LC 708: Insert into a Sorted Circular Linked List

Difficulty: Medium
Category: Linked List, Circular List
Companies: Amazon, Facebook, Google, Microsoft

Problem Statement

Given a circular linked list, represented by a Node class, insert a new value into the list while maintaining the circular and sorted order of the list.

The list is circular, so the last node points back to the first node. The list is sorted in ascending order.

Examples

Example 1:

Input: head = [3,4,1], insertVal = 2
Output: [3,4,1,2]
Explanation: Insert 2 between 1 and 3, maintaining the circular sorted order.

Example 2:

Input: head = [], insertVal = 1
Output: [1]
Explanation: Create a circular list with a single node.

Example 3:

Input: head = [1], insertVal = 0
Output: [1,0]
Explanation: Insert 0 between 1 (tail) and 1 (head), wrapping around.

Constraints

The number of nodes in the list is in the range [0, 5 * 10^4]
-10^6 <= Node.val, insertVal <= 10^6
List is sorted in ascending order
List is circular

Solution Approaches

Approach 1: One-Pass Insertion (Recommended)

Key Insight: Traverse the circular list once and look for a valid insertion point. Handle edge cases at the wrap-around point.

Algorithm:

Handle empty list by creating a self-referencing node
Traverse the circular list
Find insertion point where curr->val <= insertVal && curr->next->val >= insertVal
Handle wrap-around case where curr->next->val < curr->val (wrap point)
- Insert if insertVal >= curr->val OR insertVal <= curr->next->val
If no valid point found after full traversal, insert after current position

Time Complexity: O(n) where n is the number of nodes
Space Complexity: O(1)

/*
// Definition for a Node.
class Node {
public:
    int val;
    Node* next;

    Node() {}

    Node(int _val) {
        val = _val;
        next = NULL;
    }

    Node(int _val, Node* _next) {
        val = _val;
        next = _next;
    }
};
*/

class Solution {
public:
    Node* insert(Node* head, int insertVal) {
        // Empty list case
        if(!head) {
            Node * newNode = new Node(insertVal);
            newNode->next = newNode;
            return newNode;
        }

        Node* curr = head;
        bool toInsert = false;
        
        do {
            // Normal case: insert between curr and curr->next
            if(curr->val <= insertVal && curr->next->val >= insertVal) {
                toInsert = true;
            } 
            // Wrap-around case: curr->next->val < curr->val indicates the wrap point
            else if(curr->next->val < curr->val) {
                // Insert at wrap-around (largest or smallest value)
                if (insertVal >= curr->val || insertVal <= curr->next->val){
                    toInsert = true;
                }
            }
            
            if(toInsert) {
                Node* ptr = new Node(insertVal);
                ptr->next = curr->next;
                curr->next = ptr;
                return head;
            }
            curr = curr->next;
        } while(curr != head);

        // All values are the same or insert at current position
        curr->next = new Node(insertVal, curr->next);
        return head;
    }
};

Approach 2: Two-Pass with Preprocessing

Algorithm:

First pass: Find the node with maximum value
Second pass: Search from max node’s next to find insertion point
Handle all same values case

Time Complexity: O(n)
Space Complexity: O(1)

class Solution {
public:
    Node* insert(Node* head, int insertVal) {
        if(!head) {
            Node* newNode = new Node(insertVal);
            newNode->next = newNode;
            return newNode;
        }

        // Find the maximum node
        Node* maxNode = head;
        Node* curr = head->next;
        
        while(curr != head) {
            if(curr->val >= maxNode->val) {
                maxNode = curr;
            }
            curr = curr->next;
        }

        // Insert at the end if value is too large
        if(insertVal >= maxNode->val || insertVal <= maxNode->next->val) {
            Node* newNode = new Node(insertVal, maxNode->next);
            maxNode->next = newNode;
            return head;
        }

        // Find the correct insertion point
        curr = maxNode->next;
        while(curr->next->val < insertVal) {
            curr = curr->next;
        }

        Node* newNode = new Node(insertVal, curr->next);
        curr->next = newNode;
        return head;
    }
};

Approach 3: Simplified Logic

Algorithm: Streamlined version that handles all cases more elegantly.

class Solution {
public:
    Node* insert(Node* head, int insertVal) {
        Node* newNode = new Node(insertVal);
        
        // Empty list
        if(!head) {
            newNode->next = newNode;
            return newNode;
        }

        Node* curr = head;
        
        while(curr->next != head) {
            // Normal insertion point
            if(curr->val <= insertVal && insertVal <= curr->next->val) {
                break;
            }
            // Wrap-around insertion point
            if(curr->val > curr->next->val && 
               (insertVal >= curr->val || insertVal <= curr->next->val)) {
                break;
            }
            curr = curr->next;
        }
        
        // Insert at current position
        newNode->next = curr->next;
        curr->next = newNode;
        return head;
    }
};

Algorithm Analysis

Key Insights

Circular List Boundary: The “wrap” happens when curr->val > curr->next->val
Insertion Point Detection: Need to check both normal range and wrap-around cases
Edge Cases: Empty list, single node, all same values
Traversal Guard: Use do-while to ensure at least one iteration

Understanding the Wrap-Around Logic

Sorted circular list: [3, 4, 1] → 1 points to 3

When curr = 4, curr->next = 1:
  - We're at the wrap point (largest → smallest)
  - insertVal = 2: insertVal >= 4? No, insertVal <= 1? No → continue
  - insertVal = 5: insertVal >= 4? Yes → insert here
  - insertVal = 0: insertVal <= 1? Yes → insert here

Implementation Details

Empty List Handling

if(!head) {
    Node * newNode = new Node(insertVal);
    newNode->next = newNode;  // Self-referencing
    return newNode;
}

Normal Insertion Case

// Insert between curr and curr->next
if(curr->val <= insertVal && curr->next->val >= insertVal) {
    Node* newNode = new Node(insertVal, curr->next);
    curr->next = newNode;
    return head;
}

Wrap-Around Insertion Case

// At the wrap point (largest to smallest)
if(curr->next->val < curr->val) {
    // Insert if value is larger than max OR smaller than min
    if(insertVal >= curr->val || insertVal <= curr->next->val) {
        // Insert here
    }
}

Edge Cases

Empty List: Create a circular list with single node
Single Node: Insert anywhere (trivially maintains order)
All Same Values: Insert at any position
Insert at Head: Special care needed for wrap logic
Insert Largest Value: Should go after maximum node
Insert Smallest Value: Should go before minimum node

Follow-up Questions

What if the list is not guaranteed to be sorted?
How would you handle duplicate insertion values?
What if you need to insert multiple values at once?
How would you delete a value from a circular list?

LC 23: Swap Nodes in Pairs - Linked list manipulation
LC 25: Reverse Nodes in k-Group - Linked list reversal
LC 141: Linked List Cycle - Detect cycle in linked list
LC 708: Insert into Sorted Circular List (This problem)

Optimization Techniques

Single Pass: Most efficient with O(n) time
Early Exit: Return immediately after insertion
Edge Case Handling: Handle empty list, single node separately
Wrap Detection: Identify wrap point by comparing adjacent values

Code Quality Notes

Readability: Clear variable names and logic separation
Correctness: Handles all edge cases properly
Performance: Optimal O(n) time complexity
Memory: O(1) space complexity

This problem demonstrates sophisticated circular list manipulation and requires careful handling of wrap-around cases and edge conditions.