Chapter 1: Introduction
Progress is possible only if we
train ourselves to think about
programs without thinking of
them as pieces of executable
code. (Edsger Dijkstra)
What is an Algorithm? 2
Definition of an Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
Example: Euclid’s Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Pseudocode for Euclid’s Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
Sieve of Eratosthenes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
Fundamentals of Algorithmic Problem Solving 6
Design and Analysis Steps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
Algorithm Design Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Important Problem Types 8
Important Problem Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Fundamental Data Structures 9
Abstract Data Types. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
Linear Data Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
Trees . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
Binary Search Trees . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
First Child-Next Sibling Representation . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
Sets and Dictionaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
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What is an Algorithm? 2
Definition of an Algorithm
An algorithm is a sequence of unambiguous instructions for solving a problem in a
finite amount of time. An input to an algorithm is an instance of the problem.
CS 3343 Analysis of Algorithms Chapter 1: Slide – 2
Example: Euclid’s Algorithm
Euclid’s algorithm solves the problem of finding the greatest common divisor of
two positive integers.
The allowed inputs and desired output of the problem must be specified.
Each step in the algorithm must be unambiguous.
The order of steps must be unambiguous.
We will use pseudocode in the b ook’s style.
CS 3343 Analysis of Algorithms Chapter 1: Slide – 3
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