**QUESTION**:

**Palindrome**: Implement a function to check if a linked list is a palindrome.

**SOLUTION:**

To approach this problem, we can picture a palindrome like 0 – > 1 – > 2 – > 1 – > 0. We know that, since it’s a palindrome, the list must be the same backwards and forwards. This leads us to our first solution.

**Solution #1: Reverse and Compare**

- Our first solution is to reverse the linked list and compare the reversed list to the original list.
- If they’re the same, the lists are identical.
- Note that when we compare the linked list to the reversed list, we only actually need to compare the first half of the list.
- If the first half of the normal list matches the first half of the reversed list, then the second half of the normal list must match the second half of the reversed list.

boolean isPalindrome(LinkedListNode head) { LinkedListNode reversed= reverseAndClone(head); return isEqual(head, reversed); } LinkedlistNode reverseAndClone(LinkedListNode node) { LinkedListNode head= null; while (node != null) { LinkedListNode n = new LinkedlistNode(node.data); // Clone n.next = head; head n; node= node.next; } return head; } boolean isEqual(LinkedListNode one, LinkedListNode two) { while (one != null && two != null) { if (one.data != two.data) { } return false; one one.next; two two.next; } return one== null && two== null; }

- Observe that we’ve modularized this code into reverse and is Equal functions.
- We’ve also created a new class so that we can return both the head and the tail of this method.
- We could have also returned a two-element array, but that approach is less maintainable.

**Solution #2: Iterative Approach**

- We want to detect linked lists where the front half of the list is the reverse of the second half.
- How would we do that? By reversing the front half of the list. A stack can accomplish this.
- We need to push the first half of the elements onto a stack. We can do this in two different ways, depending on whether or not we know the size of the linked list.
- If we know the size of the linked list, we can iterate through the first half of the elements in a standard for loop, pushing each element onto a stack.
- We must be careful, of course, to handle the case where the length of the linked list is odd.
- If we don’t know the size of the linked list, we can iterate through the linked list, using the fast runner/ slow runner technique described in the beginning of the chapter. At each step in the loop, we push the data from the slow runner onto a stack.
- When the fast runner hits the end of the list, the slow runner will have reached the middle of the linked list. By this point, the stack will have all the elements from the front of the linked list, but in reverse order.

Now, we simply iterate through the rest of the linked list. At each iteration, we compare the node to the top of the stack. If we complete the iteration without finding a difference, then the linked list is a palindrome.

boolean isPalindrome(LinkedListNode head) { LinkedListNode fast= head; LinkedListNode slow= head; Stack<Integer> stack= new Stack<Integer>(); /* Push elements from first half of linked list onto stack. When fast runner * (which is moving at 2x speed) reaches the end of the linked list, then we * know we're at the middle*/ while (fast != null && fast.next != null) { stack.push(slow.data); slow slow.next; fast= fast.next.next; } /* Has odd number of elements, so skip the middle element*/ if (fast!= null) { slow= slow.next; } while (slow != null) { int top= stack.pop().intValue(); /* If values are different, then it's not a palindrome*/ if (top != slow.data) { return false; } slow= slow.next; } return true; }

**Solution #3: Recursive Approach**

- First, a word on notation: in this solution, when we use the notation node Kx, the variable K indicates the value of the node data, and x (which is either for b) indicates whether we are referring to the front node with that value or the back node.
- For example, in the below linked list node 2b would refer to the second (back) node with value 2.
- Now, like many linked list problems, you can approach this problem recursively.
- We may have some intuitive idea that we want to compare element 0 and element n – 1, element 1 and element n – 2, element 2 and element n-3, and so on, until the middle element(s). For example:

0 ( 1 ( 2 ( 3 ) 2 ) 1 ) 0

- In order to apply this approach, we first need to know when we’ve reached the middle element, as this will form our base case.
- We can do this by passing in length – 2 for the length each time.
- When the length equals 0 or 1, we’re at the center of the linked list. This is because the length is reduced by 2 each time.
- Once we’ve recursed Yi times, length will be down to 0.

recurse(Node n, int length) { if (length== 0 I I length== 1) { return [something]; // At middle } recurse(n.next, length - 2); }

This method will form the outline of the isPalindrome method. The “meat” of the algorithm though is comparing node i to node n – i to check if the linked list is a palindrome. How do we do that?

