# https://leetcode.com/problems/maximum-twin-sum-of-a-linked-list/description/
"""
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:
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.

Example 2:
Input: head = [4,2,2,3]
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:
Input: head = [1,100000]
Output: 100001
Explanation:
There is only one node with a twin in the linked list having twin sum of 1 + 100000 = 100001.

Constraints:
The number of nodes in the list is an even integer in the range [2, 105].
1 <= Node.val <= 105
"""
from typing import Optional

from puzzles.utils import ListNode


def pair_sum(head: Optional[ListNode]) -> int:
    vals = []
    cur = head
    while cur:
        vals.append(cur.val)
        cur = cur.next
    n = len(vals)
    ret = 0
    for i in range(n // 2):
        ret = max(ret, vals[i] + vals[n - 1 - i])
    return ret
