1. CSCI N301: Fundamental Computer Science Concepts Copyright ©2004  Department of Computer & Information Science Algorithm Development

2. N301: Fundamental Computer Science Concepts Copyright ©2004  Department of Computer & Information Science Goals By the end of this lecture, you should understand: How we develop algorithmsHow we develop algorithms The Four Concepts of Algorithm Development:The Four Concepts of Algorithm Development: –Algorithms are language-independent –Algorithm development requires many iterations –Algorithms are best defined using modularity. –Algorithm development requires almost continuous refinement.

3. N301: Fundamental Computer Science Concepts Copyright ©2004  Department of Computer & Information Science Machine Language In the past few weeks, we have figured out how to encode programming instructions, and have traced the circuitry that processes those instructions through the fetch-execute cycle.In the past few weeks, we have figured out how to encode programming instructions, and have traced the circuitry that processes those instructions through the fetch-execute cycle. We saw that machine language is very error prone and time consuming – after all, it is comprised only of 0’s and 1’s.We saw that machine language is very error prone and time consuming – after all, it is comprised only of 0’s and 1’s.

4. N301: Fundamental Computer Science Concepts Copyright ©2004  Department of Computer & Information Science Assembly Language To address the “barrier to entry” machine language posed, programming engineers developed a higher level language called assembly.To address the “barrier to entry” machine language posed, programming engineers developed a higher level language called assembly. Assembly language replaces the binary values of instruction codes with English mneumonics, and (typically) the binary values of data and memory locations with hexidecimal values.Assembly language replaces the binary values of instruction codes with English mneumonics, and (typically) the binary values of data and memory locations with hexidecimal values. The last lab required assembly language programming for solution.The last lab required assembly language programming for solution.

5. N301: Fundamental Computer Science Concepts Copyright ©2004  Department of Computer & Information Science Assembly Language Programming: Lessons Learned We learned that assembly language requires memory management – we had to insure that where we stored our program data was not overwritten by instructions.We learned that assembly language requires memory management – we had to insure that where we stored our program data was not overwritten by instructions. In higher level languages, this memory management was taken over by the growing feature content of an operating system.In higher level languages, this memory management was taken over by the growing feature content of an operating system.

6. N301: Fundamental Computer Science Concepts Copyright ©2004  Department of Computer & Information Science Assembly Language Programming: Lessons Learned (cont) We also saw an importance of understanding the specific xComputer simulator programming instructions, as our problems required use of specific commands within the specific toolset of our simulator.We also saw an importance of understanding the specific xComputer simulator programming instructions, as our problems required use of specific commands within the specific toolset of our simulator. Similarly, there are are many versions of assembly languages, each with a slightly different toolset (or set of commands), each tied to a specific type of processor chip.Similarly, there are are many versions of assembly languages, each with a slightly different toolset (or set of commands), each tied to a specific type of processor chip.

7. N301: Fundamental Computer Science Concepts Copyright ©2004  Department of Computer & Information Science Assembly Language Programming: Lessons Learned (cont) Finally, we learned the programming power of labeling addresses.Finally, we learned the programming power of labeling addresses. Once an instruction is given a label, we can write “relative” code, code that allows us to modify execution flow to return to specific instructions, or branch away from others.Once an instruction is given a label, we can write “relative” code, code that allows us to modify execution flow to return to specific instructions, or branch away from others. The concept of labeling was so powerful that it continued to grow – in higher level languages, labels replaced cell locations to become variables.The concept of labeling was so powerful that it continued to grow – in higher level languages, labels replaced cell locations to become variables.

8. N301: Fundamental Computer Science Concepts Copyright ©2004  Department of Computer & Information Science No Magic, Though Keep in mind that as we move up the ladder of abstraction to look at higher level languages, nothing has really changed …Keep in mind that as we move up the ladder of abstraction to look at higher level languages, nothing has really changed … Instead, translation programs have been developed that take the higher level languages, and translate them ultimately into machine language.Instead, translation programs have been developed that take the higher level languages, and translate them ultimately into machine language.

9. N301: Fundamental Computer Science Concepts Copyright ©2004  Department of Computer & Information Science Programs as a Toolset Before we look at higher level languages, though, we need to position them as a toolset.Before we look at higher level languages, though, we need to position them as a toolset. The toolset exists to provide an execution envelope for algorithms.The toolset exists to provide an execution envelope for algorithms.

10. N301: Fundamental Computer Science Concepts Copyright ©2004  Department of Computer & Information Science Algorithms: Revisited At the beginning of the semester, we introduced the concept of an algorithm as the fundamental business of computer science.At the beginning of the semester, we introduced the concept of an algorithm as the fundamental business of computer science. We revisit the concept now, given our developed understanding of computer processing works.We revisit the concept now, given our developed understanding of computer processing works.

11. N301: Fundamental Computer Science Concepts Copyright ©2004  Department of Computer & Information Science Algorithm Development Recall what we said about algorithms: “An algorithm is a well-ordered collection of unambiguous and effectively computable operations that, when executed, produces a result and halts in a finite amount of time.”Recall what we said about algorithms: “An algorithm is a well-ordered collection of unambiguous and effectively computable operations that, when executed, produces a result and halts in a finite amount of time.” And now we are ready to consider this: How do we develop algorithms?And now we are ready to consider this: How do we develop algorithms?

12. N301: Fundamental Computer Science Concepts Copyright ©2004  Department of Computer & Information Science Algorithm Development The first thing to understand about algorithm development is to realize it is independent of any particular programming language.The first thing to understand about algorithm development is to realize it is independent of any particular programming language. Theoretically, any given algorithm could be implemented within any programming language.Theoretically, any given algorithm could be implemented within any programming language.

