Week 21 of 43
Core DSA
WEEK 21 LEARNING MODULE
Advanced Linked Lists: Doubly Linked Lists & Fast/Slow Pointers
Covers Doubly Linked Lists, in-place list reversal, Floyd's cycle-finding algorithm (Tortoise and Hare), and cycle entry detection.
4 Practice Problems4 Core ConceptsVerified Curriculum: high Confidence
What You'll Learn
- ✓Master Doubly Linked Lists supporting bidirectional traversal via `prev` and `next` pointers.
- ✓Reverse singly and doubly linked lists in-place in $O(n)$ time and $O(1)$ auxiliary memory.
- ✓Implement Floyd's Cycle Detection Algorithm to detect cycles in linked lists.
- ✓Derive the mathematical proof for finding the exact cycle entry node.
- ✓Verify palindrome linked lists in $O(n)$ time and $O(1)$ space.
Core Concepts
Doubly Linked List Mechanics
O(1) deletion with node refNodes maintaining both next and previous pointer references for O(1) bidirectional deletions.
In-place Pointer Reversal
O(n) time, O(1) spaceIteratively reversing next pointers using prev, curr, and next_node variables.
Floyd's Cycle-Finding Algorithm
O(n) time, O(1) spaceTortoise and Hare algorithm: slow moves 1 step, fast moves 2 steps; if they meet, a cycle exists.
Cycle Origin Mathematical Derivation
O(n)Resetting one pointer to head after collision and advancing both by 1 step finds the cycle start.
Algorithms Covered
In-place Linked List ReversalFloyd's Cycle DetectionCycle Entry Point FindingPalindrome Linked List Verification
Data Structures Applied
Singly Linked ListDoubly Linked List
“If you fell down yesterday, stand up today.”
— H. G. Wells