Insert Greatest Common Divisors in Linked List

class Solution {
public:
    ListNode* insertGCDs(ListNode* root) {
        // Return root if only one node is present
        if (!root->next) return root;
    
        // Pointers to navigate through the list
        ListNode* currentNode = root;
        ListNode* nextNode = root->next;
    
        // Process each node pair in the linked list
        while (nextNode != nullptr) {
            int gcd = computeGCD(currentNode->val, nextNode->val);
            ListNode* gcdNode = new ListNode(gcd);
    
            // Insert the GCD node between current and next node
            currentNode->next = gcdNode;
            gcdNode->next = nextNode;
    
            // Update pointers to move to the next nodes in the list
            currentNode = nextNode;
            nextNode = nextNode->next;
        }
    
        return root;
    }
    
private:
    // Compute GCD using Euclidean algorithm
    int computeGCD(int x, int y) {
        while (y != 0) {
            int remainder = y;
            y = x % y;
            x = remainder;
        }
        return x;
    }
};

This solution presents a method to modify a linked list by inserting nodes containing the Greatest Common Divisor (GCD) of consecutive values. The code is written in C++ and defines a class Solution with the method insertGCDs to perform the operation on the linked list.

Steps involved in the code:

1. Check if the linked list has only one node. In this case, return the root as no insertion is required.
2. Initialize two pointers, currentNode and nextNode, to traverse the linked list starting from the root.
3. For each pair of consecutive nodes, compute the GCD of their values using the nested function computeGCD, which implements the Euclidean algorithm.
4. Create a new node (gcdNode) with the computed GCD value and insert it between the current node and the next node.
5. Adjust the next pointers to ensure currentNode now points to gcdNode and gcdNode points to nextNode.
6. Continue the process by moving currentNode and nextNode forward in the list.
7. Once all GCD nodes are inserted, return the modified root of the list.

The computeGCD private member function iteratively applies the Euclidean algorithm to find the GCD, ensuring the nodes inserted contain accurate GCD values. Through the use of pointers and dynamic node creation, the linked list is effectively modified in-place.

class Solution {
    
    public ListNode addGCDNodes(ListNode head) {
        if (head.next == null) return head;
    
        ListNode current = head;
        ListNode nextNode = head.next;
    
        while (nextNode != null) {
            int gcd = findGCD(current.val, nextNode.val);
            ListNode newGCDNode = new ListNode(gcd);
    
            current.next = newGCDNode;
            newGCDNode.next = nextNode;
    
            current = nextNode;
            nextNode = nextNode.next;
        }
    
        return head;
    }
    
    private int findGCD(int x, int y) {
        while (y != 0) {
            int t = y;
            y = x % y;
            x = t;
        }
        return x;
    }
}

The Java code you provided defines a method to insert nodes into a linked list, where each new node's value is the greatest common divisor (GCD) of the values of adjacent nodes. Here's a breakdown of how this function operates:

• The method addGCDNodes begins by checking if the list contains only one node. If it does, the list is returned unchanged.

• A while loop iterates through the nodes of the list. During each iteration, it calculates the GCD of the values of two consecutive nodes (current and nextNode). This is accomplished through the helper method findGCD.

• A new node, storing the computed GCD, is created and inserted between current and nextNode.

• The list traversal continues until all appropriate GCD nodes have been added.

The findGCD function employs Euclid's algorithm to compute the GCD of two integers. It repeatedly replaces the larger number with the remainder of the two numbers until one of the numbers becomes zero, at which point the other number is the GCD.

When utilizing this code in your linked list operations, you ensure that every pair of adjacent nodes contributes a new node containing their GCD, enriching the data structure with meaningful mathematical relationships between its elements. This method efficiently processes linked list nodes and inserts new nodes as required, all while maintaining the linked list's structural integrity.

class Solution:
    def insertGCDNodes(
        self, head: Optional[ListNode]
    ) -> Optional[ListNode]:
        # Method to find GCD using the Euclidean algorithm
        def compute_gcd(x, y):
            while y != 0:
                x, y = y, x % y
            return x
    
        # Return early if the list has only one node
        if not head.next:
            return head
    
        # Starting pointers for the list iteration
        current = head
        next_node = head.next
    
        # Iterate through the linked list and insert GCD nodes
        while next_node:
            gcd = compute_gcd(current.val, next_node.val)
            gcd_new_node = ListNode(gcd)
    
            # Link the new GCD node between current and next_node
            current.next = gcd_new_node
            gcd_new_node.next = next_node
    
            # Update pointers to next relevant nodes
            current = next_node
            next_node = next_node.next
    
        return head

This Python solution is designed to manage a linked list by inserting nodes that represent the Greatest Common Divisor (GCD) of consecutive nodes. The solution employs the Euclidean algorithm to compute the GCD. Here is an overview of the process:

1. Define a helper function compute_gcd(x, y) to calculate the GCD using the Euclidean algorithm.
2. Check if the linked list has only one node and return the head if it does.
3. Initialize pointers, current and next_node, to traverse the linked list starting from the head.
4. Iterate through the linked list. For each pair of consecutive nodes:
   • Compute the GCD of their values.
   • Create a new node with the GCD value.
   • Insert the new GCD node between the current and the next node.
   • Update the current pointer to the node right after the newly inserted GCD node.
   • Continue this process until the end of the linked list.
5. Return the modified linked list head with the new GCD nodes inserted.

This method ensures the linked list is augmented efficiently with the GCD values in place, maintaining the original list structure while integrating valuable computational nodes.