1. Chapter 2: Algorithm Discovery and Design
Invitation to Computer Science,
C++ Version, Third Edition
Slides added or modified by Shannon Steinfadt, Spring 2005

2. Objectives In this chapter, you will learn about:
Representing algorithms
Examples of algorithmic problem solving
Invitation to Computer Science, C++ Version, Third Edition

3. Introduction
This chapter discusses algorithms and algorithmic problem solving using three problems:
Searching lists
Finding maxima and minima
Matching patterns
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4. Figure 1.2: Algorithm for Adding Two m-digit Numbers
Given: m ≥ 1 and two positive numbers each containing m digits, am-1 am-2 … a0 and bm-1 bm-2 … b0
Wanted: cm cm-1 cm-2 … c0, where cm cm-1 cm-2 … c0 = (am-1 am-2 … a0) + (bm-1 bm-2 … b0)
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5. Figure 1.2:Alg. for Adding Two m-digit Numbers (con’t)
Step 1 Set the value of carry to 0.
Step 2 Set the value of i to 0.
Step 3 While the value of i is less than or equal to m-1,
repeat the instructions in steps 4 through 6
Step 4 Add the two digits ai and bi to the current value of carry to get ci.
Step 5 If ci ≥ 10, then reset ci to (ci - 10) and reset the value of carry to 1; otherwise, set the new value of carry to 0.
Step 6 Add 1 to i, effectively moving one column to the left.
Step 7 Set cm to the value of carry.
Step 8 Print out the final answer, cm cm-1 cm-2 … c0.
Step 9 Stop.
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6. Representing Algorithms
Natural language
Language spoken and written in everyday life
Examples: English, Spanish, Arabic, etc.
Problems with using natural language for algorithms
Verbose
Imprecise
Relies on context and experiences
to give precise meaning to a word or phrase
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7. The Addition Algorithm of Figure 1.2 Expressed in Natural Language
Invitation to Computer Science, C++ Version, Third Edition

