Conceptos basicos algoritmos

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Denitions Some Applications of Algorithms Specic Algorithmic Problems Exercise

ALGORITHMS CLASS
Basic Concepts Juan Mendivelso, PhD(c)
Department of Computer and Industrial Engineering National University of Colombia

February 28, 2012

Juan Mendivelso PhD(c)

Algorithms

Denitions Some Applications of Algorithms Specic Algorithmic Problems Exercise

Outline
1

DenitionsComputer Program Computational Problem Algorithm Data Structure Eciency NP-Complete Problems Analysis of Algorithms Some Applications of Algorithms Specic Algorithmic Problems Exercise
Juan Mendivelso PhD(c) Algorithms

2 3 4

Denitions Some Applications of Algorithms Specic Algorithmic Problems Exercise

Program Computational Problem Algorithm Data Structure Eciency NP-CompleteProblems Analysis of Algorithms

Outline
1

Denitions Computer Program Computational Problem Algorithm Data Structure Eciency NP-Complete Problems Analysis of Algorithms Some Applications of Algorithms Specic Algorithmic Problems Exercise
Juan Mendivelso PhD(c) Algorithms

2 3 4

Denitions Some Applications of Algorithms Specic Algorithmic Problems Exercise

Program ComputationalProblem Algorithm Data Structure Eciency NP-Complete Problems Analysis of Algorithms

Program
Sequence of instructions written to perform a specied task with a computer. A computer requires programs to function. Computer source code is written by computer programmers. Source code is written in a programming language. Source code may be converted into an executable le by a compiler.

JuanMendivelso PhD(c)

Algorithms

Denitions Some Applications of Algorithms Specic Algorithmic Problems Exercise

Program Computational Problem Algorithm Data Structure Eciency NP-Complete Problems Analysis of Algorithms

Outline
1

Denitions Computer Program Computational Problem Algorithm Data Structure Eciency NP-Complete Problems Analysis of Algorithms Some Applications of AlgorithmsSpecic Algorithmic Problems Exercise
Juan Mendivelso PhD(c) Algorithms

2 3 4

Denitions Some Applications of Algorithms Specic Algorithmic Problems Exercise

Program Computational Problem Algorithm Data Structure Eciency NP-Complete Problems Analysis of Algorithms

Computational Problem
Relationship between a set of instances (input) and a set of solutions (output). Formallyestablishes the relationship between the input and the output of an algorithm. Example Sorting Problem Input: A sequence of n numbers a1 , a2 , . . . , a . Output:A permutation (reordering) a1 , a2 , . . . , a input such that a1 ≤ a2 ≤ . . . ≤ a .
n n

n

of the

Juan Mendivelso PhD(c)

Algorithms

Denitions Some Applications of Algorithms Specic Algorithmic Problems Exercise

ProgramComputational Problem Algorithm Data Structure Eciency NP-Complete Problems Analysis of Algorithms

Outline
1

Denitions Computer Program Computational Problem Algorithm Data Structure Eciency NP-Complete Problems Analysis of Algorithms Some Applications of Algorithms Specic Algorithmic Problems Exercise
Juan Mendivelso PhD(c) Algorithms

2 3 4

Denitions Some Applications ofAlgorithms Specic Algorithmic Problems Exercise

Program Computational Problem Algorithm Data Structure Eciency NP-Complete Problems Analysis of Algorithms

Algorithm
Well-dened computational procedure that takes some set of instances and produces some set of solutions. Sequence of computational steps that transform the input into the output. Tool for solving a well-specied computational problem.Example For the instance 31, 41, 59, 26, 41, 58 , a sorting algorithm must produce 26, 31, 41, 41, 58, 59 .
Juan Mendivelso PhD(c) Algorithms

Denitions Some Applications of Algorithms Specic Algorithmic Problems Exercise

Program Computational Problem Algorithm Data Structure Eciency NP-Complete Problems Analysis of Algorithms

Correctness
Correct Algorithm An algorithm is correct...
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