One Pager Cheat Sheet

• To detect a loop in a linked list, implement a detectLoop method to take the linked list head node as the parameter and return true or false accordingly with the constraints of time and space complexities of O(n) and O(1), respectively.
• A walk is a path through a graph that can either be simple or multiple, and a cycle is a closed walk with no vertex/edge repetitions, starting and ending at the same vertex.
• A brute force solution to detect a loop in a linked list might be to manually traverse each node and check if there is any node that has a next pointer to a previous node.
• We can use a nested loop to check for cycles in a graph by keeping track of the previously-encountered vertices.
• We can solve this problem by nested traversal, which requires us to traverse each node and then re-traverse the nodes already visited in the outer loop to identify any nodes that have been repeated.
• The optimized algorithm only needs two pointers to traverse the graph, with constant space complexity, to detect any duplicate nodes.
• A Linked List is a linear data structure composed of multiple nodes, each containing data and a pointer to the next node, allowing for efficient insertion, deletion, and navigation.
• The key advantage of an array over a linked list is that it is much faster to access an element due to its contiguous block of memory, allowing random access with a calculatable memory address, contrasted with the nodes and pointers of linked lists, which requires node traversal.
• A doubly linked list provides efficient traversal both forward and backward compared to a singly linked list, which only offers forward traversal.
• By using two pointers to traverse the linked list - one slow and one fast - we can detect whether there is a loop present.
• Floyd's Cycle-Finding Algorithm is a well-known Computer Science technique used to detect if there is a loop in a linked list by moving two pointers at different speeds through the list.
• Two pointers will meet in a fixed-length cycle due to their distance increase of 1 per iteration, resulting in an O(1) space complexity.
• The algorithm has a time complexity of O(n), as it traverses the array n times to reach its end.
• Hybrid linked list is a combination of different types of linked lists to create a unique list, rather than an existing type of linked list.
• A circular linked list has a pointer from the last node to the first node, forming a loop rather than a NULL pointer.
• A circular linked list provides an infinite loop-like structure in which each node contains the address of the next node, eliminating the need for a null pointer.
• The time complexity to add an element to a linked list is O(n) due to the need to traverse the entire list to find the null pointer.

This is our final solution.

To visualize the solution and step through the below code, click Visualize the Solution on the right-side menu or the VISUALIZE button in Interactive Mode.

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}

var assert = require('assert');

​

function detectLoop(head) {

  let pointer1, pointer2;

  pointer1 = head;

  pointer2 = head;

​

  while (pointer2.next.next) {

    pointer1 = pointer1.next;

    pointer2 = pointer2.next.next;

​

    if (pointer1 == pointer2) {

      return true;

    }

  }

  return false;

}

​

function Node(val) {

  this.val = val;

  this.next = null;

}

​

function LinkedListNode(val) {

  this.val = val;

  this.next = null;

}

​

var list1 = new LinkedListNode(3);

var nodes1 = [4, 5, 6, 7, 8, 9, 10];

createNodes(list1, nodes1);

​

Great job getting through this. Let's move on.

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