# LC 2130. Maximum Twin Sum of a Linked List

### [Problem link](https://leetcode.com/problems/maximum-twin-sum-of-a-linked-list/)

###### tags: `leedcode` `python` `medium` `Linked List`

In a linked list of size <code>n</code>, where <code>n</code> is **even** , the <code>i^th</code> node ( **0-indexed** ) of the linked list is known as the **twin** of the <code>(n-1-i)^th</code> node, if <code>0 <= i <= (n / 2) - 1</code>.

- For example, if <code>n = 4</code>, then node <code>0</code> is the twin of node <code>3</code>, and node <code>1</code> is the twin of node <code>2</code>. These are the only nodes with twins for <code>n = 4</code>.

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

Given the <code>head</code> of a linked list with even length, return the **maximum twin sum** of the linked list.

**Example 1:**
<img alt="" src="https://assets.leetcode.com/uploads/2021/12/03/eg1drawio.png" style="width: 250px; height: 70px;" />

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:**
<img alt="" src="https://assets.leetcode.com/uploads/2021/12/03/eg2drawio.png" style="width: 250px; height: 70px;" />

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:**
<img alt="" src="https://assets.leetcode.com/uploads/2021/12/03/eg3drawio.png" style="width: 200px; height: 88px;" />

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 <code>[2, 10⁵]</code>.
- <code>1 <= Node.val <= 10⁵</code>

## Solution 1 - Linked-List and List

# 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:
        pair = []
        res = 0

        while head:
            pair.append(head.val)
            head = head.next

        for i in range(len(pair)//2):
            res = max(res, pair[i] + pair[-(i + 1)])

        return res

## Solution 2 - Linked-List

# 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:
        # reverse the first half of head
        fast = head
        cur = head
        pre = None

        while fast and fast.next:
            fast = fast.next.next

            tmp = cur.next
            cur.next = pre
            pre = cur
            cur = tmp

        # cal maximum
        res = float("-inf")
        while cur and pre:
            res = max(res, cur.val + pre.val)
            cur = cur.next
            pre = pre.next

        return res

>### Complexity
>n = The number of nodes in the list
>| | Time Complexity | Space Complexity |
>| ----------- | --------------- | ---------------- |
>| Solution 1 | O(n) | O(n) |
>| Solution 2 | O(n) | O(1) |

## Note
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