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1
00:00:00,000 --> 00:00:03,381
>> [MUSIC PLAYING]

2
00:00:03,381 --> 00:00:04,604

3
00:00:04,604 --> 00:00:05,520
DOUG LLOYD: All right.

4
00:00:05,520 --> 00:00:07,860
So if you just finished that
video on singly-linked lists sorry

5
00:00:07,860 --> 00:00:09,568
I left you off on a
bit of a cliffhanger.

6
00:00:09,568 --> 00:00:12,790
But I'm glad you're here to finish
the story of doubly-linked lists.

7
00:00:12,790 --> 00:00:15,250
>> So if you recall from
that video, we talked

8
00:00:15,250 --> 00:00:18,500
about how singly-linked
lists do attend our ability

9
00:00:18,500 --> 00:00:22,090
to deal with information
where the number of elements

10
00:00:22,090 --> 00:00:24,442
or the number of items in
a list can grow or shrink.

11
00:00:24,442 --> 00:00:26,400
We can now deal with
something like that, where

12
00:00:26,400 --> 00:00:28,310
we couldn't deal with it with arrays.

13
00:00:28,310 --> 00:00:30,560
>> But they do suffer from one
critical limitation which

14
00:00:30,560 --> 00:00:33,790
is that with a singly-linked
list, we can only ever move

15
00:00:33,790 --> 00:00:36,200
in a single direction through the list.

16
00:00:36,200 --> 00:00:39,010
And the only real situation
where that can become a problem

17
00:00:39,010 --> 00:00:41,250
was when we were trying to
delete a single element.

18
00:00:41,250 --> 00:00:46,000
And we didn't even discuss how to do it
in a singly-linked list in pseudocode.

19
00:00:46,000 --> 00:00:48,797
It is certainly doable, but
it can be a bit of a hassle.

20
00:00:48,797 --> 00:00:50,630
So if you find yourself
in a situation where

21
00:00:50,630 --> 00:00:53,175
you're trying to delete
single elements from the list

22
00:00:53,175 --> 00:00:55,430
or it's going to be required
that you'll be deleting

23
00:00:55,430 --> 00:00:57,970
single elements from
the list, you might want

24
00:00:57,970 --> 00:01:02,090
to consider using a doubly-linked
list instead of a singly-linked list.

25
00:01:02,090 --> 00:01:06,320
Because doubly-linked lists allow you
to move both forwards and backwards

26
00:01:06,320 --> 00:01:09,340
through the list instead of
just forward through the list--

27
00:01:09,340 --> 00:01:13,950
just by adding one extra element
to our structure definition

28
00:01:13,950 --> 00:01:16,690
for the doubly-linked list node.

29
00:01:16,690 --> 00:01:19,770
>> Again, if you're not going to
be deleting single elements

30
00:01:19,770 --> 00:01:24,810
from the list-- because we're adding
an extra field to our structure

31
00:01:24,810 --> 00:01:28,340
definition, the nodes themselves
for doubly-linked lists

32
00:01:28,340 --> 00:01:29,550
are going to be larger.

33
00:01:29,550 --> 00:01:31,600
They're going to take
up more bytes of memory.

34
00:01:31,600 --> 00:01:34,160
And so if this is not something
you're going to need to do,

35
00:01:34,160 --> 00:01:36,300
you might decide it's
not worth the trade off

36
00:01:36,300 --> 00:01:39,360
to have to spend the extra
bytes of memory required

37
00:01:39,360 --> 00:01:43,940
for a doubly-linked list if you're not
going to be deleting single elements.

38
00:01:43,940 --> 00:01:46,760
But they're also cool
for other things too.

39
00:01:46,760 --> 00:01:51,260
>> So as I said, we just have to add
one single field to our structure

40
00:01:51,260 --> 00:01:55,360
definition-- this notion
of a Previous pointer.

41
00:01:55,360 --> 00:01:58,620
So with a singly-linked list, we
have the value and the Next pointer,

42
00:01:58,620 --> 00:02:02,850
so the doubly-linked list just has
a way to move backwards as well.

