Week 1 - Data Structures and Algorithms

Data Structures and
Algorithms
Week 1: Intro to Data Structures and Algorithms
Ferdin Joe John Joseph, PhD
Faculty of Information Technology
Thai-Nichi Institute of Technology, Bangkok

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Faculty of Information Technology, Thai -
Nichi Institute of Technology
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DSA 107 – A Road Map
Attendance
(10%)
Mid Exam
(40%)
How GPA
works for
DSA 107?
Final Exam
(50%)
3

Textbooks
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What is Program
• A Set of Instructions
• Data Structures + Algorithms
• Data Structure = A Container stores Data
• Algoirthm = Logic + Control
Lecture series for Semester 2, Data
Science and Analytics
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Functions of Data Structures
• Add
• Index
• Key
• Position
• Priority
• Search
• Change
• Delete
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Common Data Structures
• Array
• Stack
• Queue
• Linked List
• Tree
• Heap
• Hash Table
• Priority Queue
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How many Algorithms?
• Countless
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Algorithm Strategies
• Greedy
• Divide and Conquer
• Dynamic Programming
• Exhaustive Search
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Which Data Structure or Algorithm is
better?
• Must Meet Requirement
• High Performance
• Low RAM footprint
• Easy to implement
• Encapsulated
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Chapter 1 Basic Concepts
• Overview: System Life Cycle
• Algorithm Specification
• Data Abstraction
• Performance Analysis
• Performance Measurement
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1.1 Overview: system life cycle (1/2)
• Good programmers regard large-scale computer
programs as systems that contain many complex
interacting parts.
• As systems, these programs undergo a
development process called the system life cycle.
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1.1 Overview (2/2)
• We consider this cycle as consisting of
five phases.
• Requirements
• Analysis: bottom-up vs. top-down
• Design: data objects and operations
• Refinement and Coding
• Verification
• Program Proving
• Testing
• Debugging
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1.2 Algorithm Specification
• 1.2.1 Introduction
• An algorithm is a finite set of instructions that accomplishes a
particular task.
• Criteria
• input: zero or more quantities that are externally supplied
• output: at least one quantity is produced
• definiteness: clear and unambiguous
• finiteness: terminate after a finite number of steps
• effectiveness: instruction is basic enough to be carried out
• A program does not have to satisfy the finiteness criteria.
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1.2 Algorithm Specification
• Representation
• A natural language, like English or Chinese.
• A graphic, like flowcharts.
• A computer language, like C++, Java etc.
• Algorithms + Data structures = Programs
• Sequential search vs. Binary search
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1.3 Data abstraction (1/4)
• Data Type
A data type is a collection of objects and a set of
operations that act on those objects.
• For example, the data type int consists of the objects {0, +1, -1,
+2, -2, …, INT_MAX, INT_MIN} and the operations +, -, *, /, and
%.
• The data types of Java
• The basic data types: char, int, float and double etc
• The group data types: array and arraytype data type
• The user-defined types
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• Abstract Data Type
• An abstract data type(ADT) is a data type
that is organized in such a way that
the specification of the objects and
the operations on the objects is separated from
the representation of the objects and
the implementation of the operations.
• We know what is does, but not necessarily how it will do it.
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• Specification vs. Implementation
• An ADT is implementation independent
• Operation specification
• function name
• the types of arguments
• the type of the results
• The functions of a data type can be classify into several
categories:
• creator / constructor
• transformers
• observers / reporters
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• Example [Abstract data type Natural_Number]
::= is defined as
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1.4 Performance analysis (1/4)
• Criteria
• Is it correct?
• Is it readable?
• …
• Performance Analysis (machine independent)
• space complexity: storage requirement
• time complexity: computing time
• Performance Measurement (machine dependent)
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• 1.4.1 Space Complexity:
S(P)=C+SP(I)
• Fixed Space Requirements (C)
Independent of the characteristics
of the inputs and outputs
• instruction space
• space for simple variables, fixed-size structured variable, constants
• Variable Space Requirements (SP(I))
