Insert GCD Nodes in a Linked List

Interview Problem Interview Medium Same-direction Pointers Linked List Euclidean GCD

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Problem

Implement Solution.insertGreatestCommonDivisors(head). Between every pair of original adjacent nodes, insert a node containing their greatest common divisor and return head.

Starter code

class Solution:
    def insertGreatestCommonDivisors(self, head):
        pass

Test cases

sample

{
  "args": [
    {
      "$type": "linked-list",
      "values": [
        18,
        6,
        10,
        3
      ]
    }
  ]
}

Expected: {"$type":"linked-list","values":[18,6,6,2,10,1,3]}

Wizard outline

Step 1: Initialize Solution.insertGreatestCommonDivisors
Replace the empty starter with the first real state owned by Solution.insertGreatestCommonDivisors. A small, named state is easier to verify than a complete algorithm. Establish it before adding the branch or loop that changes it.
Step 2: Assemble the primary transition
Extend the initialized state with the next contiguous part of the popular solution. The transition explains how one input element or operation changes the state; boundaries are easier to reason about after this invariant is visible.
Step 3: Pass the One Node case
Complete the readable core algorithm for one representative Interview case. Save the next original node before inserting so generated nodes are not processed again.
Step 4: Harden the Sample boundary
Repair the reviewed boundary and pass the complete submission contract. Each iteration processes exactly one original adjacent pair and inserts its gcd between them without changing original order. Advancing to the saved neighbor ensures every and only original pair is processed.

Footguns and prerequisites

Advance to the saved original neighbor, not to the newly inserted node.
linked lists
operators and expressions

Reviewed references

LeetCode 2807 — Insert Greatest Common Divisors in Linked List

Practice prerequisites

Relink Nodes Safely(opens in a new tab)
Relink Nodes Safely isolates every untouched node keeps its original next link, and at most one predecessor changes to the removed node’s former successor. That focused state discipline is required when implementing insert gcd linked list as a complete Interview Problem.

Recommended approach and implementation

While current has an original next node, save it, insert gcd(current.val,next.val), link the inserted node to next, then advance current to next.

Why it works: Each iteration processes exactly one original adjacent pair and inserts its gcd between them without changing original order. Advancing to the saved neighbor ensures every and only original pair is processed.

class Solution:
    def insertGreatestCommonDivisors(self, head):
        """
        Checkpoint 1: initialize the state owned by this Interview contract.
        Checkpoint 2: assemble the primary transition without hiding the boundary.
        """
        from math import gcd
        current = head
        while current and current.next:
            following = current.next
            current.next = ListNode(gcd(current.val, following.val), following)
            current = following
        return head