1. Invitation to Computer Science 6th Edition
Chapter 2
The Algorithmic Foundations of Computer Science

2. Objectives In this chapter, you will learn about:
Representing algorithms
Examples of algorithmic problem solving
Algorithm: clear, precise, unambiguous
Searching lists
Finding maxima
Minima
Matching patterns
Invitation to Computer Science, 6th Edition

3. Introduction Chapter 1 This chapter
Introduced algorithms and algorithmic problem solving
This chapter
Develops more fully the notions of algorithm and algorithmic problem solving
In chapter1, we introduced algorithms and algorithmic problem solving.
Develops more fully the notions of algorithms and algorithmic problem solving and applies these ideas to problems that are of interest to computer scientists
Searching lists
Finding maxima
Minima
Matching patterns
Invitation to Computer Science, 6th Edition

4. Representing Algorithms
Pseudocode
Natural language: used to express algorithms
Problems using natural language to represent algorithms
Natural language can be extremely verbose
Lack of structure makes it difficult to locate specific sections of the algorithm
Natural language is too “rich” in interpretation and meaning
3 explicit problem
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5. P45
When you are finished with that operation
At the end of Row 7
Confuse
High level langauge
Figure 2.1 The Addition Algorithm of Figure 1.2 Expressed in Natural Language
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6. Representing Algorithms(continued)
High-level programming language
Examples: C++, Java
Problem with using a high-level programming language for algorithms
During the initial phases of design, we are forced to deal with detailed language issues
Invitation to Computer Science, 6th Edition

7. High-Level Programming Language
API Application programming interface
is a protocol intended to be used as an interface by software components to communicate with each other.
Figure 2.2 The Beginning of the Addition Algorithm of Figure 1.2 Expressed in a
High-Level Programming Language
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8. Pseudocode (continued)
Natural languages
Not sufficiently precise to represent algorithms
High-level programming language
During the initial phases of design, we are forced to deal with detailed language issues
Invitation to Computer Science, 6th Edition

9. Pseudocode Pseudocode Used to design and represent algorithms
A compromise between the two extremes of natural and formal languages
a program code unrelated to the hardware of a particular computer and requiring conversion to the code used by the computer before the program can be used.
Pseudo code represents a compromise between the two extremes of natural and formal languages.
Invitation to Computer Science, 6th Edition

10. Figure 1.2 Algorithm for Adding Two m-digit Numbers
Before talking about the detail of this algorithm, another concept need to explain
Mathematic formation need variable
The problem here is that one variable is only range from 0 to 10. but two digits add up, it sum may larger then 10. we use the another variable named carry to store this information.
The valve of carry can be adjusted during the algorithm.
Figure 1.2 Algorithm for Adding Two m-digit Numbers
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11. Pseudocode(continued)
English language constructs modeled to look like statements available in most programming languages
Steps presented in a structured manner (numbered, indented, and so on)
No fixed syntax for most operations is required
This is a set of english language constructs designed to resemble statements in a programming language but that do not actually run on a computer
Invitation to Computer Science, 6th Edition

12. Pseudocode(continued)
Less ambiguous and more readable than natural language
Emphasis is on process, not notation
Well-understood forms allow logical reasoning about algorithm behavior
Can be easily translated into a programming language
Invitation to Computer Science, 6th Edition

13. Sequential Operations
Basic sequential operations
Computation, input, and output
Instruction for performing a computation and saving the result
Set the value of “variable” to “arithmetic expression”
Variable
Storage location that can hold a data value
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14. Sequential Operations (continued)
Pseudocode
Not a precise set of notational rules to be memorized and rigidly followed
Input operations
Submit to the computing agent data values from the outside world that it may then use in later instructions
Output operations
Send results from the computing agent to the outside world
Add a and b to get c
Set the value of c to (a+b)
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15. Figure 2.3 Algorithm for Computing Average Miles per Gallon
Variable in computation
Variable in input
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16. Invitation to Computer Science, 6th Edition

17. Conditional and Iterative Operations
Sequential algorithm
Sometimes called a straight-line algorithm
Executes its instructions in a straight line from top to bottom and then stops
Control operations
Conditional and iterative
Allow us to alter the normal sequential flow of control in an algorithm
It can not solve all the problem in our real life.
It can not select among alternative operations or perform a block of instructions more than once.
Virtually all real-world problems are not straight-line in nature.
They involve non-sequential operations such as branching and repetition
Invitation to Computer Science, 6th Edition

