【北大是如何考DFS的】【我们一起60天准备考研算法面试（大全）-第十六天 16/60】【DFS】

**北大是如何考DFS的**

在北大的计算机系考研算法面试中，深度优先搜索（Depth-First Search, DFS）是一个常见且重要的题目。下面我们将一起探讨北大是如何考DFS的，以及如何准备考研算法面试中的DFS题目。

**什么是DFS**

DFS是一种图论和树论中用于遍历图或树的算法。它通过递归地访问图或树中的每个节点来实现。DFS有两种基本类型：前序 DFS 和后序 DFS。

**北大考DFS的常见题目**

在北大的计算机系考研面试中，DFS通常会出现在以下几类题目中：

1. **查找路径**:给定两个图或树中的节点，要求找到从第一个节点到第二个节点的最短路径。
2. **检测环**:给定一个图或树，要求检测是否存在环路。
3. **寻找祖先**:给定一个图或树中的节点和一个目标值，要求找到该值在图或树中的所有祖先节点。

**如何准备考研算法面试中的DFS题目**

为了准备考研算法面试中的DFS题目，我们需要掌握以下几点：

1. **理解DFS的基本概念**:熟悉DFS的定义、前序 DFS 和后序 DFS 的区别，以及 DFS 的应用场景。
2. **掌握DFS的实现方法**:了解如何使用递归或迭代来实现 DFS，包括如何处理图或树中的边和节点。
3. **练习DFS题目**:通过大量的练习来熟悉 DFS 的各种应用场景和实现方法。

**DFS 的代码示例**

下面是几个 DFS 的代码示例：

### 前序 DFS

def preorder_dfs(graph, start):
 """
 Perform a pre-order DFS on the graph starting from the given node.

 Args:
 graph (dict): The graph represented as an adjacency list.
 start (node): The node to start the DFS from.

 Returns:
 A list of nodes in the order they were visited.
 """
 visited = set()
 result = []

 def dfs(node):
 visited.add(node)
 result.append(node)
 for neighbor in graph[node]:
 if neighbor not in visited:
 dfs(neighbor)

 dfs(start)
 return result

def postorder_dfs(graph, start):
 """
 Perform a post-order DFS on the graph starting from the given node.

 Args:
 graph (dict): The graph represented as an adjacency list.
 start (node): The node to start the DFS from.

 Returns:
 A list of nodes in the order they were visited.
 """
 visited = set()
 result = []

 def dfs(node):
 visited.add(node)
 for neighbor in graph[node]:
 if neighbor not in visited:
 dfs(neighbor)
 result.append(node)

 dfs(start)
 return result

def find_path(graph, start, end):
 """
 Find the shortest path between two nodes in a graph.

 Args:
 graph (dict): The graph represented as an adjacency list.
 start (node): The starting node.
 end (node): The ending node.

 Returns:
 A list of nodes representing the shortest path from start to end.
 """
 visited = set()
 queue = [(start, [start])]

 while queue:
 node, path = queue.pop(0)
 if node == end:
 return path for neighbor in graph[node]:
 if neighbor not in visited:
 queue.append((neighbor, path + [neighbor]))
 visited.add(neighbor)

 return None

def has_cycle(graph):
 """
 Detect whether a graph contains a cycle.

 Args:
 graph (dict): The graph represented as an adjacency list.

 Returns:
 True if the graph contains a cycle, False otherwise.
 """
 visited = set()
 recursion_stack = set()

 def dfs(node):
 visited.add(node)
 recursion_stack.add(node)

 for neighbor in graph[node]:
 if neighbor not in visited:
 if dfs(neighbor):
 return True elif neighbor in recursion_stack:
 return True recursion_stack.remove(node)
 return False for node in graph:
 if node not in visited and dfs(node):
 return True return False

def find_ancestors(graph, target_value):
 """
 Find all ancestors of a given value in a graph.

 Args:
 graph (dict): The graph represented as an adjacency list.
 target_value: The value to find ancestors for.

 Returns:
 A set of values representing the ancestors of the target value.
 """
 visited = set()
 result = set()

 def dfs(node):
 visited.add(node)
 result.add(node)

 for neighbor in graph[node]:
 if neighbor not in visited and neighbor != target_value:
 dfs(neighbor)

 for node in graph:
 if node != target_value:
 dfs(node)

 return result