2807. Insert Greatest Common Divisors in Linked List - Explanation

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Description

You are given the head of a linked list head, in which each node contains an integer value.

Between every pair of adjacent nodes, insert a new node with a value equal to the greatest common divisor of them.

Return the head of the linked list after insertion.

The greatest common divisor of two numbers is the largest positive integer that evenly divides both numbers.

Example 1:

Input: head = [12,3,4,6]

Output: [12,3,3,1,4,2,6]

Example 2:

Input: head = [2,1]

Output: [2,1,1]

Constraints:

• 1 <= The length of the list <= 5000.
• 1 <= Node.val <= 1000

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1. Simulation

# Definition for singly-linked list.
# class ListNode:
#     def __init__(self, val=0, next=None):
#         self.val = val
#         self.next = next
class Solution:
    def insertGreatestCommonDivisors(self, head: Optional[ListNode]) -> Optional[ListNode]:
        def gcd(a, b):
            while b > 0:
                a, b = b, a % b
            return a

        cur = head
        while cur.next:
            n1, n2 = cur.val, cur.next.val
            cur.next = ListNode(gcd(n1, n2), cur.next)
            cur = cur.next.next

        return head

Time & Space Complexity

• Time complexity: $O(n * \log (min(a, b)))$
• Space complexity:
  • $O(n)$ space for the gcd ListNodes.
  • $O(1)$ extra space.

Where $n$ is the length of the given list, and $a$ and $b$ are two numbers passed to the $gcd()$ function.