algorithms and data structures teach that algorithms and data structures an algorithm does...
TRANSCRIPT
Algorithms and Data Structures
TEACH THAT
Algorithms and Data Structures
An algorithm does something, solves some problem, in a mechanical way.It is a bit like a “machine” or a specialised tool
Algorithms and Data Structures
A data structure is some way to represent and store dataso that we can process that data efficiently
Algorithms and Data Structures
Data structures use algorithms
Algorithms use data structures
Algorithms and Data Structures
Data Structures and Algorithmsa Computer Scientist’s building blocks
Algorithms and Data Structures
Computer Scientist invent and study algorithms and data structures and problems
Algorithms and Data Structures
Computer Scientists do other things too
Our website, link from moodle
Lecture
14
Why don’t I just go away and read the book myself?
Why come to lectures? • meet new exciting people• keep in touch with fashion, trends, …• be part of the “in” crowd•
ADS2 Lecture 1
Lectures … Aye, right.
Algorithms&
Data Structures
Algorithms
&
Data Structures
Great!
Now and then I will take an attendance register
Lassie, what’s in this ADS2 course ? Will it be interesting?
woof!
Content
• linked lists• single/doubly-linked, • insert, delete, find, min, max, …
• stacks• push/pop/size• bracket matching, RP calculator
• queues• enqueue/dequeue/size• circular queue (in array)
• recursion• see above
• big O
Content
• trees• n-ary trees: representations & properties• binary trees
• representations & properties & traversals• binary search trees
• insert/find/delete/traverse/height …• AVL trees• heap
• insert/delete/sort• splay trees (maybe)• red-black trees (maybe)
Continued
Content
• skip lists (maybe)• Sorting
• bubble/insert/sift sort• merge sort• quick sort• bucket sort (pigeon hole sort)• bead sort (maybe)
• Dictionaries• maps and hash tables
• open and closed hashing
Continued
ContentContinued
• 5 pieces of practical work• 2 of above are assessed (20%)• exam in May (80%)• lab every 2nd week• woof
Algorithms&
Data Structures
Algorithms
&
Data Structures
Great!
our ADS2 website under construction
(permanently)
Home
News
The lectures
The lectures
code & api
Lots of code in there
demos
Links to interesting & useful stuff
Links to interesting & useful stuff
exercises
exercises
exercises
Questions & Answers
… and now for something completely different!!!
Lassie, why are algorithms and data structures important?
Lassie, will there be anything in the course that is challenging and exciting?
I just hope I get feedback, continuously
Lassie, will you teach us to “THINK LIKE A COMPUTER SCIENTIST”?
Lassie, honestly, I’m not that experienced as a programmer. Will you help us with our programming?
Will we use BIG data sets?
woof!
1st lecture … “Who cares?”
algorithms are ancient
Many algorithms predate computers
But first … what is an algorithm?
What is an algorithm?
A finite sequence of instructions, each with a clear meaning, and can be performed with a
finite amount of effort in a finite length of time [Aho, Hopcroft, Ullman 1983]
Before some of you were born
Abu Jafar Mohammed ibm Musa Al Khwarizmi
800AD
Before I was born
Euclid of Alexandria
325BC to 265BC
GCD
Data Structures … what’s that then?
ways to organise data/information efficiently
where will I (not) see data structures?
Data structure
Data structure
Data structure
Not a Data structure – ADT (see next slide)
abstract data types?
Definitions contd.
• Basically an ADT is an “abstract” entity• But a data structure has a fixed implementation (as well as
“structural” properties).
60ADS2 Lecture 2
Who cares?Machines are getting
bigger, faster, cheaper … do efficient data structures and
algorithms really matter?
