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Properties and Importance of Algorithms: Learning Objectives and Algorithmic Thinking

This text explains the five essential properties of an algorithm, the similarities and differences between algorithms, programs, and heuristic solutions. It includes learning objectives, such as understanding the importance of alphabetical order and the barrier abstraction for correctness. The text also explores the process of algorithmic thinking and how algorithms can be applied in various cases. Additionally, it discusses the characteristics of algorithms, such as being general, resource-efficient, understandable, clear, and precise. The text concludes by discussing how algorithms can be verified and introduces the Selection Sort algorithm.

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Properties and Importance of Algorithms: Learning Objectives and Algorithmic Thinking

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  1. Learning Objectives • List the five essential properties of an algorithm • Explain similarities and differences among algorithms, programs, and heuristic solutions • Use the Intersect Alphabetized List algorithm to do the following: • Follow the flow of the instruction execution • Follow an analysis to pinpoint assumptions • Demonstrate algorithmic thinking by being able to do the following: • Explain the importance of alphabetical order on the solution • Explain the importance of the barrier abstraction for correctness

  2. Experience with Algorithms • Programs are algorithms and all of the applications you use daily are programs • You use algorithms all the time • You learn algorithms, too: • In elementary school you learned basic algorithms—for the operations of addition, subtraction, multiplication, and division

  3. Is it an Algorithm? • The process of doing something step-by-step may not be not an algorithm • An algorithm is a “systematic method for producing a specified result” • Searching is purposeful, and provides direction…with no guarantee of a result! • Algorithms ALWAYS work! • Heuristic might describe the search! Heuristics are helpful procedures for finding a result

  4. Algorithm Properties • An algorithm must have five properties: • Input specified • Output specified • Definiteness • Effectiveness • Finiteness

  5. 1. Input Specified • The input is the data to be transformed during the computation to produce the output. • What data do you need to begin to get the result you want? • Input precision requires that you know what kind of data, how much and what form the data should be

  6. 2. Output Specified • The output is the data resulting from the computation (your intended result) • Frequently the name of the algorithm contains the output: • “Algorithm to compute batting average” • Output precision also requires that you know what kind of data, how much and what form the output should be (or even if there will be any output at all!)

  7. 3. Definiteness • Algorithms must specify every step and the order the steps must be taken in the process • Definiteness means specifying the sequence of operations for turning input into output • Details of each step must be also be spelled out (including how to handle errors)

  8. 4. Effectiveness • For an algorithm to be effective, it means that all those steps that are required to get to output MUST BE DOABLE!

  9. 5. Finiteness • The algorithm must stop, eventually! • Stopping may mean that you get the expected output OR you get a response that no solution is possible • Finiteness is not usually an issue for noncomputer algorithms • Computer algorithms often repeat instructions with different data and finiteness may be a problem

  10. Other Algorithmic Characteristics • “Algorithms Should Be General” and be applicable to several cases • “Algorithms Should Use Resources Efficiently”: • Fast Speed • Minimal RAM or Disk Space • Algorithms Should Be Understandable” so that the operations are clear to readers

  11. Other Algorithmic Characteristics • “Algorithms Should Be Clear and Precise” despite the language used • Natural languages are ambiguous in that words or phrases may have multiple meanings • Programming languages are formal languages with clear, unambiguous rules

  12. Algorithm Facts • Algorithms can be specified at different levels of detail • Algorithms use functions to simplify the algorithmic description • These functions (such as scan) may have their own algorithms associated with them

  13. Algorithm Facts • Algorithms always build on functionality previously defined and known to the user • Assume the use familiar functions and algorithms • For example, how might scan be defined? Would it be consistent for everyone? Could it mean alphabetize? Look for similar formats? Are these the same?

  14. Algorithm Facts • Different algorithms can solve the same problem differently, and the different solutions can take different amounts of time (or space)

  15. How Do We Know it Works? • Algorithm solution is clear and simple and efficient • Then, how do we know it works? • If there is no loop, the program runs, gets to an end, and we can check the result • What if there is a loop? • Programs with loops cannot be absolutely verified that it works…there are too many possible cases

  16. Then, what? • The way to know that an algorithm works is to know why it works… • Strategy for knowing why it works: • Find one or more properties that ensure the algorithm works • Explain, using the program, why they make it work.

  17. Selection Sort • Search entire list looking for smallest item and swap it into its correct position. • Search remaining list for next smallest item and swap it into the second position. • Continue searching for next smallest item swapping it into its correct position until n-1 items have been swapped. • The nth item will now be in its correct position.

  18. Selection Sort Initial configuration: 7 3 9 8 1 6 4 5 Step #1: 1 3 9 8 7 6 4 5 Step #2: 1 3 9 8 7 6 4 5 Step #3: 1 3 4 8 7 6 9 5 Step #4: 1 3 4 5 7 6 9 8 Step #5: 1 3 4 5 67 9 8 Step #6: 1 3 4 5 6 7 9 8 Step #7: 1 3 4 5 6 7 89

  19. Summary • We use algorithms daily, and we continually create them as we instruct other people in how to do something. • Everyday algorithms can be sometimes be unclear because natural language is imprecise. • Algorithms have five fundamental properties.

  20. Summary • Algorithms can be given at different levels of detail depending on the abilities of the agent. • Problems can be solved by different algorithms in different ways. • Algorithms always work—either they give the answer, or say no answer is possible—and they are evaluated on their use of resources such as space and time..

  21. Summary • Intersect Alphabetized Lists algorithm is used in Web search, and is preferred over other solutions. • Two properties of the Intersect Alphabetized Lists algorithm tell us why it works: the Alpha-Ordering and Barrier properties.

  22. Summary • Abstractions and their properties are the essence of algorithmic thinking. Algorithmic thinking can become second nature, helping us to be effective problem solvers.

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