighbors ("B", "C") to the open queue: open = ["B", "C"], close = ["A"].
  • Visit node "B". Add its neighbors ("D", "E", "F") to the open queue: open = ["C", "D", "E", "F"], close = ["A", "B"].
  • Visit node "C". Add its neighbors ("G", "E", "I") to the open queue: open = ["D", "E", "F", "G", "E", "I"], close = ["A", "B", "C"].
  • Visit node "D". Add its neighbor ("J") to the open queue: open = ["E", "F", "G", "E", "I", "J"], close = ["A", "B", "C", "D"].
  • Visit node "E". Add its neighbor ("K") to the open queue: open = ["F", "G", "E", "I", "J", "K"], close = ["A", "B", "C", "D", "E"].
  • Visit node "F". Add its neighbor ("L") to the open queue: open = ["G", "E", "I", "J", "K", "L"], close = ["A", "B", "C", "D", "E", "F"].
  • Visit node "G". Add its neighbor ("M") to the open queue: open = ["E", "I", "J", "K", "L", "M"], close = ["A", "B", "C", "D", "E", "F", "G"].
  • Continue visiting nodes "E", "I", "J", "K", "L", and "M" in order.

The output is:

['A', 'B', 'C', 'D', 'E', 'F', 'G', 'I', 'J', 'K', 'L', 'M']
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