18. Conditional and Iterative Operations (continued)
Conditional statements
Ask questions and choose alternative actions based on the answers
If then else
Example
if x is greater than 25 then
print x
else
print x times 100
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19. Figure 2.4 The If/Then/Else Pseudocode Statement
Flow chart
Diamond to represent condition
Rectangle to represent process
Arrow to represent the order of these operations.
Figure 2.4 The If/Then/Else Pseudocode Statement
Invitation to Computer Science, 6th Edition

20. Figure 2.5 Second Version of the Average Miles per Gallon Algorithm
Extends
Figure 2.5 Second Version of the Average Miles per Gallon Algorithm
Invitation to Computer Science, 6th Edition

21. Conditional and Iterative Operations (continued)
Loop
The repetition of a block of instructions
While statement
Continuation condition
Determines if statement is true or false
Infinite loop
Continuation condition never becomes false
The real power of a computers comes not from doing a calculation once but from doing it many, many times.
Invitation to Computer Science, 6th Edition

22. Conditional and Iterative Operations (continued)
Examples
while j > 0 do
set s to s + aj
set j to j – 1 do
print ak
set k to k + 1
while k < n
Invitation to Computer Science, 6th Edition

23. Figure 2.6 Execution of the While Loop
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24. Conditional and Iterative Operations (continued)
Loop example
Step Operation
1 Set the value of count to 1
2 While (count ≤ 100) do step 3 to step 5
3 Set square to (count x count)
4 Print the values of count and square
5 Add 1 to count
the start position of the loop body lines farther from the edge of the page than the line of while
Set space or set back
It is clear to reader of the algorithm which operations belong inside the loop
Invitation to Computer Science, 6th Edition

25. Conditional and Iterative Operations (continued)
Pretest loop
Continuation condition is tested at the beginning of each pass through the loop
Posttest loop
Continuation condition is tested at the end of the loop body, not the beginning
Primitives
Instructions that computing agent understands and is capable of executing without further explanation
Invitation to Computer Science, 6th Edition

26. Figure 2.7 Third Version of the Average Miles per Gallon Algorithm
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27. Figure 2.8 Execution of the Do/While Posttest Loop
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28. Invitation to Computer Science, 6th Edition

29. Figure 2.9 Summary of Pseudocode Language Instructions
Invitation to Computer Science, 6th Edition

30. Examples of Algorithmic Problem Solving
Go Forth and Multiply: Multiply two numbers using repeated addition
Sequential search: Find a particular value in an unordered collection
Find maximum: Find the largest value in a collection of data
Pattern matching: Determine if and where a particular pattern occurs in a piece of text
Invitation to Computer Science, 6th Edition

31. Examples of Algorithmic Problem Solving
Example 1: Go Forth and Multiply
Given 2 nonnegative integer values, a ≥ 0, b ≥ 0, compute and output the product (a 3 b) using the technique of repeated addition. That is, determine the value of the sum a + a + a a (b times)
Invitation to Computer Science, 6th Edition

32. Examples of Algorithmic Problem Solving((continued))
Algorithm outline
Create a loop that executes exactly b times, with each execution of the loop adding the value of a to a running total
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33. Set the values of count to 0 Set the value of product to 0
Get values for a and b
Set the values of count to 0
Set the value of product to 0
While (count < b) do
Set the value of product to (product + a)
Set the value of count to (count + 1)
End of loop
Print the value of product
Remember of Chapter 1 that one of the fundamental characteristics of an algorithm is that it produces an observable result.
In chapter 1, we stated that it is not only algorithmic correctness we are after but efficiency and elegance as well.
Invitation to Computer Science, 6th Edition

34. More to say the algorithmic efficiency and elegance in Chapter 3
Figure 2.10 Algorithm for Multiplication of Nonnegative Values via Repeated Addition
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35. Invitation to Computer Science, 6th Edition

36. Invitation to Computer Science, 6th Edition

37. Modified version of Multiply
Devise an algorithm that uses a loop to take in a positive integer n and a real number x as the input and computes and print xn . Assume that the computing agent knows how to multiply but do not know how to calculate exponential. Hint: x0 = 1; x1 = x; x2 = x*x; x3= x*x*x; etc. Make sure you stop the algorithm at some point.
Most interesting computational problems deal not with a few numbers but with huge collections of data, such as lists of names, sequences of characters, or sets of experimental data.
Invitation to Computer Science, 6th Edition

38. Example 2: Looking, Looking, Looking
Algorithm discovery
Finding a solution to a given problem
Sequential search
Standard algorithm for searching an unordered list of values
Binary Search (extended example)
In computer science, a binary search or half-interval search algorithm finds the position of a specified value (the input “key”) within a sorted array.
It is the most challenging and creative part of the problem-solving process.
Studying these examples, together with lots of practice, is by far the best way to learn creative problem solving.
Invitation to Computer Science, 6th Edition