Bigger, faster, cheaper machines
Bigger data sets, greater expectations
An Example: from problem to program
Sequencing traffic lightsA Formal Model
A-left
A-right
A-left
A-right
B-right
B-leftB-straight
A-left
A-right
B-right
B-leftB-straight
C-straight
AL
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CS
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Draw a line (edge) between turns that CANNOT occur atthe same time
Draw a line (edge) between turns that CANNOT occur atthe same time
AL
AR
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Draw a line (edge) between turns that CANNOT occur atthe same time
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Draw a line (edge) between turns that CANNOT occur atthe same time
Draw a line (edge) between turns that CANNOT occur atthe same time
AL
AR
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BS
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Draw a line (edge) between turns that CANNOT occur atthe same time
AL
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Draw a line (edge) between turns that CANNOT occur atthe same time
Draw a line (edge) between turns that CANNOT occur atthe same time
AL
AR
BR
BS
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CS
Draw a line (edge) between turns that CANNOT occur atthe same time
Draw a line (edge) between turns that CANNOT occur atthe same time
AL
AR
BR
BS
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CS
Draw a line (edge) between turns that CANNOT occur atthe same time
Draw a line (edge) between turns that CANNOT occur atthe same time
AL
AR
BR
BS
BL
CS
Draw a line (edge) between turns that CANNOT occur atthe same time
Draw a line (edge) between turns that CANNOT occur atthe same time
AL
AR
BR
BS
BL
CS
Label turns that have an edge between them (adjacent) differently.The minimum number of labels used Is the minimum (maximum) number of concurrent turns disallowed (allowed)
AL
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BS
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Label turns that have an edge between them (adjacent) differently.The minimum number of labels used Is the minimum (maximum) number of concurrent turns disallowed (allowed)
For “label” let’s use “colour”
AL
AR
BR
BS
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Label turns that have an edge between them (adjacent) differently.The minimum number of labels used Is the minimum (maximum) number of concurrent turns disallowed (allowed)
For “label” let’s use “colour”
AL
AR
BR
BS
BL
CS
Label turns that have an edge between them (adjacent) differently.The minimum number of labels used Is the minimum (maximum) number of concurrent turns disallowed (allowed)
For “label” let’s use “colour”
Label turns that have an edge between them (adjacent) differently.The minimum number of labels used Is the minimum (maximum) number of concurrent turns disallowed (allowed)
AL
AR
BR
BS
BL
CS
Label turns that have an edge between them (adjacent) differently.The minimum number of labels used Is the minimum (maximum) number of concurrent turns disallowed (allowed)
For “label” let’s use “colour”
AL
AR
BR
BS
BL
CS
Label turns that have an edge between them (adjacent) differently.The minimum number of labels used Is the minimum (maximum) number of concurrent turns disallowed (allowed)
For “label” let’s use “colour”
AL
AR
BR
BS
BL
CS
Label turns that have an edge between them (adjacent) differently.The minimum number of labels used Is the minimum (maximum) number of concurrent turns disallowed (allowed)
For “label” let’s use “colour”
AL
AR
BR
BS
BL
CS
Label turns that have an edge between them (adjacent) differently.The minimum number of labels used Is the minimum (maximum) number of concurrent turns disallowed (allowed)
For “label” let’s use “colour”
AL
AR
BR
BS
BL
CS
Therefore we could allow same colouredturns to go at the same time: blue, green, pink and it will be collision-free
AL
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BR
BS
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We have 3 time steps
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Could we do it in less than 3 time steps?Is this solution unique?What is the “underlying” problem?What is its complexity?Are there any algorithms that can be used?
AL
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Is Dobie’s Loan actually scheduled optimally?
AL
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Might this be an obvious solution?
B
C
A
E
D
Try This
One way
JoJo’s intersection, Princeton
B
C
A
E
D
JoJo’s intersection, Princeton
ABACADBABCBDDADBDCEAEBECED
turns
B
C
A
E
D
JoJo’s intersection, Princeton
ED
EC
EB
EA
DC
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DA
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BC
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AD
AC
AB
EDECEBEADCDBDABDBCBAADACAB
B
C
A
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JoJo’s intersection, Princeton
ED
EC
EB
EA
DC
DB
DA
BD
BC
BA
AD
AC
AB
EDECEBEADCDBDABDBCBAADACAB
1111
11111
111
111
11111
11111
11
111
11111
1111
JoJo’s intersection, Princeton, USA (allowed a right turn against the lights)
B
C
A
E
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JoJo’s intersection, Princeton
ED
EC
EB
EA
DC
DB
DA
BD
BC
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AD
AC
AB
EDECEBEADCDBDABDBCBAADACAB
1111
11111
111
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11111
11
111
11111
1111
ED
EA
BC
EC
EB
DC
DA
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AD
AC
DB
AB
BD
B
C
A
E
D
JoJo’s intersection, Princeton
ED
EC
EB
EA
DC
DB
DA
BD
BC
BA
AD
AC
AB
EDECEBEADCDBDABDBCBAADACAB
1111
11111
111
111
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11
111
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ED
EA
BC
EC
EB
DC
DA
BA
AD
AC
DB
AB
BD
JoJo’s intersection, Princeton, USA (allowed a right turn against the lights)
B
C
A
E
D
JoJo’s intersection, Princeton
ED
EC
EB
EA
DC
DB
DA
BD
BC
BA
AD
AC
AB
EDECEBEADCDBDABDBCBAADACAB
1111
11111
111
111
11111
11111
11
111
11111
1111
ED
EA
BC
EC
EB
DC
DA
BA
AD
AC
DB
AB
BD
B
C
A
E
D
JoJo’s intersection, Princeton
ED
EC
EB
EA
DC
DB
DA
BD
BC
BA
AD
AC
AB
EDECEBEADCDBDABDBCBAADACAB
1111
11111
111
111
11111
11111
11
111
11111
1111
ED
EA
BC
EC
EB
DC
DA
BA
AD
AC
DB
AB
BD
4 colours4 steps
B
C
A
E
D
JoJo’s intersection, Princeton
ED
EC
EB
EA
DC
DB
DA
BD
BC
BA
AD
AC
AB
EDECEBEADCDBDABDBCBAADACAB
1111
11111
111
111
11111
11111
11
111
11111
1111
ED
EA
BC
EC
EB
DC
DA
BA
AD
AC
DB
AB
BD
4 colours4 steps
4-clique!
