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Using sentinel nodes in Linked List operations

I was solving a problem on Remove Linked List elements on Leetcode, when I came across the concept of "Sentinel/Dummy Nodes" through the provided solution. Using such nodes is supposed to make operations in Linked Lists easier in certain cases, such as empty lists or lists with one element, etc.
The problem description is -
Remove all elements from a linked list of integers that have value
val.
Example:
Input: 1->2->6->3->4->5->6, val = 6 Output: 1->2->3->4->5
The given solution is -
class Solution {
public ListNode removeElements(ListNode head, int val) {
ListNode sentinel = new ListNode(0);
sentinel.next = head;
ListNode prev = sentinel, curr = head;
while (curr != null) {
if (curr.val == val) prev.next = curr.next;
else prev = curr;
curr = curr.next;
}
return sentinel.next;
}
}
Let's consider this linked list -
1 -> 1 -> 2 -> 3 -> NULL, and the value of nodes to be removed being 1.
So, the result list should be 2 -> 3 -> NULL with head of this list pointing to 2.
In this line - sentinel.next = head; we make the sentinel as the first node in the list, with it's next node being "head", like so -
0 -> 1 -> 1 -> 2 -> 3 -> NULL,
Note that head still points to 1 (the first node with value 1 in the list).
Before the while loop begins, we set prev to sentinel and curr to head.
During the loop, prev and curr move along the list, both pointing to other nodes in the list. Note that head still points to the first 1.
After the loop, prev points to the last node in the list (with value 3), while curr becomes null.
However, head still refers to the very first node in the list (with value 1), and sentinel.next refers to this very node. So, when we run return sentinel.next -> we get a reference to this first node in the list (with value 1), whose next property doesn't point to any other node. So this is a node by itself.
How does this work correctly then? The ListNode that should be returned should refer to the node with value 2, not 1.
This is based on my knowledge about how references work in Java. Because, when we start out with this -
ListNode sentinel = new ListNode(0);
sentinel.next = head;
ListNode prev = sentinel, curr = head;
We get something like this - [sentinel] -> [head] with prev pointing to sentinel and curr pointing to head.
But the problem is that both prev and curr change references during the list, while sentinel and head do not. So, sentinel.next still points to the old head.
EDIT 1
To make my question clearer, here's a screenshot of the result. What I want to know is - how does sentinel.next refer to the node with the value 2? At the start, sentinel.next was set to head, and this didn't change anywhere. So, sentinel.next should refer to the original head of the list - the node with value 1.
EDIT 2
I think I got it now. The change happens in this line prev.next = curr.next;
Because prev and sentinel both refer to the same list element (at this stage), sentinel.next gets set correctly.

I guess this might be incorrect:
when we run return sentinel.next -> we get a reference to this first
node in the list
prev does not move for the first two values, I guess. Only its link is being moved to the next node.
Another thing is that sentinel is final, does not change:
class Solution {
public ListNode removeElements(
final ListNode head,
final int val
) {
final ListNode sentinel = new ListNode(0);
sentinel.next = head;
ListNode prev = sentinel;
ListNode curr = head;
while (curr != null) {
if (curr.val == val) {
prev.next = curr.next;
}
else {
prev = curr;
}
curr = curr.next;
}
return sentinel.next;
}
}
Maybe it would be good to note that also we are not removing any values (values are there in the memory), we are just changing the links of the Linked List.
Finally, we are only interested in the head of the Linked List, which would be sentinel.next, we are not interested to see where prev is.
Iteratively
class Solution {
public ListNode removeElements(ListNode head, int val) {
if (head == null)
return null;
head.next = removeElements(head.next, val);
return head.val == val ? head.next : head;
}
}
The link in between 1 and 1 is still there, forgot to draw that.

