Day 2 - Rotate a Linked List.md

Difficulty	Medium
Source	160 Days of Problem Solving
Tags	Linked-List

🚀 Day 2. Rotate a linked list 🧠

The problem can be found at the following link: Problem Link

💡 Problem Description:

You are given the head of a singly linked list and an integer k. Your task is to left-rotate the linked list k times.

🔍 Example Walkthrough:

Input:
head = 10 -> 20 -> 30 -> 40 -> 50, k = 4
Output:
50 -> 10 -> 20 -> 30 -> 40
Explanation:
Rotate 1: 20 -> 30 -> 40 -> 50 -> 10
Rotate 2: 30 -> 40 -> 50 -> 10 -> 20
Rotate 3: 40 -> 50 -> 10 -> 20 -> 30
Rotate 4: 50 -> 10 -> 20 -> 30 -> 40

Input:
head = 10 -> 20 -> 30 -> 40, k = 6
Output:
30 -> 40 -> 10 -> 20
Explanation:
Since k = 6 exceeds the length of the list (4), k is reduced to k % length = 2. After two left rotations:
10 -> 20 -> 30 -> 40 → 20 -> 30 -> 40 -> 10 → 30 -> 40 -> 10 -> 20.

Constraints:

• $1 <= number of nodes <= 10^5$
• $0 <= k <= 10^9$
• $0 <= data of node <= 10^9$

🎯 My Approach:

1. Key Observations:

   • If k is greater than the length of the list, we only need to perform k % length rotations, as rotating the list length times results in the same list.
   • Breaking the linked list into two parts and re-linking the tail to the head helps achieve the rotation efficiently.

2. Algorithm:

   • Compute the length of the list (len).
   • Reduce k to k % len to handle large values of k.
   • If k = 0, return the original list as no rotation is required.
   • Traverse the list to find the new tail (the node at position len - k) and the new head (the node at position len - k + 1).
   • Break the list into two parts by setting the next pointer of the new tail to nullptr.
   • Re-link the old tail to the original head.
   • Return the new head.

🕒 Time and Auxiliary Space Complexity

• Expected Time Complexity: O(n), where n is the length of the linked list. This is because we traverse the list twice: once to calculate its length and once to locate the new head and tail.
• Expected Auxiliary Space Complexity: O(1), as no additional space is used apart from a few pointers.

📝 Solution Code

Code (C++)

class Solution {
 public:
  Node* rotate(Node* head, int k) {
    if (!head || !head->next || !k) return head;
    int len = 1;
    Node* tail = head;
    while (tail->next) tail = tail->next, len++;
    k %= len;
    if (!k) return head;
    Node* newTail = head;
    for (int i = 1; i < k; i++) newTail = newTail->next;
    Node* newHead = newTail->next;
    newTail->next = nullptr;
    tail->next = head;
    return newHead;
  }
};

👨‍💻 Alternative Approach

Alternative Approach: Optimized Left Rotation

The idea is similar but involves fewer intermediate calculations. We aim to find the breaking point in one traversal. Here's the implementation:

class Solution {
 public:
  Node* rotate(Node* head, int k) {
    if (!head || !head->next || k == 0) {
      return head;
    }
    int len = 1;
    Node* tail = head;
    while (tail->next) {
      tail = tail->next;
      len++;
    }
    k %= len;
    if (k == 0) {
      return head;
    }
    Node* newTail = head;
    for (int i = 1; i < k; i++) { // LEFT rotation
      newTail = newTail->next;
    }
    Node* newHead = newTail->next;
    newTail->next = nullptr;
    tail->next = head;
    return newHead;
  }
};

Code (Java)

class Solution {
  public Node rotate(Node head, int k) {
    if (head == null || head.next == null || k == 0) return head;
    int len = 1;
    Node tail = head;
    while (tail.next != null) {
      tail = tail.next;
      len++;
    }
    k %= len;
    if (k == 0) return head;
    Node newTail = head;
    for (int i = 1; i < k; i++) {
      newTail = newTail.next;
    }
    Node newHead = newTail.next;
    newTail.next = null;
    tail.next = head;
    return newHead;
  }
}

Code (Python)

class Solution:
    def rotate(self, head, k):
        if k == 0 or head is None:
            return head
        curr = head
        length = 1
        while curr.next is not None:
            curr = curr.next
            length += 1
        k %= length
        if k == 0:
            curr.next = None
            return head
        curr.next = head
        curr = head
        for _ in range(1, k):
            curr = curr.next
        newHead = curr.next
        curr.next = None
        return newHead

🎯 Contribution and Support:

For discussions, questions, or doubts related to this solution, feel free to connect on LinkedIn: Any Questions. Let’s make this learning journey more collaborative!

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