43
00:02:02,850 --> 00:02:04,960
>> Now in the singly-linked
list video, we talked

44
00:02:04,960 --> 00:02:07,210
about these are five of the
main things you need to be

45
00:02:07,210 --> 00:02:09,449
able to do to work with linked lists.

46
00:02:09,449 --> 00:02:12,880
And for most of these, the fact
that it's a doubly-linked list

47
00:02:12,880 --> 00:02:14,130
isn't really a big jump.

48
00:02:14,130 --> 00:02:17,936
We can still search through by just
moving forward from start to end.

49
00:02:17,936 --> 00:02:20,810
We can still create a node out of
thin air, pretty much the same way.

50
00:02:20,810 --> 00:02:23,591
We can delete lists pretty
much the same way too.

51
00:02:23,591 --> 00:02:25,340
The only things that
are subtly different,

52
00:02:25,340 --> 00:02:28,970
really, are inserting
new nodes into the list,

53
00:02:28,970 --> 00:02:33,722
and we'll finally talk about deleting
a single element from the list as well.

54
00:02:33,722 --> 00:02:35,430
Again, pretty much
the other three, we're

55
00:02:35,430 --> 00:02:37,888
not going to talk about them
right now because they're just

56
00:02:37,888 --> 00:02:43,920
very minor tweaks on the ideas discussed
in the singly-linked list video.

57
00:02:43,920 --> 00:02:46,292
>> So let's insert a new node
into a doubly-linked list.

58
00:02:46,292 --> 00:02:48,750
We talked about doing this for
singly-linked lists as well,

59
00:02:48,750 --> 00:02:52,020
but there's a couple of extra
catches with doubly-linked lists.

60
00:02:52,020 --> 00:02:55,280
We're [? passing ?] in the head of the
list here and some arbitrary value,

61
00:02:55,280 --> 00:02:58,600
and we want to get the new head
of the list out of this function.

62
00:02:58,600 --> 00:03:01,414
That's why it returns a dllnode star.

63
00:03:01,414 --> 00:03:02,330
So what are the steps?

64
00:03:02,330 --> 00:03:04,496
They are, again, very similar
to singly-linked lists

65
00:03:04,496 --> 00:03:05,670
with one extra addition.

66
00:03:05,670 --> 00:03:08,900
We want to allocates space for a new
node and check to make sure it's valid.

67
00:03:08,900 --> 00:03:11,510
We want to fill that node up
with whatever information we

68
00:03:11,510 --> 00:03:12,564
want to put in it.

69
00:03:12,564 --> 00:03:15,480
The last thing we need to do-- the
extra thing we need to do, rather--

70
00:03:15,480 --> 00:03:19,435
is to fix the Previous pointer
of the old head of the list.

71
00:03:19,435 --> 00:03:21,310
Remember that because
of doubly-linked lists,

72
00:03:21,310 --> 00:03:23,110
we can move forward
and backwards-- which

73
00:03:23,110 --> 00:03:27,080
means that each node actually points
to two other nodes instead of just one.

74
00:03:27,080 --> 00:03:29,110
And so we need to fix
the old head of the list

75
00:03:29,110 --> 00:03:32,151
to point backward to the new head of
the linked list, which was something

76
00:03:32,151 --> 00:03:33,990
we didn't have to do before.

77
00:03:33,990 --> 00:03:37,420
And as before, we just return a
pointer to the new head of the list.

78
00:03:37,420 --> 00:03:38,220
>> So here's a list.

79
00:03:38,220 --> 00:03:40,144
We want to insert 12 into this list.

80
00:03:40,144 --> 00:03:42,060
Notice that the diagram
is slightly different.

81
00:03:42,060 --> 00:03:47,710
Each node contains three fields--
data, and a Next pointer in red,

82
00:03:47,710 --> 00:03:50,170
and a Previous pointer in blue.

83
00:03:50,170 --> 00:03:54,059
Nothing comes before the 15 node,
so its Previous pointer is null.

84
00:03:54,059 --> 00:03:55,350
It's the beginning of the list.

85
00:03:55,350 --> 00:03:56,560
There's nothing before it.

86
00:03:56,560 --> 00:04:03,350
And nothing comes after the 10 node, and
so it's Next pointer is null as well.

87
00:04:03,350 --> 00:04:05,616
>> So let's add 12 to this list.