Algorithm: Merge Sort with linked list missing items

I am trying to sort my linked list with merge sort. The list is actually sorted but it is kind of missing first item(s).
Merge sort functions:
public Node mergeSort(Node head) {
if (head == null || head.next == null) {
return head;
}
Node middle = middleElement(head);
Node nextofMiddle = middle.next;
middle.next = null;
return merge(mergeSort(head), mergeSort(nextofMiddle));
}
public Node merge(Node left, Node right) {
Node temp = new Node();
Node newHead = temp;
while (left != null && right != null) {
if (left.info <= right.info) {
temp.next = left;
temp = left;
left = temp.next;
} else {
temp.next = right;
temp = right;
right = temp.next;
}
}
temp.next = (left == null) ? right : left;
return newHead;
}
public Node middleElement(Node head) {
if (head == null) {
return head;
}
Node slow = head;
Node fast = head;
while (fast.next != null && fast.next.next != null) {
slow = slow.next;
fast = fast.next.next;
}
return slow;
}
So I printed the list to the screen using traverse:
public static void main(String[] args) {
MyLinkedList mll = new MyLinkedList();
mll.insert(3);
mll.insert(5);
mll.insert(9);
mll.insert(1);
mll.insert(8);
mll.insert(7);
mll.insert(2);
mll.mergeSort(mll.head);
mll.traverse();
}
I have result like this:
1 and 2 missing!
After checking, i noticed that the "tail" of the linked list value is still 2. I don't know why can someone help?. I'm really new to programming so sorry for any inconvenience. Thank you for reading!

You're not far from a correct solution. I was able to get a working sort by adding 1 line and changing 3.
Your merge isn't doing what you think it is.
Allocating a false head node (what you call temp, not a good choice of name; try falseHead) is a fine idea. Then falseHead.next is the true head. That's what you'll finally return as the sorted list. Note that initially it's null, which is what you'd expect.
What you're missing is a variable tail to reference the current last node in the merged list. Since there is initially no last node at all, this should be initialized equal to falseHead. Consequently, when you append the first element to the tail of the current result by setting tail.next, you'll also be setting falseHead.next, i.e. creating the head element. It all works out.
Now, what is the logic for, say, removing the current head of the right list and appending it to the merge result? It's just 3 steps:
Do the append operation by making tail.next the current head of right.
Update tail to tail.next.
Remove the head of right by updating right to right.next.
Of course the left side is similar.
Good luck. You're close.

You have a couple problems that I can see. One, mentioned by #rcgldr, in the comments is that you merge method is returning the temp node newHead, but that node was no value and is not part of your graph. You need to return it's child newHead.next.
The other problem is that you never reset the head of your list. So after all the sorting, the head of mll still points to the original head, which in this case is 3. So when you traverse the list you skip 1 and 2. I'm not sure what your linked list class looks like but something like this should be close -- just assign the final node returned by mergeSort to the head of the list. Then when you traverse you should be starting in the right spot:
mll.head = mll.mergeSort(mll.head);
mll.traverse();

Reversing a linked-list

I am writing a simple recursive code to reverse a linked-list in Java. Strangely it returns the same node.
Node reverse(Node ptr) {
if (ptr.link == null)
return ptr;
Node second = ptr.link;
ptr.link = null;
Node rest = reverse(second);
rest.link = ptr;
return rest;
}
Why isn't this working?

Your current approach won't work, the rest value that's being returned from the recursive call doesn't point to the last element in the list (which should be the insertion point for the nodes), instead it's pointing to the first element of the result. In other words, this line isn't correctly building the output:
rest.link = ptr;
For successfully reversing a list, one strategy is to use an accumulator parameter, so we can insert at the head of the list as the recursion unwinds - bear in mind that the recursion starts to "go back" in reverse order with respect to the elements in the list. Try this, it's a tail-recursive solution:
Node reverse(Node ptr, Node acc) {
if (ptr == null)
return acc;
Node second = ptr.link;
ptr.link = acc;
return reverse(second, ptr);
}
Call the above method like this:
Node reversedList = reverse(list, null);
Be aware that the input list will be modified in-place and won't be the same after the method returns, any variable that holds a reference to list will be affected. If that's a problem, you should create a copy of list before passing it to reverse().

