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Graph Traversal with BFS and DFS

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Your question is Graph Traversal with BFS and DFS. Start with the requirements on the right.

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Problem

At Notion, graph traversal is used to explore dependency graphs and connected components. Given a graph as an adjacency list and a starting node, implement both Breadth-First Search (BFS) and Depth-First Search (DFS) and return the order in which nodes are visited.

Formal Specification

Write a function graph_traversals(graph, start) where:

  • graph is a dictionary mapping each node to a list of its neighbors
  • start is the node where traversal begins
  • Return a dictionary with two keys:
    • "bfs": list of nodes visited in BFS order
    • "dfs": list of nodes visited in DFS preorder

If start is not in the graph, return { "bfs": [], "dfs": [] }.

Traverse neighbors in the order they appear in the adjacency list.

Constraints

  • 0 <= len(graph) <= 10^4
  • 0 <= total number of edges <= 2 * 10^4
  • Graph may be directed and may contain cycles
  • Node values are hashable
  • Neighbors should be visited in the order they appear in each adjacency list

Function Signature

def graph_traversals(graph, start):
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