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You have completed Introduction to Data Structures!
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In the last video we defined an implementation for the version of the split function that works on linked lists. In this video let's tackle the final portion - sorting and merging smaller linked lists.
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In the last video,
we defined an implementation for
0:00
the version of the split function
that works on linked lists.
0:03
It contained a tiny bit more code
than the array or list version and
0:06
that was expected.
0:10
The merge function is no different
because like with the split function,
0:11
after we carry out a comparison operation,
0:15
we also need to swap references
to corresponding nodes.
0:18
All right, let's add our merge
function over here at the bottom,
0:21
below the split function.
0:26
So we'll call this merge, and
it's going to take a left and a right.
0:28
Now, because this can get complicated,
0:33
we're going to document
this function extensively.
0:35
And as always,
we're going to start with a docstring.
0:38
So say that this function
merges two linked lists,
0:43
sorting by data in the nodes and
it returns a new, merged list.
0:49
Remember that in the merged step, we're
going to compare values across two linked
0:59
lists and then return a new linked list
with nodes where the data is sorted.
1:04
So first we need to create
that new linked list.
1:08
Let's add a comment in here.
1:11
We'll say create a new linked list that
1:13
contains nodes from, what's that?
1:17
On new line, merging left and right.
1:22
Okay, and then create a list.
1:24
So merged = new LinkedList.
1:26
To this list,
we're gonna do something unusual.
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We're going to add a fake head.
1:33
This is so that when adding sorted notes,
we can reduce the amount of code we have
1:35
to write but not worrying about
whether we're at the head of the list.
1:40
Once we're done, we can assign
the first sorted node as the head and
1:43
discard the fake head.
1:47
Now, this might not make sense at first,
but not having to worry about whether
1:49
the new linked list already contains
a head or not makes the code simpler.
1:53
We'll add another comment.
1:57
Add a fake head that is discarded later.
1:59
We'll say merged.add(0).
2:04
Like we've been doing so far,
2:07
we'll declare a variable named current
to point to the head of the list.
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Set current to the head
of the linked list and
2:14
then current = merged.head.
2:19
Next, we'll get a reference to the head on
each of the linked list, left and right.
2:23
So we'll say obtain head nodes for
2:29
left and right linked lists.
2:34
And here we'll call this
left_head = left.head and
2:38
right_head = right.head.
2:44
Okay, so with that setup out of the way,
let's start iterating over both lists.
2:51
So another comment,
2:57
iterate over left and right as long, or
2:59
we'll say until we reach
the tail node of either.
3:04
And we'll do that by saying
while left_head or right_head.
3:11
So this is a pattern that we've
been following all along.
3:17
We're going to iterate until we hit the
tail nodes of both lists and we'll move
3:20
this pointer forward every time so that we
traverse the list with every iteration.
3:24
If you remembered the logic behind this
from the earlier version, once we hit
3:29
the tail node of one list, if there are
nodes left over in the other linked list,
3:32
we don't need to carry out
a comparison operation anymore.
3:37
And we can simply add those
nodes to the merged list.
3:40
The first scenario we'll consider is if
the head of the left linked list is none.
3:44
This means we're already
past the tail of left, and
3:49
we can add all the nodes from the right
link list to the final merged list.
3:52
So you'll say,
if the head node of left is None,
3:57
we're past the tail.
4:03
Add the node from right
to merged linked list.
4:05
So here we'll say if left_head
is None: current.next_node,
4:14
remember current points to the head of
the merge list that we're going to return.
4:19
So here we're setting
its next node reference
4:26
to the head node on the right link list.
4:29
So we will say it, right head.
4:32
Then, when we do that, we'll move
the right head forward to the next node,
4:35
so we'll say right_head
= right_head.next_node.
4:43
This terminates the loop
on the next iteration.
4:48
Let's look at a visualization
to understand why.
4:51
Let's say we start off with a linked
list containing four nodes.
4:54
So we keep calling split on it until
we have lists with just a single head,
4:58
single node linked lists essentially.
5:02
So let's focus on these two down
here that we'll call left and right.
5:05
We haven't implemented the logic for
this part yet, but here,
5:08
we would compare the data values and
see which one is less than the other.
5:12
So we'll assume that left's head
is lesser than right's head.
5:16
So we'll set this as the next
node in the final merged list.
5:19
Left is now an empty linked list,
so left.head equals none.
5:23
On the next path through the loop,
5:28
left_head is none which is
the situation we just implemented.
5:30
Here we can go ahead and and
5:34
now assign right_head as the next
node in the merged linked list.
5:35
We know that right is also
a singly linked list.
5:39
Here's the crucial bit.
5:42
When we move the pointer forward by
calling next node on the right node,
5:44
there is no node and the right link,
the right link list is also empty now,
5:49
which means that both left_head and
right_head are none, and
5:55
either one of these would cause
our loop condition to terminate.