Oscar is correct that the return value from recursive call does not point to the last element.
There is another algorithm that does not use accumulator parameter:
function reverse(node) {
if (node.next == null)
return node;
var tail = reverse(node.next);
node.next.next = node;
node.next = null;
return tail;
}

Node reverseNode(Node node){
Node head = null;
While(node.next != null){
Node n = new Node(node.data);
n.next = head;
head = n;
node = node.next;
}
return head;}
You know you don't have to write a recursive function

given a node how can I find previous node in a singly linked list

Given the current node, how can I find its previous node in a Singly Linked List. Thanks. Logic will do , code is appreciated. We all know given a root node one can do a sequential traverse , I want to know if there is a smarter way that avoids sequential access overhead. (assume there is no access to root node) Thanks.

You can't.
Singly-linked lists by definition only link each node to its successor, not predecessor. There is no information about the predecessor; not even information about whether it exists at all (your node could be the head of the list).
You could use a doubly-linked list.
You could try to rearrange everything so you have the predecessor passed in as a parameter in the first place.
You could scan the entire heap looking for a record that looks like a predecessor node with a pointer to your node. (Not a serious suggestion.)

If you want to delete the current node, you can do that without finding previous node as well.
Python Code:
def deleteNode(self, node):
node.val = node.next.val
node.next = node.next.next
# Delete Node in a Linked List

Walk through the list from the beginning until you meet a node whose next link points you your current node.
But if you need to do this, perhaps you oughtn't be using a singly linked list in the first place.

Your only option for a singly-linked list is a linear search, something like below (Python-like pseudo code):
find_previous_node(list, node):
current_node = list.first
while(current_node.next != null):
if(current_node.next == node):
return current_node
else:
current_node = current_node.next
return null

Assuming that you're talking about a forward singly linked list (each node only has a pointer to 'next' etc) you will have to iterate from the start of the list until you find the node that has 'next' equal to your current node. Obviously, this is a slow O(n) operation.
Hope this helps.

Keep two-pointer(curr, prev) initially both will point to head of the list.
do a loop on the list until you either reach at the end of the list or at the required node.
for each iteration move curr node to the next of it but before moving to next store its pointer in prev pointer.
prev = curr; // first store current node in prev
curr = curr->next // move current to next
at the end of loop prev node will contain previous node.
getPrev(head, key) {
Node* curr = head;
Node* prev = head;
while(curr !=null && curr->data==key){
prev = curr;
curr = curr->next
}
return prev
}
Example:
list = 1->5->10->4->3
We want prev node of 4 So key = 4 and head point at 1 here
initially:
temp will point to 1
prev will point to 1
iteration 1:
First, assign prev=temp (prev point to 1)
move temp; temp->next (temp point to 5)
iteration 2:
First, assign prev=temp (prev point to 5)
move temp; temp->next (temp point to 10)
iteration 3:
First, assign prev=temp (prev point to 10)
move temp; temp->next (temp point to 4)
iteration 4:
temp->data == key so it will return out of loop.
return prev node

This is some kind of hack which I found out while solving the problem(Delete every even node in a list)
internal void DeleteNode(int p)
{
DeleteNode(head, p);
}
private void DeleteNode(Node head, int p)
{
Node current = head;
Node prev = null;
while (current.next != null)
{
prev = current;
current = current.next;
if (current.data == p)
{
prev.next = current.next;
}
}
}
Now here, in prev you assign the current and then move the current to next thereby prev contains the previous node.
Hope this helps...

You can do it like this.. you can replace the value of current node by value of next node.. and in the next of 2nd last node you can put null. its like delete a element from a string. here is code
void deleteNode(ListNode* node) {
ListNode *pre=node;
while(node->next)
{
node->val=node->next->val;
pre=node;
node=node->next;
}
pre->next=NULL;
}

Use a nodeAt() method and pass the head,size and the index of the current node.
public static Node nodeAt(Node head,int index){
Node n=head;
for(int i=0;i<index;i++,n=n.next)
;
return n;
}
where n returns the node of the predecessor.

Here is a small trick with linear search: just pass in the node or its position whose previous node you are searching for:
private MyNode findNode(int pos) {
//node will have pos=pos-1
pos-- = 1;
MyNode prevNode = null;
int count = 0;
MyNode p = first.next; // first = head node, find it however you want.
//this is for circular linked list, you can use first!=last for singly linked list
while (p != first) {
if (count == pos) {
prevNode = p;
break;
}
p = p.next;
count++;
}
return prevNode;
}

We can traverse through the LinkedList using slow and fast pointers.
Let's say
fast pointer fast = fast.next.next
slow pointer slow = slow.next
Slow pointer will be always a previous of the fast pointer, and so we can able to find it.

