Given n 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
Approach:
Steps:
Find the Middle of the Linked List:
Use the fast and slow pointer technique to locate the midpoint of the list efficiently.
Reverse the Second Half of the List:
Reverse the second half of the linked list to facilitate pairing the twin nodes.
Calculate Twin Sums:
Traverse both halves simultaneously (one from the start and the other from the reversed list) to compute twin sums.
Find the Maximum Twin Sum:
Keep track of the maximum twin sum encountered during the traversal.
# Definition for singly-linked list.
# class ListNode(object):
# def __init__(self, val=0, next=None):
# self.val = val
# self.next = next
class Solution(object):
def pairSum(self, head):
"""
:type head: Optional[ListNode]
:rtype: int
"""
# find the middle of head
slow, fast = head, head
while fast and fast.next:
slow = slow.next
fast = fast.next.next
# reverse the second half
prev = None
while slow:
temp = slow.next
slow.next = prev
prev = slow
slow = temp
# interate 2 linked list and compute sum
max_sum = 0
first, second = head, prev
while second:
max_sum = max(max_sum, first.val + second.val)
first = first.next
second = second.next
return max_sum