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Lecture 1: Introduction to data structures and
algorithms
University of Technology and Engineering
Vietnam National University Hanoi

Outline
➢Data structures and algorithms
➢Industrial problems
➢Data types
➢Abstract data structures
➢Problem description
Data Structures and Algorithms 2

Computer programs
➢ What is a computer program?
A computer program is a set of instructions that perform
specific tasks when executed by computers.
➢ What is a good computer program?
❖Correctness
❖Efficiency
❖Simple/Understandable
❖Easy to change/maintain and upgrade
“Program = Algorithms + Data structures”
N. Wirth

Data structures?
➢ What is a data structure?
A data structure is a particular way of storing and organizing data
so that they can be used efficiently.
➢ What is a good data structure?
❖ Correctness (satisfy requirements)
❖ Memory efficiency
❖ Simple/understandable
❖ Implementable
➢ Standard data structures
❖ Array
❖ Set
❖ Map/Dictionary

Algorithms?
➢ What is an algorithm?
An algorithm is a step by step procedure to solve a problem. An algorithm can be
described by nature languages (English, Vietnamese...) or programming languages
(C++, Java, Python…)
Example: How to cook rice?
❖ Step 1: Get rice
❖ Step 2: Rinse the rice
❖ Step 3: Put the rice and water into a rice cooker
❖ Step 4: Turn on the rice cooker
❖ Step 5: Check the rice when the rice cooker turns off
➢ What is a good algorithm?
❖ Correctness
❖ Efficiency
❖ Simple/understandable
❖ Implementable

Example: Searching problem
Problem: Given a list of numbers sorted increasingly, describe
an algorithm to check if a number k is in the list.
➢ Naïve searching algorithm
Moving from the begin to the end of the list to check if k is in
the list.
➢ Binary search algorithm
Compare k to the number at the middle of the list:
❖if they are equal, finish the searching process.
❖if k is smaller, perform the search in the first half of the list
❖if k is greater, perform the search in the last half of the list

Google search

Find the shortest path (Google
map)

Traveling salesman problem
(TSP)
A salesman needs to visit n customers at n different
locations. Find the shortest path for the salesman such
as he visits each location exactly once and finally
returns to the start location.

Quiz 1: The roles of data
structures and algorithms

Quiz 2: The roles of data structures
and algorithms

Data types
➢A data type is specified by:
❖The range of values or the values it can
hold.
❖Operations on values
type range operations
bool true / false and, or, not,
char [-127, 127] ‘<‘, ‘>’, ‘=’, ‘+’, ‘-’, ‘*’, ‘/’
int -32,767 -> 32,767 ‘<‘, ‘>’, ‘=’, ‘+’, ‘-’, ‘*’, ‘/’
float ~1E-37 -> ~1E+37 ‘<‘, ‘>’, ‘=’, ‘+’, ‘-’, ‘*’, ‘/’
double ~1.7E-308 -> ~1.7E+308 ‘<‘, ‘>’, ‘=’, ‘+’, ‘-’, ‘*’, ‘/’

Structured data types
➢ Question: What data type to present a point on the
plane?
➢ Solution: Programming languages provide rules to
define a new data type T from defined data types
Example in C++:
struct PersonType {
string name;
int age;
bool gender;
};

➢ How to present a point on the plane?
struct PointType {
double x;
double y;
};
➢ How to present a line on the plane?
struct LineType {
PointType start;
PointType end;
};

➢ Define a data structure to present student information
struct StudentType {
string name;
int age;
bool gender;
}
➢ Define a data structure to present our class information
struct ClassType{
string className;
int numberStudents;
StudentType students[100];
}

Range of structured data types
➢ The range of a structured data type T is determined by
the ranges of data types that are used to construct T.
Example:
struct ComplexType {
double real;
double image;
};
➢The range of ComplextType:
❖ real: The range of ‘double’ type
❖ image: The range of ‘double’ type

Operations on structured data types
Operations on a structured data type of a program are defined by the program.
Example:
struct ComplexType {
double real;
double image;
};
ComplexType add (const ComplexType &c1, const ComplextType &c2) {
ComplexType sum;
sum.real = c1.real + c2.real;
sumimage = c1.image + c2.image;
return sum;
}
ComplexType multiply (const ComplexType &c1, const ComplextType &c2) {
ComplexType product;
product.real = (c1.real * c2.real) – (c1.image * c2.image);
product.image = (c1.real * c2.image) + (c1.image * c2.real);
return product;
}

Abstract data types
➢ Abstract components of a structured data type
Example: ComplexType
❖ real //the real component of complex number
❖ image //the image component of complex number
➢ Abstract operations of a structured data type
Example: ComplexType
❖ add (c1, c2): Add two complex numbers c1 and c2
and return their sum.
❖ multiply (c1, c2): Multiply two complex numbers c1
and c2 and return their product.

Abstract data types
➢ Abstract Student data type
❖ Abstract data type components
» ID
» Name
» DOB
» Address
❖Abstract operations
» initializeStudent (ID, Name, DOB, Address)
» compareStudents (student1, student2)
» getID (student)
» getName (student)
» getDOB (student)
» getAddress (student)

Quiz 3
➢Abstract TEACHER data type
➢Abstract COMPUTER data type
➢Abstract RECTANGLE data type

Problem description
➢ Description:
❖What is the nature of problem?
❖What questions need to be solved?
❖What data and constrains are given?
❖What results are expected?
❖Examples
➢ Input: Describe the input and their specific
constrains
➢ Output: Describe the output and their
specific requirements

Birthday cake selection
➢ Problem: Today is Anna’s birthday and she is going to buy a birthday cake.
The cake shop has many birthday cakes with different sizes. As a kid, Anna
wants to pick the largest one. For example, if there are 4 birthday cakes
with sizes 1, 5, 3, and 7, Anna will pick the cake with size 7. Your task is to
write a program to find the largest birthday cake for Anna.
➢ Input: Data come from file BirthdayCakes.txt as following:
❖ The first line contains a single integer number n, denoting the
number of birthday cakes at the shop (0 < n < 10000).
❖ The second line contains n space-separated integer numbers each
describes the size of one cake.
➢ Output: Write to file BirthdayCakes.out an integer number which is the
size of the largest birthday cake.
Example:
BirthdayCakes.txt BirthdayCakes.out
4 7
1 5 3 7

Quiz 4
➢Describe the problem of finding the
product of two big integer numbers
➢Describe the problem of sorting
students according to their final
examinations
➢Describe the problem of finding the
shortest path between two locations

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