It can possible to deleteNode if only given node not root or head. How ?
It can achieve by reversing value in node
4-> 2 -> 1 -> 9 given 2 as node to remove. as above other can't access previous node which is correct because singly linked list we don't store predecessor. What can do is swap value of next of give node to given node and change link to next of next of give node
nextNode = node.next // assigning given node next to new pointer
node.val = nextNode.val // replacing value of given node to nextNode value
node.next = nextNode.next // changing link of given node to next to next node.
I tried this approach and its working fine.

assuming you are using forward singly linked list your code should look like
while(node)
{
previous = node
node = node.next
// Do what ever you want to do with the nodes
}

how to reverse a list with O(1) space and O(n) time?

I am looking for a method that reverses the same instance of a given list, with O(1) additional space and O(n) time.
this is not HW nor I am looking for some library method to do the job for me, as this is only an exercise for myself, and out of pure curiousity.
any ideas how to do it with O(1) additional space and O(n) time? (and if possible without reflection as well)?
signature is public <T> void reverse(List<T> list).
(*)assume get() to the head and tail of the list is O(1), but to the middle of it is O(n).
I came up with a recursive solution, but it is O(n) space, O(n) time
public <T> void reverseAux(List<T> list,int size) {
if (size == 0) return;
T elem = list.remove(size-1);
reverseAux(list,size-1);
list.add(0,elem);
}
public <T> void reverse(List<T> list) {
reverseAux(list, list.size());
}
EDIT: I am looking for a java solution, for List<T>, only assumption on implementation is access time O(1) for head and tail, and using List<T> interface.

Just read one of the following. It is the thing you're talking about.
Please note that we're talking about singly 'linked' lists.
http://www.teamten.com/lawrence/writings/reverse_a_linked_list.html
http://www.mytechinterviews.com/reverse-a-linked-list
http://www.geekpedia.com/code48_Reverse-a-linked-list.html
http://www.codeproject.com/KB/recipes/ReverseLinkedList.aspx
Plus an extra question for you:
How would you find Nth element from the tail of a linked list assuming it is singly linked and you have only head pointer with O(1) space and O(N) time?

using ListIterators:
ListIterator<T> head = list.listIterator();
ListIterator<T> tail = list.listIterator(size);//assuming this can be done in O(1) though O(n) doesn't hurt that much and total is still O(n)
while(head.nextIndex()<tail.previousIndex()){
T tmp = head.next();
head.set(tail.previous());
tail.set(tmp);
}

You already know the length. So just use 1 temporary variable and start at index 0 and go on swapping list[0] and list[length -1], then list[1] and list[length-2], and so on. O(n) time and O(1) space for 1 temporary variable.
EDIT: Just noticed you assume O(n) for accessing the middle of the list. oh well. nevermind.
alternatively, store the next/previous pointers of the two elements you swapped to move towards the middle (assuming it's a doubly linked list). Then you get O(n) time.

The best performance you can get from comparison sorts like merge sort or quick sort is O(nlogn). You can get O(n) performance from non-comparison sorts like radix sort.
If you are reversing a linked-list, then you can reverse the list in O(n) time with using just 3 extra items. You need 3 pointers to keep track of what you're currently pointing to, what is before your current item and what is after your current item. The code is:
Node current = head;
Node next = null;
Node prev = null;
while (current != null) {
next = current.next;
current.next = prev;
prev = current;
current = next;
}
return prev;