88
00:04:05,616 --> 00:04:08,070
We need [INAUDIBLE] space for the node.

89
00:04:08,070 --> 00:04:11,480
We put 12 inside of it.

90
00:04:11,480 --> 00:04:14,840
And then again, we need to be really
careful not to break the chain.

91
00:04:14,840 --> 00:04:17,144
We want to rearrange the
pointers in the correct order.

92
00:04:17,144 --> 00:04:19,519
And sometimes that might mean--
as we'll see particularly

93
00:04:19,519 --> 00:04:24,120
with delete-- that we do have some
redundant pointers, but that's OK.

94
00:04:24,120 --> 00:04:25,750
>> So what do we want to do first?

95
00:04:25,750 --> 00:04:28,290
I would recommend the
things you should probably

96
00:04:28,290 --> 00:04:35,350
do are to fill the pointers of the 12
node before you touch anybody else.

97
00:04:35,350 --> 00:04:38,640
So what is 12 going to point to next?

98
00:04:38,640 --> 00:04:39,860
15.

99
00:04:39,860 --> 00:04:42,430
What comes before 12?

100
00:04:42,430 --> 00:04:43,640
Nothing.

101
00:04:43,640 --> 00:04:46,280
Now we've filled the
extra information in 12

102
00:04:46,280 --> 00:04:49,320
so it has Previous, Next, and value.

103
00:04:49,320 --> 00:04:53,505
>> Now we can have 15-- this extra
step we were talking about-- we

104
00:04:53,505 --> 00:04:56,590
can have 15 point back to 12.

105
00:04:56,590 --> 00:04:59,634
And now we can move the head of
the linked list to also be 12.

106
00:04:59,634 --> 00:05:02,550
So it's pretty similar to what we
were doing with singly-linked lists,

107
00:05:02,550 --> 00:05:06,940
except for the extra step of
connecting the old head of the list

108
00:05:06,940 --> 00:05:09,810
back to the new head of the list.

109
00:05:09,810 --> 00:05:12,170
>> Now let's finally delete
a node from a linked list.

110
00:05:12,170 --> 00:05:14,350
So let's say we have
some other function that

111
00:05:14,350 --> 00:05:18,080
is finding a node we want to delete
and has given us a pointer to exactly

112
00:05:18,080 --> 00:05:19,710
the node that we want to delete.

113
00:05:19,710 --> 00:05:22,360
We don't even need-- say the
head is still globally declared.

114
00:05:22,360 --> 00:05:23,590
We don't need head here.

115
00:05:23,590 --> 00:05:26,830
All this function is doing is we've
found a pointer to exactly the node we

116
00:05:26,830 --> 00:05:28,090
want to get rid of.

117
00:05:28,090 --> 00:05:28,940
Let's get rid of it.

118
00:05:28,940 --> 00:05:31,859
It's a lot easier with
doubly-linked lists.

119
00:05:31,859 --> 00:05:33,650
First-- it's actually
just a couple things.

120
00:05:33,650 --> 00:05:38,760
We just need to fix the surrounding
nodes' pointers so that they skip over

121
00:05:38,760 --> 00:05:40,240
the node we want to delete.

122
00:05:40,240 --> 00:05:43,484
And then we can delete that node.

123
00:05:43,484 --> 00:05:45,150
So again, we're just going through here.

124
00:05:45,150 --> 00:05:49,625
We have apparently decided that
we want to delete the node X.

125
00:05:49,625 --> 00:05:51,500
And again, what I'm
doing here-- by the way--

126
00:05:51,500 --> 00:05:54,580
is a general case for a
node that is in the middle.

127
00:05:54,580 --> 00:05:56,547
There are a couple of
extra caveats that you

128
00:05:56,547 --> 00:05:59,380
need to consider when you're deleting
the very beginning of the list

129
00:05:59,380 --> 00:06:01,040
or the very end of the list.

130
00:06:01,040 --> 00:06:03,730
There's a couple of special
corner cases to deal with there.

131
00:06:03,730 --> 00:06:07,960
>> So this works for deleting any node
in the middle of the list-- one that

132
00:06:07,960 --> 00:06:11,550
has a legitimate pointer forward
and a legitimate pointer backward,

133
00:06:11,550 --> 00:06:14,460
legitimate Previous and Next pointer.

