Leetcode #2130: Maximum Twin Sum of a Linked List
In this guide, we solve Leetcode #2130 Maximum Twin Sum of a Linked List in Python and focus on the core idea that makes the solution efficient.
You will see the intuition, the step-by-step method, and a clean Python implementation you can use in interviews.
Problem Statement
In a linked list of size n, where n is even, the ith node (0-indexed) of the linked list is known as the twin of the (n-1-i)th node, if 0 <= i <= (n / 2) - 1. For example, if n = 4, then node 0 is the twin of node 3, and node 1 is the twin of node 2.
Quick Facts
- Difficulty: Medium
- Premium: No
- Tags: Stack, Linked List, Two Pointers
Intuition
The constraints hint that we can reason about two ends of the data at once, which is perfect for a two-pointer scan.
Moving one pointer at a time keeps the invariant intact and avoids nested loops.
Approach
Place pointers at the left and right ends and move them based on the comparison or target condition.
This yields a clean linear pass after any required sorting.
Steps:
- Set left and right pointers.
- Move a pointer based on the condition.
- Update the best answer while scanning.
Example
Input: head = [5,4,2,1]
Output: 6
Explanation:
Nodes 0 and 1 are the twins of nodes 3 and 2, respectively. All have twin sum = 6.
There are no other nodes with twins in the linked list.
Thus, the maximum twin sum of the linked list is 6.
Python Solution
# Definition for singly-linked list.
# class ListNode:
# def __init__(self, val=0, next=None):
# self.val = val
# self.next = next
class Solution:
def pairSum(self, head: Optional[ListNode]) -> int:
s = []
while head:
s.append(head.val)
head = head.next
n = len(s)
return max(s[i] + s[-(i + 1)] for i in range(n >> 1))
Complexity
The time complexity is and the space complexity is , where is the number of nodes in the linked list. The space complexity is , where is the number of nodes in the linked list.
Edge Cases and Pitfalls
Watch for boundary values, empty inputs, and duplicate values where applicable. If the problem involves ordering or constraints, confirm the invariant is preserved at every step.
Summary
This Python solution focuses on the essential structure of the problem and keeps the implementation interview-friendly while meeting the constraints.