# 2130 Maximum Twin Sum of a Linked List

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`. These are the only nodes with twins for `n = 4`.

The twin sum is defined as the sum of a node and its twin.

Given the `head` of a linked list with even length, return the maximum twin sum of the linked list.

Example 1:

``````(5) ->  ->  -> (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.
``````

Example 2:

``````(4) ->  ->  -> (3)
Output: 7
Explanation:
The nodes with twins present in this linked list are:
- Node 0 is the twin of node 3 having a twin sum of 4 + 3 = 7.
- Node 1 is the twin of node 2 having a twin sum of 2 + 2 = 4.
Thus, the maximum twin sum of the linked list is max(7, 4) = 7.
``````

Example 3:

``````(1) -> (100000)
• The number of nodes in the list is an even integer in the range `[2, 105]`.
• `1 <= Node.val <= 105`
 `````` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 `````` ``````# Definition for singly-linked list. # class ListNode: # def __init__(self, val=0, next=None): # self.val = val # self.next = next """ Using queue """ from collections import deque class Solution: def pairSum(self, head: Optional[ListNode]) -> int: q = deque() while head: q.append(head.val) head = head.next max_sum = -1 while q: max_sum = max(max_sum, q.popleft() + q.pop()) return max_sum """ Reversing second half of the list """ class Solution: def pairSum(self, head: Optional[ListNode]) -> int: slow, fast = head, head maxVal = 0 # Get middle of linked list while fast and fast.next: fast = fast.next.next slow = slow.next # Reverse second part of linked list curr, prev = slow, None while curr: curr.next, prev, curr = prev, curr, curr.next # Get max sum of pairs while prev: maxVal = max(maxVal, head.val + prev.val) prev = prev.next head = head.next return maxVal``````