This code implements the **Breadth-First Search (BFS)** algorithm to traverse...
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:
-
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. -
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 theopen
queue. - The first node in
open
is removed usingpop(0)
, and if it has not already been visited (not inclose
), it is added to theclose
list. - Then, all neighbors of the current node (from
graph[node]
) are appended to theopen
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.
- The function
-
Return Statement: After the traversal, the list
close
contains the order of nodes visited in BFS. -
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']