Java, C++, Python and a plethora of different programming languages implement the linked list data structure for storing information in a linear pattern.
Linked lists are basically information and elements that are stored in a linear format with their physical location not particularly described in memory.
Since the data in a Linked List is stored in a linear format, you will sometimes observe the formation of a Loop in a linked list data structure.
A loop in the context of a linked list can be found when the programmer is not able to locate the end of a list.
We have iterated further on the concept of removing loop in linked list further in the blog.
Linked lists and arrays are data structures that can be multi dimensional according to the requirements of the programmer.
Hence, in the context of arrays the term count inversions is used to refer to the number of steps it will take for an array to be sorted.
What is a Linked List?
The operations conducted by a linked list can be defined by the fact that each node or element in a linked list contains the address for the adjacent element within the chain.
The objects within a linked list are stored on a random basis and in order to traverse a linked list you can follow a specific pointer.
The pointer system facilitates traversing a list in a systematic format. You can traverse a linked list in both the ascending or the descending order.
Since the structure of a linked list resembles a linear pattern, it is very common to spot loops.
This makes traversing the linked list more complicated and difficult than usual.
If there is a presence of a Loop in a linked list, it means that the list has no end and also by default no beginning.
Take a look at some of the algorithms that you can apply for detecting a loop in a linked list.
How do you determine the presence of a Loop in a Linked List?
Follow the algorithms mentioned below to check the presence of a Loop in a given linked list:
Problem statement:
You have been given a linked list. Check whether the list consists of a Loop or not.
Method 1:
Hashing algorithm
According to this approach the programmer is required to construct a hashing table and traverse the list thoroughly by analysing each element.
The constructed hashmap requires you to start placing elements and node addresses within the hash table.
If by chance you encounter a NULL statement then you can confirm that the linked list is free of any sort of loops.
But, on the other hand if you figure out that any of the elements within the node is pointing towards a specific address for an adjacent node, it will be considered as a loop.
Time complexity: You are only required to traverse the node once for this algorithm hence, it optimises time in an efficient manner.
Method 2:
Modification of the hashing algorithm
You can modify the hashing algorithm and solve it without using a hashmap. Use the following steps for modifying the basic linked list structure:
- Use a flag or a pointer for each node that you visit.
- Traverse the whole list and keep visiting each node and its adjacent node as well.
- If you find repeating nodes then you can make sure that the linked list certainly consists of a Loop.
- This algorithm can work with the O(n) time complexity but certainly require a few additional information with each node.
- Now, as we have mentioned in the title of this approach. You can modify this approach without having to change the data structure by using a variation of a hashmap.
- All you have to do is start storing the addresses for the nodes within the hashmap and mark the addresses as visited
In case there is a presence of a Loop you will find that the same address is inputted within the hashmap twice. After finding this output, print the statement as true and your program will be executed.
Time complexity: Since we are dealing with a linked list in the given set of data, you will observe that the time complexity for the algorithm is the same as the last method.
You are only required to traverse the list once in order to find the placement of the loop.
Method 3:
Flood’s cycle finding approach
This algorithm makes use of two different pointers for figuring out the target within a given set.
The Floyd’s cycle finding approach in the context of finding a loop within a given linked list can be explained as follows:
- Start by traversing the linked list using two different pointers.
- Start by moving the first pointer in a relatively slower pace than the second.
- You can detect the presence of a Loop if both the pointers arrive at the same address after traversing the whole list. If that is not the case then the given linked list contains absolutely no loops.
Time complexity: The time constraint for this algorithm is the same as the other approaches. This is because the linked list is a linear structure and you are only required to traverse the list once in order to detect the loop.
Method 4:
Marking the nodes
This is the last and probably the easiest approach that you can apply for figuring out the position of the potential loop in a given linked list.
In this approach you have to start with generating a temporary node while also using the pointer. Follow the steps mentioned below to apply this concept:
- Create a temporary node.
- Start traversing the node from the adjat node to the temporary node.
- Use a pointer to mark the address of each node and this way you can flag the nodes that have already been visited.
- Check out every node to make sure that they are pointing towards the temporary node or not. If that is the case then you may confirm that there is a presence of a Loop. Otherwise the program can be printed as NULL.
Time complexity: Here in this case you need to traverse the node twice.
Wrapping Up
Remove loop in linked list and the concept of count inversions in an array definitely initiate a close resemblance.
You will find that in both the procedures you will have to visit each element or node in order to figure out the target statement.
