14. Implement a function to partition a linked list around a given value, such that all nodes less than the value come before all nodes greater than or equal to the value.

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14. Implement a function to partition a linked list around a given value, such that all nodes less than the value come before all nodes greater than or equal to the value.

Overview

Partitioning a linked list around a given value such that all nodes less than the value come before all nodes greater than or equal to the value is a common problem in linked list interview questions. This technique is crucial for preparing data within linked lists for operations like sorting, searching, or even for specific algorithms that require data to be pre-organized in a certain way. Understanding how to efficiently partition a linked list is essential for optimizing performance and demonstrates a deep understanding of linked list operations.

Key Concepts

  1. Linked List Traversal: Iterating over each node to evaluate its value against the partition value.
  2. Node Reordering: Efficiently rearranging nodes without altering their inherent data.
  3. Two-Pointer Technique: Utilizing multiple pointers to track different parts of the linked list during partitioning.

Common Interview Questions

Basic Level

  1. Explain how a linked list works and how nodes are linked together.
  2. Write a function to append nodes to a linked list.

Intermediate Level

  1. How would you traverse a linked list to find a specific value?

Advanced Level

  1. Implement a function to partition a linked list around a given value, ensuring all nodes less than the value come before all nodes greater or equal to the value.

Detailed Answers

1. Explain how a linked list works and how nodes are linked together.

Answer: A linked list is a data structure consisting of nodes where each node contains data and a reference (or link) to the next node in the sequence. The first node is called the head, and the last node, which points to null, is called the tail. Linked lists are dynamic, allowing efficient insertions and deletions.

Key Points:
- Each node contains data and a reference to the next node.
- The head node marks the beginning of the list.
- The tail node is the last node, pointing to null, indicating the end of the list.

Example:

public class ListNode
{
    public int Value { get; set; }
    public ListNode Next { get; set; }

    public ListNode(int value)
    {
        this.Value = value;
        this.Next = null;
    }
}

public class LinkedList
{
    public ListNode Head { get; private set; }

    public void Append(int value)
    {
        if (Head == null)
        {
            Head = new ListNode(value);
        }
        else
        {
            ListNode current = Head;
            while (current.Next != null)
            {
                current = current.Next;
            }
            current.Next = new ListNode(value);
        }
    }
}

2. Write a function to append nodes to a linked list.

Answer: Appending a node to a linked list involves traversing the list to find the tail node and then linking a new node to the tail's next reference.

Key Points:
- Traversal to find the tail node.
- Creation of a new node.
- Linking the new node as the next of the tail.

Example:

// Using the ListNode and LinkedList classes defined above

public void Append(int value)
{
    if (Head == null)
    {
        Head = new ListNode(value);
    }
    else
    {
        ListNode current = Head;
        while (current.Next != null)
        {
            current = current.Next;
        }
        current.Next = new ListNode(value);
    }
}

4. Implement a function to partition a linked list around a given value, ensuring all nodes less than the value come before all nodes greater or equal to the value.

Answer: To partition a linked list, we can create two separate lists: one for elements less than the partition value and one for elements greater or equal. After processing each element, we merge these lists.

Key Points:
- Creating two separate linked lists for partitioning.
- Traversing the original list once.
- Merging the two lists without altering the inherent data of nodes.

Example:

public ListNode Partition(ListNode head, int x)
{
    ListNode beforeHead = new ListNode(0), afterHead = new ListNode(0);
    ListNode before = beforeHead, after = afterHead;

    while (head != null)
    {
        if (head.Value < x)
        {
            before.Next = head;
            before = before.Next;
        }
        else
        {
            after.Next = head;
            after = after.Next;
        }
        head = head.Next;
    }

    // Preventing a cycle
    after.Next = null;
    // Merging the two lists
    before.Next = afterHead.Next;

    return beforeHead.Next;
}

This function efficiently partitions the list by iterating through it once and reassigning nodes to the 'before' or 'after' lists based on the partition value. Finally, it merges these lists to achieve the desired partitioned list.

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