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Let's continue adding operations to our data structure to make it useful. In this video we'll implement an insert operation that takes an index as an insertion point.
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Insert operations on link
lists are quite interesting.
0:00
Unlike arrays, where you insert and
element into the array,
0:03
all elements after the particular
index need to be shifted.
0:07
Within linked lists,
0:10
we just need to change the references to
next on a few nodes, and we're good to go.
0:12
Since each node points to the next one,
by swapping out these references,
0:17
we can insert a node at any point
in the list in constant time.
0:21
Much like binary search,
though, there's a catch.
0:25
To find the node at that
position we want to insert,
0:28
we need to traverse the list and
get to that point.
0:31
We just implemented our search
algorithm for the linked list type.
0:35
And we know that his runs in linear time.
0:38
So while actually inserting is fast,
0:40
finding the position in the list
you want to insert it is not.
0:43
This is why I mentioned that there
were some caveats to inserting.
0:47
Anyway, let's see what
this looks like in code.
0:50
We'll define a method named
insert that takes data to insert
0:54
along with an index position.
0:58
So we'll do this after search, right here.
1:00
Say, def insert.
1:03
And this takes some data to insert and
a position to insert it at.
1:08
You may be thinking, wait a minute.
1:14
Linked lists don't have
index positions right?
1:16
And you're correct, but we can mimic that
behavior by just counting the number of
1:19
times we access next node.
1:24
If the index value passed
into this argument is 0,
1:26
that means we want to insert the new
node at the head of the list.
1:29
This is effectively the same
behavior as calling add,
1:34
which means the logic is the same.
1:37
So we don't need to repeat it.
1:39
We can call the add
method we wrote earlier.
1:41
So we'll say, if index, if index == 0,
1:43
or if index is 0, then, self.add data.
1:48
If the index is greater than 0,
1:53
then we need to traverse the list to
find the current node at that index.
1:56
So if index > 0.
2:01
Now, before we do that,
2:05
we need to create a new node
containing the data we want to insert.
2:06
So we'll say new = node, with some data.
2:10
I'm going to assign index the argument
passed to our function to a local
2:15
variable named position and the head of
the list to a variable named current.
2:20
position = index.
2:25
current = self.head.
2:28
Every time we call current.next_node,
meaning we're moving to the next node
2:32
in the list,
we'll decrease the value of position by 1.
2:37
When position is 0, we'll have
arrived at the node that's currently
2:41
at the position we want to insert it.
2:45
In reality though,
we don't to decrease it all the way to 0.
2:48
Imagine we have a list with five nodes and
we want to insert in node at position 3.
2:52
To insert a node at position 3, we need
to modify the node at position 2 and 3.
2:57
Node 2's next node attribute is
going to point to the new node.
3:03
And the new node's next node
attribute will point to node 3.
3:07
In this way,
an insert is a constant time operation.
3:11
We don't need to shift
every single element,
3:15
we just modify a few next node references.
3:18
In a doubly linked list, we can use node
3 to carry out both of these operations.
3:20
Node 3 in a doubly linked list would
have a reference to node 2, and
3:26
we can use this reference to
modify all the unnecessary links.
3:31
And a singly linked list though,
which is what we have,
3:35
if we kept decreasing positions until
we're at 0, we arrive at node 3.
3:39
We can then set the new node's next
node property to point to node 3, but
3:44
we have no way of getting a reference
to node 2, which we also need.
3:48
For this reason,
3:53
it's easier to decrease position to just
1 when it equals 1 and stop at node 2.
3:55
So in here we'll say, while position > 1.
4:01
That while the position is > 1,
we'll keep calling next_node and
4:08
reassigning the current node.
4:12
So, current = node.next_node.
4:14
And at the same time,
we'll decrement position.
4:18
So position = position- 1,
4:21
which you can also
succinctly write as -= 1.
4:25
This way, when the position equals 1,
the loop exits and
4:31
current will refer to the node at
the position before the insert point.
4:36
So outside the while loop, we'll say,
4:41
prev = current, and
next = current.next node.
4:45
To make things more clear, what I've done
here is name the node before the new
4:51
one prev and
the node after the new one next.
4:56
All that's left to do now is to insert
the new node between prev and next.
4:59
So we'll say prev.next_ node = new.
5:04
And then, new next.node = next.
5:10
Now it seems like there's an issue
with variable naming here,
5:17
and I'm most probably conflicting with
some globally named next variable.
5:19
So I should go ahead and
call this next_node and prev_node,
5:24
so that we don't mess things up here,
prev_node.
5:29
So the .next_node is obviously
the attribute on a node, but
5:36
this is just a local variable.
5:40
Lets document this method.
5:42
So up the top, we'll add a doc string and
5:43
we'll say, Inserts a new node
containing data and index position.
5:48
Insertion takes constant time
5:57
But finding the node at the insertion
6:04
point takes the linear time.
6:11
Let's add this to the next line,
there we go.
6:16
And then we'll say therefore,
it takes an overall, Linear time.
6:20
This is why even though we can easily
insert a new node without having to
6:28
shift the rest, ultimately,
adding either to the head or the tail,
6:32
if you have a reference
is much more efficient.
6:36
We have one more operation to add to our
linked list that will make it a robust
6:39
data structure.
6:43
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