AlgoDaily - Detect Loop in Linked List

Good morning! Here's our prompt for today.

What is the best way to find out if a linked list contains a loop? You're given the following data structure as the definition of a linked list node:

JAVASCRIPT

1class LinkedListNode {
2	constructor(val) {
3		this.val = val;
4		this.next = null;
5	}
6}

A loop or a cycle in graph theory is a path of nodes and edges where a node is reachable from itself.

Implement a detectLoop method that takes a linked list head node as the parameter and returns true or false depending on whether there's a cycle.

Constraints

Length of the linked list <= 10000
Value stored in each node will be between -1000000000 and 1000000000
Expected time complexity : O(n)
Expected space complexity : O(1)

Try to solve this here or in Interactive Mode.

How do I practice this challenge?

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    'PASSED: Assuming list1.head.next.next.next.next = list1.head, we can detect an artificial loop in the linked list'
 
var assert = require('assert');
​
function detectLoop(head) {
  // Fill in this method
  return head;
}
​
class LinkedListNode {
  constructor(val) {
    this.val = val;
    this.next = null;
  }
}
​
const list1 = new LinkedListNode(3);
const nodes = [4, 5, 6, 7, 8, 9, 10];
let head = list1;
for (let i = 0; i < nodes.length; i++) {
  const newNode = new LinkedListNode(nodes[i]);
  head.next = newNode;
  head = newNode;
}
list1.next.next.next.next.next.next = list1.next.next;
console.log(detectLoop(list1));
​
function Node(val) {
  this.val = val;
  this.next = null;
}

We'll now take you through what you need to know.

How do I use this guide?

Build your intuition. Is this statement true or false?

A walk is a sequence of at least two vertices where nodes and edges may repeat. A cycle is a sequence of at least two vertices where nodes and edges cannot repeat.

Press true if you believe the statement is correct, or false otherwise.

Image credit to https://www.includehelp.com

Usually linked lists end with a node with no next reference, but we're looking for a sequence with a next pointer to a previous node. What might be the brute force solution here?

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// 1 -> 3 <-> 5
//      |
//      7

In the above example, once we get to the second 3 node, how do we know we've got a cycle? We need some reference that we've previously encountered this vertex before.

What if we used a nested loop for tracking purposes? Let's take a look at what would happen in pseudocode:

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iterate through 1 -> 3 -> 5 -> 3 -> 7
  iterate through what we've seen so far

At outer loop node 1, we'd inner loop through 1.

At outer loop node 3, we'd inner loop through 1 -> 3.

At outer loop node 5, we'd inner loop through 1 -> 3 -> 5.

At outer loop node 3 again, we'd inner loop through 1 -> 3 -> 5 -> 3.

So the brute force way to do it is to conduct a nested traversal-- we can traverse all the nodes, and then at each iteration, traverse through the nodes already visited by the outer loop. In the inner loop, if we encounter a node twice, we know it's been repeated.

Build your intuition. Click the correct answer from the options.

The minimum number of pointers needed in the optimized algorithm is:

Click the option that best answers the question.

Try this exercise. Is this statement true or false?

A linked list is a linear data structure.

Press true if you believe the statement is correct, or false otherwise.

Build your intuition. Click the correct answer from the options.

Which of the following is an advantage of Arrays over Linked Lists?

Click the option that best answers the question.

Arrays can contain different types of data elements
Accessing an element in an array is faster
Insertions in Arrays is faster
Deletions in an Array is faster

Try this exercise. Fill in the missing part by typing it in.

In a doubly linked list, traversal can be preformed in ___ directions.

Write the missing line below.

The fastest method is to traverse the linked list using two pointers. This is a well known Computer Science technique: move one pointer by one node at a time, and the other pointer by two at a time.

If these pointers meet at the same node, then there's a loop. If the pointers don't meet, then the linked list doesn’t have a loop.

The intuition here is that the faster pointer will go through the entire list at least once, and will inevitably meet the slower node at the beginning again. If there is a loop, they'll eventually converge.

Let's test your knowledge. Fill in the missing part by typing it in.

The pointer algorithm that moves through a sequence at two different speeds is called ___.

Write the missing line below.

Another way to think about it, notice that the distance between the two pointers increase by 1 after every iteration (one travels by 2, one travels by 1, so the distance increases). The distance is always going to be original distance + distance increase each iteration (which is 1, 2, 3, ..). Because they are moving in a fixed-length cycle, they'll eventually meet.

The space complexity of the algorithm is O(1).

Are you sure you're getting this? Fill in the missing part by typing it in.

The time complexity of the above algorithm is __.

Write the missing line below.

Try this exercise. Click the correct answer from the options.

Which of the following is not a type of linked list?

Click the option that best answers the question.

doubly linked list
singly linked list
circular linked list
hybrid linked list

Are you sure you're getting this? Is this statement true or false?

In circular linked list, last node of the list points to the first node of the list.

Press true if you believe the statement is correct, or false otherwise.

Try this exercise. Fill in the missing part by typing it in.

A __ does not contain null pointer in any of its nodes

Write the missing line below.

Try this exercise. Fill in the missing part by typing it in.

Asymptotic time complexity to add an element in a linked list is ___.

Write the missing line below.

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);
​

Alright, well done! Try another walk-through.

If you had any problems with this tutorial, check out the main forum thread here.

Constraints

Try to solve this here or in Interactive Mode.

We'll now take you through what you need to know.

Build your intuition. Is this statement true or false?

Build your intuition. Click the correct answer from the options.

Click the option that best answers the question.

Try this exercise. Is this statement true or false?

Build your intuition. Click the correct answer from the options.

Click the option that best answers the question.

Try this exercise. Fill in the missing part by typing it in.

Let's test your knowledge. Fill in the missing part by typing it in.

Are you sure you're getting this? Fill in the missing part by typing it in.

Try this exercise. Click the correct answer from the options.

Click the option that best answers the question.

Are you sure you're getting this? Is this statement true or false?

Try this exercise. Fill in the missing part by typing it in.

Try this exercise. Fill in the missing part by typing it in.

One Pager Cheat Sheet

This is our final solution.

Alright, well done! Try another walk-through.

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