depend on the instance characteristic I
• number, size, values of inputs and outputs associated with I
• recursive stack space, formal parameters, local variables, return
address
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• 1.4.2 Time Complexity:
T(P)=C+TP(I)
• The time, T(P), taken by a program, P, is the sum of its
compile time C and its run (or execution) time, TP(I)
• Fixed time requirements
• Compile time (C), independent of instance characteristics
• Variable time requirements
• Run (execution) time TP
• TP(n)=caADD(n)+csSUB(n)+clLDA(n)+cstSTA(n)
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• A program step is a syntactically or semantically
meaningful program segment whose execution
time is independent of the instance
characteristics.
• Example
(Regard as the same unit machine independent)
• abc = a + b + b * c + (a + b - c) / (a + b) + 4.0
• abc = a + b + c
• Methods to compute the step count
• Introduce variable count into programs
• Tabular method
• Determine the total number of steps contributed by each
statement step per execution × frequency
• add up the contribution of all statements
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Array ADT – Java Implementation
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An Array-Based Implementation
of the ADT List
public class ListArrayBased
implements ListInterface {
private static final int MAX_LIST = 50;
private Object items[];
// an array of list items
private int numItems;
// number of items in list
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of the ADT List
public ListArrayBased() {
items = new Object[MAX_LIST];
numItems = 0;
} // end default constructor
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of the ADT List
public boolean isEmpty() {
return (numItems == 0);
} // end isEmpty
public int size() {
return numItems;
} // end size
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Insertion into Array
What happens if you want to insert an item at a specified
position in an existing array?
• Write over the current contents at the given index (which might not
be appropriate), or
• The item originally at the given index must be moved up one
position, and all the items after that index must shuffled up
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of the ADT List
public void add(int index, Object item)
throws ListException,
ListIndexOutOfBoundsException {
if (numItems >= MAX_LIST) {
throw new ListException("ListException on add:"+
" out of memory");
} // end if
if (index < 1 || index > numItems+1) {
// index out of range
throw new ListIndexOutOfBoundsException(
"ListIndexOutOfBoundsException on add");
} // end if
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of the ADT List
// make room for new element by shifting all items at
// positions >= index toward the end of the
// list (no shift if index == numItems+1)
for (int pos = numItems; pos >= index; pos--) {
items[pos] = items[pos-1];
} // end for
// insert new item
items[index-1] = item;
numItems++;
} //end add
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Removal from Arrays
What happens if you want to remove an item from a specified
position in an existing array?
• Leave gaps in the array, i.e. indices that contain no elements, which
in practice, means that the array element has to be given a special
value to indicate that it is “empty”, or
• All the items after the (removed item’s) index must be shuffled
down
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of the ADT Listpublic void remove(int index)
throws ListIndexOutOfBoundsException {
if (index >= 1 && index <= numItems) {
// delete item by shifting all items at
// positions > index toward the beginning of the list
// (no shift if index == size)
for (int pos = index+1; pos <= size(); pos++) {
items[pos-2] = items[pos-1];
} // end for
numItems--;
}
else { // index out of range
"ListIndexOutOfBoundsException on remove");
} // end if
} // end remove Lecture series for Semester 2, Data
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of the ADT List
public Object get(int index)
throws ListIndexOutOfBoundsException {
if (index >= 1 && index <= numItems) {
return items[index-1];
}
else { // index out of range
"ListIndexOutOfBoundsException on get");
} // end if
} // end get
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An Array-Based Implementation -
Summary
• Good things:
• Fast, random access of elements
• Very memory efficient, very little memory is required
other than that needed to store the contents (but see
bellow)
• Bad things:
• Slow deletion and insertion of elements
• Size must be known when the array is created and is
fixed (static)
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Recommended Reading
https://www.quora.com/Does-a-data-scientist-need-
to-know-algorithms-and-data-structures-as-well-as-
a-software-engineer
35

Next Week
Linked List ADT
Doubly Linked List
Circular Linked List
Implementation in Java
36

Week 1 - Data Structures and Algorithms

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