def dfs(node):
if node in on_stack:
return False # Back-edge found (cycle)
if node in visited:
return True
on_stack.add(node)
visited.add(node)
for neighbor in graph.get(node, []):
if not dfs(neighbor):
return False
on_stack.remove(node)
return True
return all(dfs(node) for node in graph)
响应
def is_dag_dfs(graph):
"""
Determines if a directed graph is a Directed Acyclic Graph (DAG) using Depth-First Search (DFS).
Args:
graph (dict): A dictionary representing the graph. Keys are nodes, and values are lists of their neighbors.
Returns:
bool: True if the graph is a DAG, False otherwise.
"""
visited = set()
on_stack = set() # Track nodes on recursion stack
def dfs(node):
"""
Performs Depth-First Search starting from a given node.
Args:
node (object): The node to start the DFS from.
Returns:
bool: True if no cycle is detected, False otherwise.
"""
if node in on_stack:
return False # Back-edge found (cycle)
if node in visited:
return True
on_stack.add(node)
visited.add(node)
for neighbor in graph.get(node, []):
if not dfs(neighbor):
return False
on_stack.remove(node)
return True
return all(dfs(node) for node in graph)