13. N301: Fundamental Computer Science Concepts Copyright ©2004  Department of Computer & Information Science Algorithm Development An algorithm is expressed in high level, non-technical terms.An algorithm is expressed in high level, non-technical terms. This expression is said to be documented within “pseudo-code.”This expression is said to be documented within “pseudo-code.”

14. N301: Fundamental Computer Science Concepts Copyright ©2004  Department of Computer & Information Science Algorithm Development The second thing to understand about algorithm development is to realize that it best occurs iteratively.The second thing to understand about algorithm development is to realize that it best occurs iteratively. In the first pass, we should write high level, pseudo-code statements.In the first pass, we should write high level, pseudo-code statements. In subsequent passes, we give these high level statements more and more detail.In subsequent passes, we give these high level statements more and more detail.

15. N301: Fundamental Computer Science Concepts Copyright ©2004  Department of Computer & Information Science Algorithm Development The process of beginning with high level statements and successively adding more detail is called top-down development with stepwise refinement.The process of beginning with high level statements and successively adding more detail is called top-down development with stepwise refinement. The third thing to know about algorithm development is that it best occurs modularly.The third thing to know about algorithm development is that it best occurs modularly. What this means is that key tasks are identified, and thought about as components.What this means is that key tasks are identified, and thought about as components.

16. N301: Fundamental Computer Science Concepts Copyright ©2004  Department of Computer & Information Science Algorithm Development This “divide and conquer” approach allows both development efficiencies and debug focus.This “divide and conquer” approach allows both development efficiencies and debug focus. Modular programming is so important that often the modular blocks are composed as empty skeleton code for early execution, while we add functionality later.Modular programming is so important that often the modular blocks are composed as empty skeleton code for early execution, while we add functionality later. Modular iterative programming is called stub programming, since we only create stubs in the early passes.Modular iterative programming is called stub programming, since we only create stubs in the early passes.

17. N301: Fundamental Computer Science Concepts Copyright ©2004  Department of Computer & Information Science Algorithm Development The final thing to realize about algorithm development is that all algorithms require refinement.The final thing to realize about algorithm development is that all algorithms require refinement. Even if an algorithm works correctly on the first try – and this is unlikely – it could benefit from performance improvements (working faster, or with less memory, or on an expanded data set).Even if an algorithm works correctly on the first try – and this is unlikely – it could benefit from performance improvements (working faster, or with less memory, or on an expanded data set).

18. N301: Fundamental Computer Science Concepts Copyright ©2004  Department of Computer & Information Science Let’s Try One With these four key principles in mind, let’s try our hand at algorithm developmentWith these four key principles in mind, let’s try our hand at algorithm development Let’s look at a simple problem – a variation on one we have coded in assembly language – the problem of asking adding numbers together and storing their sum …Let’s look at a simple problem – a variation on one we have coded in assembly language – the problem of asking adding numbers together and storing their sum …

19. N301: Fundamental Computer Science Concepts Copyright ©2004  Department of Computer & Information Science Algorithm Development The first step is to document a complete problem specification. In commercial applications, this process results in a functional specification.The first step is to document a complete problem specification. In commercial applications, this process results in a functional specification. In our lab assignments, we will settle for disambiguated, non-technical problem statements.In our lab assignments, we will settle for disambiguated, non-technical problem statements.

20. N301: Fundamental Computer Science Concepts Copyright ©2004  Department of Computer & Information Science Specification Development What sort of questions would you ask to disambiguate the problem description?What sort of questions would you ask to disambiguate the problem description? Good questions would include:Good questions would include: –How will you get the numbers to be added – user input, read a file, etc.? –What kind of numbers will the program add – integers, decimals, negatives, etc.? –How many numbers will the program add?

21. N301: Fundamental Computer Science Concepts Copyright ©2004  Department of Computer & Information Science Specification Development Now we can re-express our problem: “Add two integer values from memory and store their sum.”Now we can re-express our problem: “Add two integer values from memory and store their sum.”

22. N301: Fundamental Computer Science Concepts Copyright ©2004  Department of Computer & Information Science Task Chunking In the second phase of algorithm development, you try to identify the major sub-tasks of the algorithm.In the second phase of algorithm development, you try to identify the major sub-tasks of the algorithm. One way of modularizing our current problem might be to call out the following sub-tasks:One way of modularizing our current problem might be to call out the following sub-tasks: –Store numbers to be added into memory –Add the numbers –Store the result

23. N301: Fundamental Computer Science Concepts Copyright ©2004  Department of Computer & Information Science Stepwise Refinement During stepwise refinement, the major sub-tasks are fleshed out with minor sub- set tasks.During stepwise refinement, the major sub-tasks are fleshed out with minor sub- set tasks. Here is an example - add the numbers:Here is an example - add the numbers: –Access first number from memory –Access second number from memory –Perform arithmetic addition

24. N301: Fundamental Computer Science Concepts Copyright ©2004  Department of Computer & Information Science Algorithm Implementation Once we have disambiguated the problem statement (as much as is reasonable), identified key tasks and then successively detailed our stepwise refinement, we can implement our algorithm.Once we have disambiguated the problem statement (as much as is reasonable), identified key tasks and then successively detailed our stepwise refinement, we can implement our algorithm. Theoretically, the language doesn’t matter – you could utilize any language to implement your algorithm.Theoretically, the language doesn’t matter – you could utilize any language to implement your algorithm.

25. N301: Fundamental Computer Science Concepts Copyright ©2004  Department of Computer & Information Science Questions?