Insert Greatest Common Divisors in Linked List

Insert Greatest Common Divisors in Linked List

1. What is this problem about?

The Insert Greatest Common Divisors in Linked List interview question is a combination of pointer manipulation and number theory. You are given a linked list of integers. Between every two adjacent nodes, you must insert a new node whose value is the Greatest Common Divisor (GCD) of the values of those two nodes.

2. Why is this asked in interviews?

Companies like Microsoft and Google use the GCD in Linked List coding problem to test basic data structure fluency and knowledge of standard mathematical algorithms. It evaluations your ability to traverse a list, handle node insertion, and implement the Euclidean algorithm for GCD. It’s a great example of a multi-step Linked List interview pattern.

3. Algorithmic pattern used

This problem follows the Linked List Traversal and Insertion pattern.

1. Traverse: Move through the list using a current pointer.
2. Calculate: For current and current.next, calculate gcdVal = gcd(current.val, current.next.val).
3. Insert: Create a new node with gcdVal, point its next to current.next, and point current.next to the new node.
4. Advance: Move the pointer past the newly inserted node to the next original node.

4. Example explanation

List: 18 -> 6 -> 10

1. First pair: 18 and 6. $gcd(18, 6) = 6$.
   • Insert 6: 18 -> 6 (new) -> 6 -> 10.
2. Move to original 6. Next is 10. $gcd(6, 10) = 2$.
   • Insert 2: 18 -> 6 -> 6 -> 2 (new) -> 10. Final List: 18 -> 6 -> 6 -> 2 -> 10.

5. Common mistakes candidates make

• Infinite Loop: Forgetting to skip the newly inserted node, causing the algorithm to repeatedly calculate the GCD of the first node and the new node.
• Euclidean Algorithm Errors: Mistakes in implementing the recursive or iterative GCD function.
• Null Checks: Failing to check if current.next exists before attempting to calculate a pair GCD.

6. Interview preparation tip

Always keep the GCD formula in mind: gcd(a, b) is gcd(b, a % b) with a base case of b == 0. It’s a tiny snippet of code that demonstrates Math interview pattern proficiency.