Given a linked list, find length of the longest palindrome list that exist in that linked list.

Examples:

Input : List = 2->3->7->3->2->12->24 Output : 5 The longest palindrome list is 2->3->7->3->2 Input : List = 12->4->4->3->14 Output : 2 The longest palindrome list is 4->4

A simple solution could be to copy linked list content to array and then find longest palindromic subarray in array, but this solution is not allowed as it requires extra space.

The idea is based on iterative linked list reverse process. We iterate through given linked list and one by one reverse every prefix of linked list from left. After reversing a prefix, we find the longest common list beginning from reversed prefix and list after the reversed prefix.

Below is C++ implementation of above idea.

// C++ program to find longest palindrome // sublist in a list in O(1) time. #include<bits/stdc++.h> using namespace std; //structure of the linked list struct Node { int data; struct Node* next; }; // function for counting the common elements int countCommon(Node *a, Node *b) { int count = 0; // loop to count coomon in the list starting // from node a and b for (; a && b; a = a->next, b = b->next) // increment the count for same values if (a->data == b->data) ++count; else break; return count; } // Returns length of the longest palindrome // sublist in given list int maxPalindrome(Node *head) { int result = 0; Node *prev = NULL, *curr = head; // loop till the end of the linked list while (curr) { // The sublist from head to current // reversed. Node *next = curr->next; curr->next = prev; // check for odd length palindrome // by finding longest common list elements // beginning from prev and from next (We // exclude curr) result = max(result, 2*countCommon(prev, next)+1); // check for even length palindrome // by finding longest common list elements // beginning from curr and from next result = max(result, 2*countCommon(curr, next)); // update prev and curr for next iteration prev = curr; curr = next; } return result; } // Utility function to create a new list node Node *newNode(int key) { Node *temp = new Node; temp->data = key; temp->next = NULL; return temp; } /* Drier program to test above functions*/ int main() { /* Let us create a linked lists to test the functions Created list is a: 2->4->3->4->2->15 */ Node *head = newNode(2); head->next = newNode(4); head->next->next = newNode(3); head->next->next->next = newNode(4); head->next->next->next->next = newNode(2); head->next->next->next->next->next = newNode(15); cout << maxPalindrome(head) << endl; return 0; }

Output :

5

Time Complexity : O(n^{2})

Note that the above code modifies the given linked list and may not work if modifications to linked list are not allowed. However we can finally do one more reverse to get original list back.

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