**Let’s examine what the call stack looks like:**

```
vl = is Palindrome: list = 0 ( 1 ( 2 ( 3 ) 2 ) 1 ) 0. length = 7
v2 = isPalindrome: list = 1 ( 2 ( 3 ) 2 ) 1 ) 0. length = 5
v3 = isPalindrome: list = 2 ( 3 ) 2 ) 1 ) 0. length = 3
v4 = is Palindrome: list = 3 ) 2 ) 1 ) 0. length = 1
returns v3
returns v2
returns vl
returns ?
```

Code language: PHP (php)

In the above call stack, each call wants to check if the list is a palindrome by comparing its head node with the corresponding node from the back of the list. That is:

- Line 1 needs to compare node 0f with node 0b
- Line 2 needs to compare node 1 f with node lb
- Line 3 needs to compare node 2f with node 2b
- Line 4 needs to compare node 3f with node 3b.

**If we rewind the stack, passing nodes back as described below, we can do just that:**

- Line 4 sees that it is the middle node (since length = 1), and passes back head. next. The value head equals node 3, so head. next is node 2b.
- Line 3 compares its head, node 2f, to returned_node (the value from the previous recursive call), which is node 2b. lf the values match, it passes a reference to node lb (returned_node. next) up to line 2.
- Line 2 compares its head (node 1 f) to returned_node (node lb). If the values match, it passes a reference to node 0b (or, returned_node. next) up to line 1.
- Line 1 compares its head, node 0f, to returned_node, which is node 0b. If the values match, it returns true.

To generalize, each call compares its head to returned_node and then passes returned_node. next up is the stack. In this way, every node I get is compared to node n – i. If at any point the values do not match, we return false, and every call up the stack checks for that value.

- But wait, you might ask, sometimes we said we’ll return a boolean value, and sometimes we’re returning a node. Which is it?
- It’s both. We create a simple class with two members, a boolean and a node, and return an instance of that class.

class Result { public LinkedlistNode node; public boolean result; }

The example below illustrates the parameters and return values from this sample list.

isPalindrome: list = 0 ( 1 ( 2 ( 3 ( 4 ) 3 ) 2 ) 1 ) 0. len = 9 is Palindrome: list = 1 ( 2 ( 3 ( 4 ) 3 ) 2 ) 1 ) 0. len = 7 is Palindrome: list = 2 ( 3 ( 4 ) 3 ) 2 ) 1 ) 0. len = 5 is Palindrome: list = 3 ( 4 ) 3 ) 2 ) 1 ) 0, len = 3 isPalindrome: list = 4 ) 3 ) 2 ) 1 ) 0. len = 1 returns node 3b, true returns node 2b, true returns node lb, true returns node 0b, true returns null, true

Implementing this code is now just a matter of filling in the details.

boolean isPalindrome(LinkedListNode head) { int length= lengthOflist(head); Result p = isPalindromeRecurse(head, length); return p.result; } Result isPalindromeRecurse(LinkedListNode head, int length) { if (head== null I I length<= 0) { II Even number of nodes return new Result(head, true); } else if (length== 1) { II Odd number of nodes return new Result(head.next, true); } /* Recurse on sublist. */ Result res = isPalindromeRecurse(head.next, length - 2); /* If child calls are not a palindrome, pass back up * a failure. */ if (! res.result I I res.node== null) { return res; } /* Check if matches corresponding node on other side. */ res.result= (head.data== res.node.data); /* Return corresponding node. */ res.node= res.node.next; return res; } int lengthOfList(LinkedListNode n) { int size= 0; while (n != null) { size++; n = n.next; } return size; }

- Some of you might be wondering why we went through all this effort to create a special Result class.
- Isn’t there a better way? Not really-at least not in Java.

However, if we were implementing this in C or C ++, we could have passed in a double-pointer.

`bool isPalindromeRecurse(Node head, int length, Node** next) { .... }`

It’s ugly, but it works.