2807 Insert Greatest Common Divisors in Linked List

Intuition

The problem is straightforward in that we iterate till the second last element and keep on adding a new node after the current node we are at.

We calculate the GCD using a function (or by yourself) - and point our current.next to new_gcd_node. Also remember to save current.next in a temp variable since it’s necessary for traversing.

Also, ensure to point new_gcd_node.next to the temp variable you saved. This way insertion is complete.

Code

Python3

def insertGreatestCommonDivisors(self, head: Optional[ListNode]) -> Optional[ListNode]:
    result = ListNode(0)
    result.next = head
    cur = head
 
    while cur.next:
        gcdNode = ListNode(gcd(cur.val, cur.next.val))
 
        tmpNext = cur.next
 
        gcdNode.next = tmpNext
        cur.next = gcdNode
 
        cur = tmpNext
 
    return result.next

Big O Analysis

• Runtime

  The runtime complexity here is $O(N)$ since we are traversing all nodes in the list atleast once and also proportionately adding (N-1) new nodes (the gcd nodes).

• Memory

  The memory usage is $O(1)$ since we are not using any extra data structure.

— A

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