Find middle element in circular linked list

In the problem of finding the middle element in a circular linked list, we are dealing with a data structure called a circular linked list. A circular linked list is a variation of a traditional linked list where the last node points back to the first node instead of having a NULL reference. The challenge is to find the middle element of this circular linked list, which is not a trivial task due to the circular nature of the structure.

Problem Statement

Given a circular linked list, we need to find the middle element in the list. If the number of nodes in the list is odd, the middle element is the one exactly in the middle. If the number of nodes is even, there are two middle elements, and we can choose either of them as the middle element.

Example

Consider a circular linked list with the following elements: 1 -> 2 -> 3 -> 4 -> 5 -> 6 -> 7. The middle element in this case is 4.

Idea to Solve the Problem

To find the middle element in a circular linked list, we can use the "tortoise and hare" approach. In this approach, two pointers traverse the linked list at different speeds. The slower pointer (tortoise) moves one step at a time, while the faster pointer (hare) moves two steps at a time. When the faster pointer reaches the end of the list, the slower pointer will be at the middle element.

Pseudocode

Here's the pseudocode to find the middle element in a circular linked list using the "tortoise and hare" approach:

function findMiddle(circularLinkedList):
    if circularLinkedList.head is NULL:
        print "Empty Linked List"
    else:
        tortoise = hare = circularLinkedList.head
        while hare is not NULL and hare.next is not circularLinkedList.head:
            hare = hare.next.next
            tortoise = tortoise.next
        print "Middle Node is:", tortoise.data

Algorithm Explanation

1. Start with both the tortoise and hare pointers pointing to the head of the circular linked list.
2. Loop while hare is not NULL and hare.next is not pointing back to the head. This condition ensures that hare traverses the list twice as fast as tortoise.
3. In each iteration, move hare two steps ahead and tortoise one step ahead.
4. When the loop exits, tortoise will be at the middle element of the list.

Program List

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Resultant Output Explanation

For the provided example with the circular linked list: 1 -> 2 -> 3 -> 4 -> 5 -> 6 -> 7, the program will output:

Middle Node is : 4

This is the correct output since the middle element of the list is indeed 4.

Time Complexity

The time complexity of finding the middle element using the "tortoise and hare" approach is O(n), where n is the number of nodes in the circular linked list. This is because the faster pointer (hare) traverses the list twice as fast as the slower pointer (tortoise), leading to a linear traversal of the list. The space complexity is O(1) as we are using only two pointers regardless of the size of the list.