5:58
So what we've done here is encoded
a stopping condition for the loop.
6:02
So we need to document this
because it can get fuzzy.
6:07
So right above that line of code,
I'll say call
6:09
next on right to set
loop condition to False.
6:14
Okay, there's another way we can
arrive at this stopping condition, and
6:19
that's in the opposite direction if we
start with the right_head being none.
6:23
So here we'll say I'm going to add another
comment if, oops, not there, there.
6:26
If the head node of right is None,
6:33
we're past the tail.
6:39
And we'll say, add the tail node
from left to merged linked list.
6:43
And then we'll add that condition.
6:51
We'll say, elif right_head is None.
6:52
Now remember, we can enter these
even if left_head is None.
6:56
We can still go into this condition.
7:00
We can still enter this if statement and
execute this logic because while loop,
7:03
the loop condition here is an or
statement.
7:07
So even if left_head is false, if this
returns true because there's a value
7:10
there, there’s a node there,
the loop will keep going.
7:14
Okay, now in this case,
7:17
we want to set the head of the left linked
list as the next node on the merge list.
7:19
So this is simply the opposite
of what we did over here.
7:24
We'll set current.next_node = left_head.
7:28
And then we'll move, so after doing that,
we can move the variable pointing to
7:33
left head forward, which as we saw
earlier is past the tail node and
7:38
then results in the loop terminating.
7:41
So we'll say left_head
= left_head.next_node,
7:44
and I'll add that comment here as well.
7:48
So we'll say call next on left
to set loop condition to False.
7:52
Because here, right_head is None and
now we make left_head None.
7:59
These two conditions we looked
at were either the left_head or
8:03
right_head were at the tail
nodes of our respective lists.
8:06
Those are conditions that we run into when
we've reached the bottom of our split,
8:11
where we have single element
linked list or empty linked list.
8:16
Let's account for our final condition
8:20
where we're evaluating a node that is
neither the head nor the tail of the list.
8:22
And this condition, we need to reach into
the nodes and actually compare the data
8:28
values to one another before we can decide
which node to add first to the merge list.
8:32
So here this is an else because we've
arrived at our third condition,
8:38
third and final.
8:41
And here we'll say,
not at either tail node,
8:42
obtain node data to perform
comparison operations.
8:48
So let's get each of those data
values out of the respective nodes so
8:54
that we can compare it.
8:57
So we'll say left_data = left_head.data,
8:59
and right_data = right_head.data.
9:04
Okay, what do we do next?
9:08
Well, we compare.
9:10
But first, let's add a comment.
9:11
So we'll say if data on
left is less than right,
9:12
set current to left node.
9:19
And then move, actually,
we'll add this in a second.
9:22
So here, we'll say if left_data
is less than right_data,
9:26
then current.next_node = left_head.
9:32
And then we'll add a comment, and
9:37
we'll say move left head
to next node on that list.
9:40
So we'll say,
left_head = left_head.next_node.
9:44
Just as our comment says, we'll check if
the left_data is less than the right_data.
9:51
If it is,
since we want a list in ascending order,
9:57
we'll assign the left node to be
the next node in the merged list.
10:00
We'll also move the left_head forward
to traverse down to the next node
10:04
in that particular list.
10:08
Now if left is larger than right,
then we want to do the opposite.
10:10
So we'll go back two spaces,
add another comment.
10:14
If data on left is greater than right,
10:17
set current to right node, okay?
10:23
So else, here we assign the right_head
to be the next node in the merged list,
10:27
so current.next_node = right_head.
10:35
And then comment,
move right head to next node.
10:39
So right_head = right_head.next_node.
10:45
Okay, after doing that, we move the
right_head pointer to reference in next
10:53
node in the right list and finally, at the
end of each iteration of the while loop,
10:58
so not here but two spaces back, right?
11:03
Make sure we're indented at the same
level as the while, so we gotta go,
11:06
yep, or not the same level as
the while but the same outer scope.
11:11
And then there we're going to
say move current to next node,
11:15
so current = current.next_node.
11:21
Okay, don't worry if this is confusing,
as always,
11:26
we'll look at a visualization
in just a bit.
11:29
So we'll wrap up this function by
discarding that fake head we set earlier,
11:31
setting the correct node as head,
and returning the linked list.
11:35
So we'll add a comment, discard fake head,
11:39
and set first merged node as head.
11:45
So here we'll say head =
merged.head.next_node.
11:49
And then merged.head = head.
11:56
And finally, return merged.
11:59
Okay, we wrote a lot of code here.
12:03
A lot of it was comments but
still it's a bunch.
12:05
Let's take a quick break.
12:07
In the next video, we'll test this out,
evaluate our results, and
12:09
determine the runtime of our algorithm.
12:12
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