Download The Role of Algorithms in Computing

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Design and Analysis of Algorithms
‫تصميم وتحليل الخوارزميات‬
)‫ عال‬311(
Chapter 1
Introduction to Algorithms
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1
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Computational problems
• A computational problem specifies an input-output
relationship
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What does the input look like?
What should the output be for each input?
• Example 1:
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5
Input: an integer number n
Output: Is the number odd ( ‫ ?)هل الرقم فردي أو ال‬true
• Example 2:
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20
4
72
3
Input: array of numbers
Output: the minimum number in the array
18
3
• Example 3:
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Input: array of numbers 20 4 72 3
18
Output: the same array sorted (ascending ‫)تصاعديا‬
3
4
2
18
20
72
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Algorithms
• Algorithm is:
1. A tool for solving a well-specified computational problem
2. A sequence of instructions describing how to do a task or process
Input
•
Algorithm
Output
Algorithms must be:
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Correct: For each input produce an appropriate output
 Efficient: run as quickly as possible, and use as little memory as possible
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3
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The Problem-solving Process
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Analysis
Problem
specification
Design
Algorithm
Implementation
Program
Compilation
Executable
(solution)
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From Algorithms to Programs
Problem
Algorithm: A sequence of
instructions describing how
to do a task (or process)
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C Program
5
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Simple Algorithms
Example1 (Min Algorithm)
•
INPUT: a sequence of n numbers,
 T is an array of n elements
20
4
 T[1], T[2], …, T[n]
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OUTPUT: the smallest number among them
72
3
18
min = T[1]
for i = 2 to n do
{
if T[i] < min
min = T[i]
}
Output min
• Max, Min take time = n
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Simple Algorithms (cont.)
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Algorithms can be implemented in any programming language
Usually we use “pseudo-code” to describe algorithms
• Example 2 (MAX algorithm):
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INPUT: a sequence of n numbers,
 T is an array of n elements
 T[1], T[2], …, T[n]
OUTPUT: the largest (biggest) number among them
Max = T[1]
for i = 2 to n do
{
if T[i] > Max
Max = T[i]
}
Output Max
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