As discussed, in the general case this is not doable, you need to assume something about the complexity of the individual operations. If you have constant-time next() and previous() for the iterators, use the solution already given. It should work for both LinkedList and ArrayList.
I thought about a solution which would work for a singly-linked list (but not for something like ArrayList), but sadly the ListIterators add method inserts the element before the cursor instead of after it, thus it is not doable with the List + ListIterator interfaces (if we can't patch the ListIterator implementation to cache the pre-insert element to allow a single previous() after add in O(1)).
Here, assuming a simple Node class with next-pointer:
/**
* reverses a singly linked list.
* #param first the fist node. This will be the new last node.
* #param last the last node. This will be the new first node.
*/
void reverseList(Node first, Node last) {
while(first != last) {
Node temp = first;
first = temp.next;
temp.next = last.next;
last.next = temp;
}
}
In index terms, this would be something like this:
public void reverseList(List<T> list) {
int index = list.size() -1;
while(n > 0) {
T element = list.remove(0);
list.add(n, element);
n--;
}
}
In ListIterator terms, this would be something like this:
public void reverseList(List<T> list) {
ListIterator<T> it = list.listIterator(list.size());
while(it.previousIndex() > 0) { // we could count ourself here, too
T element = list.remove(0);
it.add(element);
it.previous();
}
}
Of course, usual singly linked list implementations will not have a O(1) previous implementation, thus it will not work there, as said before. (And they might throw a ConcurrentModificationException, or return erronous previousIndex.)

Here is a solution in Java, with O(n) time complexity (just a single pass) and O(1) space complexity (Using just two temporary variables):
private static void reverseLinkedList() {//O(n) Time complexity, O(1) space complexity
//two temp pointers
Node next = null, previous = null;
while(head.next != null){
next = head.next;//move next to next address
head.next = previous; //previous node will be the next node for head, so that head will point reverse
previous = head; //incrementing previous to the current node
head = next; //incrementing head
}
//at this point head points to last node and previous has the remaining reversed array
head.next = previous;
System.out.println("\nReversed");
}
Full code goes like:
package com.test;
public class LinkedListReverse {
private static Node head;
public static void main(String[] args) {
for(int i = 0 ; i< 10 ; i++){
addToLinkedList(i);
}
System.out.println("Added Data");
printLinkedList();
reverseLinkedList();
printLinkedList();
}
private static void reverseLinkedList() {//O(n) Time complexity, O(1) space complexity
//two temp pointers
Node next = null, previous = null;
while(head.next != null){
next = head.next;//move next to next address
head.next = previous; //previous node will be the next node for head, so that head will point reverse
previous = head; //incrementing previous to the current node
head = next; //incrementing head
}
//at this point head points to last node and previous has the remaining reversed array
head.next = previous;
System.out.println("\nReversed");
}
/* Logic for adding and printing linked list*/
private static void printLinkedList() {
System.out.println("Printing linked list");
Node temp = head;
while(temp.next != null){
System.out.print(temp.value+" ");
temp = temp.next;
}
System.out.print(temp.value+" ");//print the value at the last node
}
private static void addToLinkedList(int value){
if(head == null){
head = new Node(value, null);
}else{
Node temp = head;
while(temp.next != null){
temp = temp.next;
}
temp.next = new Node(value, null);
}
}
}
//Linked List definition
class Node{
int value;
Node next;
public Node(int value, Node next){
this.value = value;
this.next = next;
}
}
Program's Output:
Added Data
Printing linked list
0 1 2 3 4 5 6 7 8 9
Reversed
Printing linked list
9 8 7 6 5 4 3 2 1 0
Hope it helps :)

The ListIterator interface is what you're looking for (under the reasonable assumption that the list in question fully supports it; both ArrayList and LinkedList do):
ListIterator<T> fwd = list.listIterator();
ListIterator<T> back = list.listIterator(list.size());
while (fwd.nextIndex() < back.previousIndex()) {
T tmp = fwd.next();
fwd.set(back.previous());
back.set(tmp);
}
Even on linked lists, this should be linear in time.

public LinkedList Reverse(LinkedList head)
{
if (head == null) return null; // first question
if (head.Next == null) return head; // second question
// third question
// so we grab the second element (which will be the last after we reverse it)
LinkedList secondElem = head.Next;
// bug fix - need to unlink list from the rest or you will get a cycle
head.Next = null;
// then we reverse everything from the second element on
LinkedList reverseRest = Reverse(secondElem);
// then we join the two lists
secondElem.Next = head;
return reverseRest;
}