Data Structures and Algorithms: Elementary Concepts and Implementations - Prof. Juan Cebra, Study notes of Computer Science

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Data Structures and Algorithms

Elementary data structures

Computational geometry

Scientific codes

Scientific codes are usually designed to solve largecomplex problems representing natural phenomena

This requires: •^

Code modularization & maintenance

-^

Logical organization of the data

-^

Fast procedures to solve the problem

Example Makefile

EXE = run OBJ = main.o file.o

calc.o

LIB

= -llapack –lblas –lm –lgfortran

CMP = gcc –g –c --pedantic LNK = gcc $(EXE): $(OBJ)

$(LNK) –o $@ $(OBJ) $(LIB)

clean:

rm –f *.o

%.o: %.c

$(CMP) $?

Speed

The speed of a code is affected by: •^

Memory access^ – Cache vs main memory: contiguous data^ – Graphic memory vs main memory^ – Virtual memory: the end of the game

-^

Operation count^ – The total number of operations^ – Integer vs floating point operations^ – Sum / multiplications / divisions / square roots / sin-cos-exp

-^

File I/O^ – Ascii vs binary

-^

Communications^ – Shared memory vs distributed memory

Data structures

•^

Data structure are containers for storing data into thecomputer’s memory in an organized manner

-^

Data structures allow logical and efficient archival andretrieval of data items

Algorithms

•^

Algorithms are procedures to perform a specific task

-^

Data structures usually have associated algorithms forefficient access to the data stored in the data structures

Elementary data structures

•^

Arrays

-^

Linked lists

-^

Stacks

-^

Queues

-^

Hashes

Arrays

•^

An array is a fixed number of data items that are storedcontiguously and that are accessible by an index

-^

Arrays are defined as primitive in most programminglanguages (C, C++, Fortran, …)

-^

Arrays can be statically (size given when declaring thevariable) or dynamically allocated (malloc…)

-^

We refer to the ith element of an array a as: C/C++:

a[i]

Fortran:

a(i)

a

0

1

2

3

4

5

6

7

double a[100];double ptr;ptr=a;ptr=&a[0];ptr=malloc(100sizeof(double));ptr+=10;ptr=&a[10];a[10]=5.0;(ptr+10)=5.0;ptr[10]=5.0;*

Pointers in C/C++

•^

A pointer is a variable that contains a memory location

-^

A pointer can be made to point to different positions inthe computer’s memory

-^

Through a pointer one can access the data stored at thelocation pointed to by the pointer

(^0) a

1

2

3

4

5

6

7

ptr

Casting Pointers

•^

The pointer arithmetics takes into account the type ofdata being pointed to (jumps in steps of sizeof(*ptr) )

-^

Pointers can be ‘cast’ to access the memory in a different manner: float

*fptr;

char

*cptr;

cptr=(char)*

dptr;

0

1

2

3

4

5

6

7

fptr

float 1

float 2

Linked Lists

•^

Linked lists are defined as a primitive in some languages(Lisp, Logo) but not in most commonly used languages

-^

Main advantages of linked lists:^ – Dynamic data structure: can grow and shrink in size^ – Flexible in allowing items to be rearranged efficiently

-^

Disadvantages:^ – Slower than arrays^ – Need to traverse the list to find an item

Linked lists: basic operations

•^

Linked list with dummy nodes

-^

Adding an item

-^

Deleting an item

A^

B^

C^

D^

E

head

tail

A^

B^

C^

D^

E

head

tail

X

Delete link:

A^

B^

C^

D^

E

head

tail

X

Add links:

A^

B^

C^

D^

E

head

tail

X

Linked lists: pointer implementation (C)

Deletion operation: *void deleteNext(struct node n) {

n->next=n->next->next; } Insertion operation: **nodeT insertAfter(int item,struct node n) {

nodeT x=(nodeT)malloc(sizeof(x)); x->item=item; x->next=n->next; n->next=x; return x; }*

A^

B^

C^

D^

E

head

tail

X

A^

B^

C^

D^

E

head

tail

X

A^

B^

C^

D^

E

head

tail

X

Linked lists: array implementation (C)

Data structure: int

item[max+2],

next[max+2];

//

parallel

arrays

int

head=0,

tail=1,

x=2;

//

x:

next

unused

position

Initialization function: void

init()

{

next[head]=tail;

next[tail]=tail;

}