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
Invitation to Computer Science, C++ Version, Third Edition

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)
Invitation to Computer Science, C++ Version, Third Edition

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.
Invitation to Computer Science, C++ Version, Third Edition

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
Invitation to Computer Science, C++ Version, Third Edition

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
Invitation to Computer Science, C++ Version, Third Edition

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
Invitation to Computer Science, C++ Version, Third Edition

12. Types of Algorithmic Operations
Sequential
Conditional
Iterative
Invitation to Computer Science, C++ Version, Third Edition

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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