39. Example 2: Looking, Looking, Looking (Continued)
Task
Find a particular person’s name from an unordered list of telephone subscribers
Algorithm outline
Start with the first entry and check its name, then repeat the process for all entries
Assume that we have a list of names that we define as N1, N2, N3, …, N10,000, along with the 10,000 telephone numbers of those individuals, denoted as T1, T2, T3, …, T10,000
Invitation to Computer Science, 6th Edition

40. Figure 2.11 First Attempt at Designing a Sequential Search Algorithm
Invitation to Computer Science, 6th Edition

41. Example 2: Looking, Looking, Looking (continued))
For each entry, write a separate section of the algorithm that checks for a match
Problems of naïve sequential search algorithm
Only works for collections of exactly one size
Duplicates the same operations over and over
It does not use the powerful algorithmic concept of iteration.
Invitation to Computer Science, 6th Edition

42. Example 2: Looking, Looking, Looking (continued)
Correct sequential search algorithm
Uses iteration to simplify the task
Refers to a value in the list using an index (or pointer)
Handles special cases (such as a name not found in the collection)
Uses the variable Found to exit the iteration as soon as a match is found
Invitation to Computer Science, 6th Edition

43. Figure 2.12 Second Attempt at Designing a Sequential Search Algorithm
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44. Figure 2.13 The Sequential Search Algorithm
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45. Invitation to Computer Science, 6th Edition

46. Example 2: Looking, Looking, Looking (continued)
The selection of an algorithm to solve a problem is greatly influenced by the way the data for that problem is organized
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47. Example 3: Big, Bigger, Biggest
Library
Collection of useful algorithms
Problem
Given a value n ≥ 1 and a list containing exactly n unique numbers called A1, A2, , An, find and print out both the largest value in the list and the position in the list where that largest value occurred
Invitation to Computer Science, 6th Edition

48. Figure 2.14 Algorithm to Find the Largest Value in a List
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49. Invitation to Computer Science, 6th Edition

50. Invitation to Computer Science, 6th Edition

51. Example 4: Meeting Your Match
Pattern matching
Process of searching for a special pattern of symbols within a larger collection of information
Is assisting microbiologists and geneticists studying and mapping the human genome
Invitation to Computer Science, 6th Edition

52. Example 4: Meeting Your Match (continued)
Pattern-matching problem
You will be given some text composed of n characters that will be referred to as T1 T Tn. You will also be given a pattern of m characters, m ≤ n, that will be represented as P1 P Pm. The algorithm must locate every occurrence of the pattern within the text. The output of the algorithm is the location in the text where each match occurred. For this problem, the location of a match is defined to be the index position in the text where the match begins
Invitation to Computer Science, 6th Edition

53. Example 4: Meeting Your Match (continued)
STEP 1
The matching process: T1 T2 T3 T4 T5 … P1 P2 P3
STEP 2
The slide forward: T1 T2 T3 T4 T5 …
1-character slide -> P1 P2 P3
Invitation to Computer Science, 6th Edition

54. Figure 2.15 First Draft of the Pattern-Matching Algorithm
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55. Figure 2.16 Final Draft of the Pattern-Matching Algorithm
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56. Invitation to Computer Science, 6th Edition

57. Example 4: Meeting Your Match (continued)
Examples of higher-level constructs
Sort the entire list into ascending order
Attempt to match the entire pattern against the text
Find a root of the equation
Abstraction
Use of high-level instructions during the design process
Top-down design
Viewing an operation at a high level of abstraction
Invitation to Computer Science, 6th Edition

58. Summary Algorithm design Algorithm design must: Pseudocode
A first step in developing an algorithm
Algorithm design must:
Ensure the algorithm is correct
Ensure the algorithm is sufficiently efficient
Pseudocode
Used to design and represent algorithms
Invitation to Computer Science, 6th Edition

59. Summary (continued) Pseudocode Algorithm design Abstraction
Readable, unambiguous, and able to be analyzed
Algorithm design
Uses multiple drafts and top-down design to develop the best solution
Abstraction
A key tool for good design
Invitation to Computer Science, 6th Edition

60. Test 1 4 types questions (11) Close notes & Close books Panther Card
Concept: computer science, algorithm, Von Neumann architecture
Design: using Pseudocode code
Correction: verify the given algorithms
Discussion: be creative & comprehensive
Close notes & Close books
Panther Card
Feb 4th: 3:00-4:15pm
Assignment 1 due on Feb 4th before 4:15pm
Invitation to Computer Science, 6th Edition