Computations

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					    Intro to CPSC100-
102/WMST425R, Continued

     Course Preview
               this lecture
• how does a computer do specific tasks?
• how can a computer adapt to whatever
  software is run?
looking up a directory
         looking up a directory
• open the directory in roughly the place where the
  name might be. (Zhang near the end; Abbot near
  the front, Lee near the middle)
• if opened at a page with names earlier (later) in the
  alphabet than the desired name, flick a few pages
  further on (further back)
• keep doing this until you find the right page
• scan the names on that page until you find the
  right name
       levels of abstraction
looking up a phone number could be
described in terms of neuronal activation in
the brain, but we don’t normally describe
this process in this way for good reason
looking up “algorithm” in
   www.atomica.com
           looking up “algorithm”
                         definition of “algorithm”
open up web browser;     pops up in window
access www.atomica.com
                            yet more
                            communication: get
   type in “algorithm”
                            defn from server

    use                  atomica web page server
    communication        retrieves definition of
    protocol to send     “algorithm” from its
    request to server    memory
        binary search algorithm:
          programmer’s view
1. dictionary stored in an array (in computer memory)



2. compare middle array entry with query
    – if entry = query, read out answer!
    – if entry < query, remove leftmost array entries up to and
      including middle
    – if entry > query, remove rightmost array entries starting
      from middle
3. repeat step 2 until answer is read out
         elements of a program
• data structures + operations on the data
  – compare words
  – add (numerical) values
• control flow instructions
  – while/repeat
  – if ... then ... else
why did the programmer die in
         the shower?

    - the shampoo directions said
       to lather, rinse, repeat
calculating the middle array index
• middle of array from 1 to 7?

              1       2       3       4       5       6       7

• middle of array from 1 to 13?

 1   2    3       4       5       6       7       8       9       10       11   12   13

• middle of array from 1 to n (n odd)?

          1           2               ....                             n
calculating the middle index
range        middle index

1…3          2
1…5          3
1…7          4
…            …
1…n           (n+1)/2
calculating the middle index
 range        middle index

 3…9          6
 3…11         7
 3…n          (n+3)/2
 …            …
 m…n          (n+m)/2
 real java code for binary search!
private int search(int target, int first, int last)
{ int mid;
   mid = (first + last)/2;
   if (target == a[mid] result = mid;
   else if (target < a[mid])
      result = search(target, first, mid-1);
   else result = search(target, mid+1, last);
   return result;                             }
     lower level of abstraction
• information stored in bits
• complicated, multi-level storage
• primitive instruction set
  ... possibly executed by two or more processors
      representing text in binary
       symbol             bit representation

       a                  01001001
       b                  00001111
       c                  10110110
       d                  10010111

• bad is represented as “000011110100100110010111”
• what does “10110110 01001001 00001111” represent?
representing algorithms in binary
• an algorithm is just a piece of text, and so
  can be represented in binary too
• ... therein lies the true power -
  programmability- of the computer!
 inner workings of the computer

• program + data are stored in the computer’s
  memory
• the computer processor is an algorithm that
  executes the instructions in the stored program
• thus, the heart of a computer is an algorithm that
  takes as input another algorithm and executes it!
         many middle layers
• compiler: algorithm that converts a
  programmer’s code to the simple form that
  the processor understands
• operating system: algorithm that organizes
  programs and data in memory, and
  coordinate interaction with users and other
  systems
             consequences
• high level programming language must be
  automatically convertible to low-level code
• this puts constraints on the expressiveness
  of computer programming languages
• in particular, programming languages have
  to be very, very, precise
                summary
• components of a computation: input, output,
  programs, communication
• program: simple instructions on data plus
  control flow statements
• programs and data are represented in binary
  notation in a computer’s memory
• computer processor executes the instructions
  in a program
                 vocabulary
•   algorithm, protocol, program, process...
•   binary search algorithm
•   data structure, array
•   control flow statements
•   binary representation of data
•   computer processor
•   compiler, operating system
                    to do
• read articles about evolutionary language
  trees (Monday)
• prepare for “getting started” lab
• start reading the article by Hinton on the
  brain and neural networks (Wednesday)

				
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posted:8/27/2011
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