递归返回链表的中间节点

Question

A Graph is a non-linear data structure consisting of nodes and edges. The nodes are sometimes also referred to as vertices and the edges are lines or arcs that connect any two nodes in the graph. More formally a Graph can be defined as

Answer 1

Recursion is a poor choice for operating on linked lists. Almost always use a loop, which is simple to reason about, has less overhead and doesn't limit the size of the list to the call stack. It's easier to access and manipulate surrounding elements iteratively.

Getting the midpoint of a linked list is easy iteratively: keep two references to the head, then move one twice as fast as the other until the fast reference reaches the end of the list. The slow pointer will point to the middle node. The two-pointer technique is one of the fundamental tools for working with linked lists.

from collections import namedtuple

def middle_node(fast):
    slow = fast

    while fast and fast.next:
        fast = fast.next.next
        slow = slow.next

    return slow

if __name__ == "__main__":
    Node = namedtuple("Node", "val next")
    odd = Node(0, Node(1, Node(2, Node(3, Node(4, None)))))
    even = Node(0, Node(1, Node(2, Node(3, Node(4, Node(5, None))))))
    print(middle_node(odd).val) # => 2
    print(middle_node(even).val) # => 3

You can do this recursively using the exact same methodology: a fast and a slow reference. Here's an example that plugs into the above boilerplate:

def middle_node(fast, slow=None):
    if not slow:
        slow = fast

    if fast and fast.next:
        return middle_node(fast.next.next, slow.next)

    return slow

For odd-length lists with two middle elements, these methods always return the one closer to the tail, but you can add an additional fast.next.next check to the base case or loop termination conditional to return the middle element closer to the head if you need.

You can see the recursive version offers no benefits in readability or elegance to justify the added overhead and size restrictions it imposes. Recursion is better suited for nonlinear nested structures like trees where the data is wide (meaning the call stack is much more able to hold the data without overflowing). The nonlinear nature of trees makes it very awkward to use a loop and explicit stack to handle certain typical traversals.

Answer 2

The reason why this prints the right value but changing the print to a return statement doesn't work is because you don't return the node in your base case. So when you find the mid point and return the node, the previous node does not return anything or utilize the result of the recursive step. Here is a modification that will utilize the result from your recursive step and return it down the call chain.

I'm not entirely convinced you midpoint calculation was correct in every case (case of 3 nodes will return node 1 in stead of node 2) so I have modified it slightly.

def find_mid(self, node, ret_count, ):
    if node.next == None:
        self.len += 1
        return None
    else:
        self.len += 1
        # return_node will either be the midpoint if we have found it, or None if we are still searching
        return_node = self.find_mid(node.next, ret_count + 1)

        # We have found the midpoint no need to check ret_count anymore
        if return_node:
            return return_node

    # If we make it here we have not found the midpoint node but have counted the total number of Nodes.
    # Set midpoint assuming an even number of nodes
    midpoint = int(self.len/2)
    # If odd number of nodes set midpoint accordingly
    if self.len % 2 != 0:
        midpoint = int((self.len+1)/2)

    # Check if the current node is the midpoint (len = 3 or len = 4 results in node 2 being midpoint
    if ret_count == midpoint:
        # Return the node
        return node
    else:
        # Potentially not necessary but will ensure that non-midpoint recursive steps return None
        return None

Answer 3

Recursion is a great choice for processing linked lists because linked lists are recursive data structures. Recursion allows our program's structure to match that of our data's structure -

# linked_list.py

empty = None

class node:
  def __init__(self, value, next = None):
    self.value = value
    self.next = next

def to_str(t = empty):
  if not t:
    return "None"
  else:
    return f"{t.value} -> {to_str(t.next)}"

def middle(t = empty):
  def loop(t, ff):
    if not t:
      return None
    elif ff and ff.next:
      return loop(t.next, ff.next.next)
    else:
      return t.value
  return loop(t, t)

Let's get some output from our basic building blocks -

# main.py

from linked_list import node, to_str, middle

t1 = node(1, node(2, node(3)))
t2 = node(1, node(2, node(3, node(4))))
t3 = node(1, node(2, node(3, node(4, node(5)))))

print(to_str(t1)) # 1 -> 2 -> 3 -> None
print(to_str(t2)) # 1 -> 2 -> 3 -> 4 -> None
print(to_str(t3)) # 1 -> 2 -> 3 -> 4 -> 5 -> None

print(middle(t1)) # => 2
print(middle(t2)) # => 3
print(middle(t3)) # => 3

Wrapping up the functional module in a class makes it feel more pythonic -

# linked_list.py

empty = # ...

class node # ...

def to_str # ...

def middle # ...

def from_list(l = []):
  if not l:
    return empty
  else:
    return node(l[0], from_list(l[1:]))

class linked_list:
  def __init__(self, root = None):
    self.root = root
  def __str__(self):
    return to_str(self.root)
  def middle(self):
    return middle(self.root)
  def from_list(l = []):
    return linked_list(from_list(l))

Now we get all the benefits of a functional-style module with the conveniences of an oop-style interface -

from linked_list import linked_list

t1 = linked_list.from_list([1, 2, 3])
t2 = linked_list.from_list([1, 2, 3, 4])
t3 = linked_list.from_list([1, 2, 3, 4, 5])

print(t1) # 1 -> 2 -> 3 -> None
print(t2) # 1 -> 2 -> 3 -> 4 -> None
print(t3) # 1 -> 2 -> 3 -> 4 -> 5 -> None

print(t1.middle()) # => 2
print(t2.middle()) # => 3
print(t3.middle()) # => 3