The Problem:

Ah! at last a classic linked list problem. In this problem, we are given a linked list and we have to reverse it and return its new head.

Before we begin trying to figure out a solution for this problem, let’s first revisit an important concepts Linked List and Recursion.

Understanding Recursion:

Recursion is essentially a function calling itself. It is frequently used to solve problems that can be divided into smaller, similar sub-problems and can be very useful in dynamic programming. To understand recursion, it can be helpful to break it down into 3 parts:

1. Base Condition: This condition prevents the recursive function from calling itself infinitely.
2. Recursive Call: This is responsible for calling the recursive function itself.
3. Small Calculation: This step, which can come before or after the Recursive Call, is responsible for performing some calculation that we need for the recursive function or for returning some result after a recursive call has been completed.

A recursive tree is a visual representation of the recursive calls made by a function. It can be very helpful in understanding how recursion works and in analyzing the time and space complexity of recursive algorithms.

Understanding Linked List:

A linked list is a linear data structure that consists of a sequence of nodes, each containing data and a reference to the next node in the list. It is often used as an alternative to arrays, as it can be more efficient in certain operations such as insertion and deletion.

To understand linked lists, it can be helpful to break it down into 3 parts:

1. Nodes: Each node in a linked list contains some data and a reference to the next node in the list.
2. Head: The head of a linked list is the first node in the list. It is used as the starting point for many operations on the list.
3. Traversal: Traversing a linked list involves starting at the head and following the references from one node to the next until the desired node is reached or the end of the list is reached.

Linked lists can be very useful in solving problems that involve dynamic data structures, as they allow for efficient insertion and deletion of elements. They can also be used in combination with other data structures, such as stacks and queues, to solve more complex problems.

Intuition & Algorithm:

With an understanding of how recursion and linked lists work, let’s try to break down the problem. We don’t need to create our own linked list data structure because it is already provided. This is a fairly straightforward problem, so we will begin by figuring out the base condition, which in this case would be when the recursion reaches the end of the linked list (head == None) or when there is only one node left (head.next == None). In either case, we simply return head.

We then call the function recursively on head.next and store the result in a variable called newNode. This will reverse all the nodes after head and return the new head of the reversed list. We then update the next node of head.next to point to head, effectively reversing the link between head and head.next. We also set head.next to None to avoid creating a cycle in the linked list.

Finally, we return newNode, which is the new head of the reversed linked list. Let's visualize the algorithm below.

Summary of Solution

Use recursion to reverse a linked list. Call the reverseList function recursively on head.next and store the result in a variable called newNode. Update the next node of head.next to point to head and set head.next to None. Return newNode as the new head of the reversed linked list.

Code

This can be translated to code in the following way:

# Definition for singly-linked list.
# class ListNode:
#     def __init__(self, val=0, next=None):
#         self.val = val
#         self.next = next
class Solution:
    def reverseList(self, head: Optional[ListNode]) -> Optional[ListNode]:
        if head == None or head.next == None:
            return head
        newNode = self.reverseList(head.next)
        nextNode = head.next
        nextNode.next = head
        head.next = None
        return newNode

• Time Complexity O(n)
• Space Complexity O(n)

The time complexity of this solution is O(n) This is because the function needs to traverse the linked lists to reverse it. Time taken for this operation would be proportional to the size of the linked list.

Space complexity is O(n) because of recursion call stack.

This approach is simple and efficient, making it a good solution to this problem.

I hope you enjoyed this post. Stay tuned for daily LeetCode blog posts!