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More Algorithms

This lecture covers control structures in pseudocode, including sequence, selection, and repetition. It also explains Euclid's Algorithm for finding the greatest common divisor of two integers.

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More Algorithms

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  1. More Algorithms 2008/09/24: Lecture 6bCMSC 104, Section 0101 John Y. Park

  2. More Algorithms Topics • Algorithms: Elements in Depth • In-Class Project: Euclid’s Algorithm • In-Class Project: Student Voluteerizer Reading • None

  3. Pseudocode:Control Structures Any problem can be solved using only three logical control structures: • Sequence • Selection • Repetition

  4. Sequence • A series of steps or statements that are executed in the order they are written. • Example: Display “Enter two numbers: “ Read <number1> Read <number2> <sum> = <number1> + <number2> Display “sum = “, <sum>

  5. Sequence • Some languages… • Have line numbers • Allow a set of sequenced steps to be grouped as a “statement block” • Explicitly bracketed (e.g., with “begin…end” or {…} • Allow “goto”s • Evil-evil-evil!!!!!

  6. Sequence • Goto e.g.: <a> = 0 goto Label3: Label1: DISPLAY “Hello” DISPLAY “bye” Label2: <a> = <a> + 1 DISPLAY <a> goto Label1: DISPLAY “Never get here…” Label3: DISPLAY “Starting up” goto Label2:

  7. Sequence • You should try to avoid the “goto” like the plague! • In this class, you will never need to use a “goto” • DON’T USE GOTOs!!! • Why did I even mention it? • It is a vehicle for explaining what other control structures are doing, in a more logical manner

  8. Selection • Defines one or more courses of action depending on the evaluation of a condition. • Synonyms: conditional, branching, decision • Examples:If (condition is true) If (condition is true) do this do this End_if Else do that End_if

  9. Selection • More complex examples: • DISPLAY “Enter number to invert”READ <my_num>If (<my_num> < 0) DISPLAY “Don’t like negative numbers” if (<my_num> < -999) DISPLAY “… but I guess you really do!” End_ifElse_if (<my_num> == 0) <result> = 0Else <result> = 1 / <my_num>End_if

  10. Repetition • Allows one or more statements to be repeated as long as a given condition is true. • Synonyms: looping, iteration • Example: While (condition is true) do this End_while

  11. Repetition • More complex example (with mistakes) • DISPLAY “Enter number to compute factorial for”READ <my_num>While (<my_num> > 0) <factorial> = <factorial> * <my_num> <my_num> = <my_num> - 1End_whileDISPLAY “The factorial of”, <my_num>, “ is “, <factorial>

  12. Repetition • More complex example (with mistakes) • DISPLAY “Enter number to compute factorial for”READ <my_num><factorial> = 0While (<my_num> > 0) <factorial> = <factorial> * <my_num> <my_num> = <my_num> - 1End_whileDISPLAY “The factorial of”, <my_num>, “ is “, <factorial>

  13. Repetition • More complex example (with mistakes) • DISPLAY “Enter number to compute factorial for”READ <my_num><factorial> = 0<saved_my_num> = <my_num>While (<my_num> > 0) <factorial> = <factorial> * <my_num> <my_num> = <my_num> - 1End_while<my_num> = <saved_my_num> DISPLAY “The factorial of”, <my_num>, “ is “, <factorial>

  14. Pseudocode Style • Any user prompts should appear exactly as you wish the programmer to code them. • The destination of any output data should be stated, such as in “Display”, which implies the screen. • Make the data items clear (e.g., surround them by < and > ) and give them descriptive names. • Use formulas wherever possible for clarity and brevity. • Use keywords (such as Read and While) and use them consistently. Accent them in some manner.

  15. Pseudocode (con’t)[Review] • Use indentation for clarity of logic. • Avoid using code. Pseudocode should not be programming language-specific. • Always keep in mind that you may not be the person translating your pseudocode into programming language code. It must, therefore, be unambiguous. • You may make up your own pseudocode guidelines, but you MUST be consistent.

  16. Euclid’s Algorithm Problem: Find the largest positive integer that divides evenly into two given positive integers (i.e., the greatest common divisor). Algorithm: • Assign M and N the values of the larger and smaller of the two positive integers, respectively. • Divide M by N and call the remainder R. • If R is not 0, then assign M the value of N, assign N the value of R, and return to Step 2. Otherwise, the greatest common divisor is the value currently assigned to N.

  17. Finding the GCD of 24 and 9 So, 3 is the GCD of 24 and 9.

  18. Euclid’s Algorithm Tips about problem # 1 : • The user should specify the two numbers to factor. She may enter them in any order (i.e., don't assume first is greater). • You will need a new arithmetic operation for computing remainders: the '%' operator. E.g.: • "24 % 7" equals "3" • “-5 % 2” equals “-1”, and "18 % -8" equals "+2" • "7 % 0" equals "the end of the world as we know it." • The user may input one or both values as negative numbers. You must either: • explicitly test for and reject negative numbers • make sure your algorithm computes the correct answer with them

  19. Student Voluteerizer Problem: Write a generic algorithm for helping call on student “volunteers” in a “fair” manner <obviously underspecified…>

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