8. Representing Algorithms
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
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9. Figure 2.2
The Beginning of the Addition Algorithm of Figure 1.2 Expressed in a High-Level Programming Language
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10. Pseudocode
English language constructs modeled to look like statements available in most programming languages
Steps presented in a structured manner (numbered, indented, etc.)
No fixed syntax for most operations is required
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11. 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
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12. Types of Algorithmic Operations
Sequential
Conditional
Iterative
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13. Sequential Operations
3 types of sequential operations: Computation, Input, and Output
Computation operations
Example
Set the value of “variable” to “arithmetic expression”
Variable
Named storage location that can hold a data value
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14. Sequential Operations (continued)
Input operations
To receive data values from the outside world
Example
Get a value for r, the radius of the circle
Output operations
To send results to the outside world for display
Print the value of Area
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15. Algorithm for Computing Average Miles per Gallon
Figure 2.3
Algorithm for Computing Average Miles per Gallon
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16. Conditional and Iterative Operations
Sequential algorithm
Also called straight-line algorithm
Executes its instructions in a straight line from top to bottom and then stops
Control operations
Conditional operations
Iterative operations
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17. Conditional and Iterative Operations (continued)
Conditional operations
Ask questions and choose alternative actions based on the answers
Example
if x is greater than 25 then
print x
else
print x times 100
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18. Conditional and Iterative Operations (continued)
Perform “looping” behavior; repeating actions until a continuation condition becomes false
Loop
The repetition of a block of instructions
Real power of computer comes from repeating a calculation many times, not just once
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19. Conditional and Iterative Operations (continued)
Examples
while j > 0 do
set s to s + aj
set j to j - 1
repeat
print ak
set k to k + 1
until k > n
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20. Second Version of the Average Miles per Gallon Algorithm
Start building simple algorithm, make sure it works, then add to it once you are sure it is working correctly.
Figure 2.4
Second Version of the Average Miles per Gallon Algorithm
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21. Conditional and Iterative Operations (continued)
Components of a loop
Continuation condition
Loop body
Infinite loop
The continuation condition never becomes false
An error
Continuation condition: used to control the loop
Loop body: block of instructions --> indented for clarity, required in certain languages (Python)
Once the body has been executed, evaluate the continutation condition again
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22. Third Version of the Average Miles per Gallon Algorithm
Again took a working algorithm and added to it.
Figure 2.5
Third Version of the Average Miles per Gallon Algorithm
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23. Conditional and Iterative Operations
Pre-test loop
Continuation condition tested at the beginning of each pass through the loop
It is possible for the loop body to never be executed
While loop
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24. Conditional and Iterative Operations (continued)
Post-test loop
Continuation condition tested at the end of loop body
Loop body must be executed at least once
Do/While loop
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25. Summary of Pseudocode Language Instructions
From 3 primitives: computation, I/O, and Iterative statements, any valid algorithm can be represented!
Figure 2.6
Summary of Pseudocode Language Instructions
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26. Example 1: Looking, Looking, Looking
Examples of algorithmic problem solving
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
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27. Example 1: Looking, Looking, Looking (cont’d)
Task
Find a particular person’s name from an unordered list of telephone subscribers
Data: Pairs of information (Name, phone number)
Name Telephone Number N1 N2 .
N10,00 T1 T2 .
T10,00
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28. Example 1: Looking, Looking, Looking (continued)
Algorithm outline
Start with the first entry and check its name, then repeat the process for all entries
Algorithm discovery
Finding a solution to a given problem
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29. Example 1: Looking, Looking, Looking (continued)
Naïve sequential search algorithm
For each entry, write a separate section of the algorithm that checks for a match
Problems
Only works for collections of exactly one size
Duplicates the same operations over and over
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30. Example 1: 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 (like a name not found in the collection)
Uses the variable Found to exit the iteration as soon as a match is found
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31. The Sequential Search Algorithm
Figure 2.9
The Sequential Search Algorithm
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32. Example 1: Looking, Looking, Looking (continued)
The selection of an algorithm to solve a problem is greatly influenced by the way the data for that problem are organized
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33. Example 2: Big, Bigger, Biggest
Task
Find the largest value from a list of values
Formal definition of the problem
Given a value n ≥ 1 and a list containing exactly n unique numbers called A1, A2, A3, … , An, find and print out the largest value in the list and the position in the list where that largest value occurred.
Go to board, list notes
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34. Example 2: Big, Bigger, Biggest (continued)
Algorithm outline
Keep track of the largest value seen so far (initialized to be the first in the list)
Compare each value to the largest seen so far, and keep the larger as the new largest
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35. Example 2: Big, Bigger, Biggest (continued)
Once an algorithm has been developed, it may itself be used in the construction of other, more complex algorithms
Library
A collection of useful algorithms
An important tool in algorithm design and development
Largest so far is used later as a “building block” in a sorting problem.
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36. Example 2: Big, Bigger, Biggest (continued)
Find Largest algorithm
Uses iteration and indices like previous example
Updates location and largest so far when needed in the loop
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37. Algorithm to Find the Largest Value in a List
Figure 2.10
Algorithm to Find the Largest Value in a List
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38. Example 3: Meeting Your Match
Task
Find if and where a pattern string occurs within a longer piece of text
Algorithm outline
Try each possible location of pattern string in turn
At each location, compare pattern characters against string characters
Looking for a sequence of nucleotides called a probe, against the entire 3.5 billion charater genome
Replacing word in entire document
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39. Example 3: Meeting Your Match (continued)
Abstraction
Separating high-level view from low-level details
Key concept in computer science
Makes difficult problems intellectually manageable
Allows piece-by-piece development of algorithms
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40. Example 3: Meeting Your Match (continued)
Top-down design
When solving a complex problem:
Create high-level operations in first draft of an algorithm
After drafting the outline of the algorithm, return to the high-level operations and elaborate each one
Repeat until all operations are primitives
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41. Example 3: Meeting Your Match (continued)
Pattern-matching algorithm
Contains a loop within a loop
External loop iterates through possible locations of matches to pattern
Internal loop iterates through corresponding characters of pattern and string to evaluate match
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42. Final Draft of the Pattern-Matching Algorithm
Figure 2.12
Final Draft of the Pattern-Matching Algorithm
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43. Summary Algorithm design is a first step in developing an algorithm
Must also:
Ensure the algorithm is correct
Ensure the algorithm is sufficiently efficient
Pseudocode is used to design and represent algorithms
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44. Summary Pseudocode is readable, unambiguous, and analyzable
Algorithm design is a creative process; uses multiple drafts and top-down design to develop the best solution
Abstraction is a key tool for good design
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