The Question

Reverse Linked List

Given the head of a singly linked list, reverse the list in-place and return the head of the reversed list. You should implement the solution with $O(1)$ auxiliary space and $O(n)$ time complexity. Consider both iterative and recursive approaches, noting the trade-offs between them. Constraints: - The number of nodes in the list is in the range [0, 5000]. - Node values are between -5000 and 5000.

C++

Iterative Pointer Reversal

Singly Linked List

Questions & Insights

Clarifying Questions

Input Constraints: What is the maximum number of nodes in the list? (Assumption: Up to 5,000 nodes, which fits well within

O(n)

time complexity).

Memory Management: Should the reversal be performed in-place by modifying the next pointers, or are we allowed to allocate new nodes? (Assumption: In-place reversal is the standard expectation to achieve

O(1)

auxiliary space).

Edge Cases: How should the function behave for an empty list (nullptr) or a single-node list? (Assumption: Return the original head as is).

Recursion vs. Iteration: Is there a preference for an iterative approach over a recursive one? (Assumption: Iterative is generally preferred in production to avoid stack overflow for large lists, though recursive is mathematically elegant).

Thinking Process

Pointer Manipulation: To reverse a linked list, we need to flip the direction of each next pointer. Because changing curr->next breaks the link to the rest of the list, we must store the reference to the next node before modifying the current one.

Three-Pointer Strategy: Use three pointers: prev (initially nullptr), curr (initially head), and next_node (temporary).

Loop Invariant: At each step of the iteration, the sub-list from the original head to prev is already reversed, and curr points to the head of the remaining sub-list to be processed.

Termination: The loop terminates when curr becomes nullptr. At this point, prev points to the new head of the reversed list.

Implementation Breakdown

Problem Set

Functional Requirements: Reverse a singly linked list in-place.

Constraints:

Number of nodes:

[0, 5000]

Node value:

[-5000, 5000]

Time Complexity:

O(n)

Space Complexity:

O(1)

for iterative,

O(n)

for recursive (due to stack frames).

Approach

Algorithm: Iterative Pointer Reversal.

Data Structure: Singly Linked List.

Complexity:

Time:

O(n)

where

n

is the number of nodes.

Space:

O(1)

as we only use a constant amount of extra pointers.

Implementation

Wrap Up

Advanced Topics

Recursion vs. Iteration: In C++, the recursive solution is susceptible to stack overflow if the linked list length exceeds the stack limit. While many compilers perform Tail Call Optimization (TCO), the standard recursive reversal is not strictly tail-recursive without a helper function passing the prev pointer.

Memory Safety: In a real-world system using raw pointers, we must be certain of ownership. If this list were managed by std::unique_ptr, the reversal logic would need to use std::move to transfer ownership of the nodes safely.

Thread Safety: Linked list reversal is not thread-safe. In a multi-threaded environment, the list should be protected by a mutex or redesigned using persistent data structures (functional programming style) to avoid side effects.