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Project 1b is due Monday |
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Notice that the reading sequence jumps to
Chapter 17 for Monday |
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Algorithms are a familiar idea. Our goal is to
learn to specify them right so someone or something else does the work |
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Algorithm, a precise, systematic method to
produce a specified result |
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We have seen algorithms already... |
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Placeholder technique is an algorithm with an
easy specification: |
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longStringWithShortStringInIt ¬ placeholder |
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ShortString ¬ e |
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placeholder ¬ longStringWithShortStringInIt |
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For an algorithm to be well specified it must
have … |
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Inputs specified |
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Outputs specified |
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Definiteness |
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Effectiveness |
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Finiteness |
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A program is an algorithm specialized to a
particular situation |
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Algorithm: |
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longStringWithShortStringInIt ¬ placeholder |
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ShortString ¬ e |
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placeholder ¬ longStringWithShortStringInIt |
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Program: ¿¿ ¬ # |
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¿ ¬ e |
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# ¬ ¿¿ |
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1. Use Artist_of to refer to the name of group |
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2. Decide which end or the rack is to be the
start of alphabetic sequence, and call the first slot alpha |
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3. Call the slot next to alpha, beta |
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4. If Artist_of the CD in the alpha slot is
later in the alphabet than the Artist_of the CD in the beta slot,
interchange the CDs, otherwise continue on |
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5. If a slot follows the beta slot, begin
calling it the beta slot and go to step 4, otherwise continue on |
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6. If two slots follow the alpha slot, begin
calling the next one the alpha slot and the one following it the beta slot,
and go to step 4; otherwise stop |
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We have studied abstraction as a method of
removing an idea or process form a situation … abstract |
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Beta sweep -- while alpha points to a fixed
slot, beta sweeps through slots following alpha, interchanging as necessary |
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The beta sweep is a concept removed based on our
understanding of the operation of the algorithm |
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By abstracting we can analyze parts of an
algorithm … |
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The beta sweep has 4 properties: |
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Exhaustive -- it considers all CDs after alpha |
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Non-redundant -- no slot pair is checked twice |
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Progressive -- the alphabetically earliest CD
considered so far is always in the alpha slot |
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Effective -- at completion, the alphabetically
earliest CD from alpha to end is in alpha slot |
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The alpha sweep... |
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Process of sweeping through all of the CDs (but
the last) performing the beta sweep |
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Exhausitve -- considers all but last CD |
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Non-redundant -- a slot is alpha only once |
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Progressive -- when beta sweep completes the
alphabetically next CD in alpha |
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Complete -- when last beta sweep is done the
last slot’s CD is later than next to last slot |
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Effective -- the alpha sweep alphabetizes |
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We figure out most algorithms on our own,
abstracting from specific cases |
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Also we abstract parts of an algorithm or
program to understand them |
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Thinking of how the program works and reasoning
about properties that it has allows us to know why it works … and then we
can let the computer do it |
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Notes