134
00:06:14,460 --> 00:06:16,530
Again, if you're working
with the ends, you

135
00:06:16,530 --> 00:06:18,500
need to handle those
slightly differently,

136
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and we're not going to
talk about that now.

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But you can probably
figure out what needs

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to be done just by watching this video.

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>> So we've isolated X. X is the node
we want to delete from the list.

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What do we do?

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First, we need to rearrange
the outside pointers.

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We need to rearrange
9's next to skip over 13

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and point to 10-- which
is what we've just done.

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And we also need to
rearrange 10's Previous

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to point to 9 instead of pointing to 13.

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>> So again, this was the
diagram to start with.

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This was our chain.

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We need to skip over 13,
but we need to also preserve

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the integrity of the list.

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We don't want to lose any
information in either direction.

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So we need to rearrange
the pointers carefully

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so we don't break the chain at all.

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>> So we can say 9's Next pointer
points to the same place

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that thirteen's Next
pointer points right now.

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Because we're eventually
going to want to skip over 13.

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So wherever 13 points next, you
want nine to point there instead.

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So that's that.

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And then wherever 13 points back
to, whatever comes before 13,

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we want 10 to point
to that instead of 13.

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Now notice, if you follow
the arrows, we can drop 13

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without actually losing any information.

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We've kept the integrity of the list,
moving both forward and backward.

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And then we can just sort
of clean it up a little bit

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by pulling the list together.

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So we rearranged the
pointers on either side.

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And then we freed X the
node that contained 13,

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and we didn't break the chain.

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So we did good.

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>> Final note here on linked lists.

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So both singly- and doubly-linked
lists, as we've seen,

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support really efficient insertion
and deletion of elements.

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You can pretty much do
it in constant time.

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What did we have to do to delete
an element just a second ago?

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We moved one pointer.

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We moved another pointer.

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We freed X-- took three operations.

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It always takes three operations to
delete that node-- to free a node.

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>> How do we insert?

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Well, we're just always
tacking on the beginning

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if we're inserting efficiently.

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So we need to rearrange--
depending on if it's

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a singly- or doubly-linked
list, we might need to do three

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or four operations max.

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But again, it's always three or four.

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It doesn't matter how many
elements are in our list,

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it's always three or four operations--
just like deletion is always

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three or four operations.

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It's constant time.

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So that's really great.

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00:08:38,169 --> 00:08:40,620
>> With arrays, we were doing
something like insertion sort.

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You probably recall that insertion
sort is not a constant time algorithm.

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00:08:44,739 --> 00:08:46,030
It's actually pretty expensive.

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So this is a lot better for inserting.

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But as I mentioned in the
singly-linked list video,

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we've got a downside here too, right?

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We've lost the ability to
randomly access elements.

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00:08:57,580 --> 00:09:02,310
We can't say, I want element number four
or element number 10 of a linked list

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the same way that we can
do that with an array

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00:09:04,990 --> 00:09:08,630
or we can just directly index
into our array's element.

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00:09:08,630 --> 00:09:10,930
>> And so trying to find an
element in a linked list--

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00:09:10,930 --> 00:09:15,880
if searching is important--
may now take linear time.

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00:09:15,880 --> 00:09:18,330
As the list gets longer, it
might take one additional step

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00:09:18,330 --> 00:09:22,644
for every single element in the list in
order to find what we're looking for.

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00:09:22,644 --> 00:09:23,560
So there's trade offs.

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00:09:23,560 --> 00:09:25,780
There's a bit of a pro
and con element here.

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00:09:25,780 --> 00:09:29,110
>> And doubly-linked lists are not the
last kind of data structure combination

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00:09:29,110 --> 00:09:32,840
that we'll talk about,
taking all the basic building

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00:09:32,840 --> 00:09:34,865
blocks of C an putting together.

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00:09:34,865 --> 00:09:37,900
Because in fact, we can
even do better than this

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to create a data structure that
you might be able to search through

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in constant time too.

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But more on that in another video.

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>> I'm Doug Lloyd.

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This is CS50.

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