Data Structure ????

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Data Structure????

• ??? ???
• ?0321(??? 02-04)

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????

• ???????????????,?Stacks, Queues, Linked Lists,
  Trees, Hash, Graph?? ???????????????????
  ??????????(algorithm)???????????????????????????,?
  ?????????????????????(Complexity)???????????????,?
  ????????????,???????????????

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?????????

• Data Structures and Program Design in C,Kruse,
  Tondo, Leung, ????,2597-1300x338
• ??????C??,????. ????[phone]
• ????????????? http//faculty.pccu.edu.tw/cweng/
• ??????????????,???????????????

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?????????

• ???? 30
• ???? 40
• ???? 30(?????????)
• ???12001300
• ???14001600
• ???12001300
• ???15001700

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??? ??????????

1. ???????
2. ???(Algorithm)
3. ??(program)?????(programming)
4. ????????

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1. ???????

• ??(Data),???????????????(Word)???(Number)???(Sym
  bol)???(Graph)?,??????????????????????????????????
  ???????????????????????

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????

• ????????????????,??????????????????????????????,?
  ????????????,??????????(Information)

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????

• ?????????????,????????????(algorithm)???(logic)???
  ??????????????(relationship)?
• ???????????????????????????????????,??????????????
  ???,????????????????????? ?

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??????????????

• ???????????????????,?????????????
• ???????????????,???????????,???????????????(Data)
  ?????????????,????????????????(Information)?

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2.???(Algorithm)

• ?????????????????
• ???????????????????????????????
• ????????????????????????????,????????????????????
  ????

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???????

• ??(Input)0????????,????????????????
• ??(Output)??????????,??????????
• ???(Definiteness)?????????????????????
• ???(Finiteness)????????????,?????????
• ???(Effectiveness)???????,????????????????

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??????????

• ??????????????
• ???????????????,??????SPARKS?PASCA-LIKE????
• ??????????????????
• ????????)??????????????????,??????????
• ??????????????????????????????,??C???C???Java??
  ?Visual Basic???,??????C????????

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??????????????

• ???????????,????????????????,??????????????????,?
  ????????(waiting loop)?????????,??????????????????
  ???
• ??????????????????,???????????????,?????????????

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3. ??(program)?????(programming)

• ?????????
• ??????????????????,??????????
• ????????,?????????,??????????????????????
• ???????????????????,????????????
• ??????????,?????????
• ?????????????????????,???????????????????????

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???????
??????????(Basic Structure)
?????? ???
???? ???????
???? ?????????
???? ??????????????????
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???????????

• ?????????????????,???????????????????????????????
  ??,???????
• ?????????????,????????,?????????,??????????,?????
  ????

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?????????

• ??????(atomic data type)?????????(physical data
  type)
• ???????(structure data type)?????????(virtual
  data type)
• ??????(Abstract Data TypeADT)

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??????

• ?????????,????????????????????????,???????????????
  ?????C????????????(int)???(char)???????(float)????
  ???(double)?

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???????

• ???????????,?????????????????,????(string)???(set)
  ???(array)?

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??????

• ????????????,ADT????????????????????????????,?????
  ???ADT?????,???????????????(stack)???(queue)??????
  ??ADT???

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4. ????????

• Given a problem, there may be several possible
  implementations.
• Efficiency is the most important consideration
  including time and space.
• Complexity Theory to estimate the time and space
  needed for a program. Its machine independent.
• Space Complexity of a program the amount of
  memory space needed to complete a program.
• Time Complexity of a program the amount of
  computation (computer) time needed to complete a
  program.

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Space Complexity S(p)S(p)ScSp(I)

• Sc (Fix space requirement) including instruction
  space, constants, simple variables, and fix-size
  structures. The Sc is independent of the number
  and size of inputs and outputs. e.g. int i,
  sum0, A100
• Sp(I) (Variable space requirement) depends on a
  particular instance I of a problem. Instance I
  may be a function of number, size, or values of
  inputs and outputs. e.g. int n //score list
  of a course

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Time Complexity T(p)T(p)TcTp(I)

• Tc (Fix time requirement) compile time, Tc is
  independent of any instance of the problem.
  
• Tp(I) (Variable time requirement) execution time,
  depends on a particular instance I of a problem.
  e.g. matrix
  multiplication C A B
• (0,0)
  0,1 0,2 0,3 0,n 0,0
• 1,0
• 
  
  2,0
• n,0
  
• (n) (n) gt 2n 2n nn an2bnc gt 2n3
  an2bnc

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Asymptotic Notations- for measuring space and
time complexities

• O(Big-oh)
• O(omega)
• ?(theta)

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Big-oh???

• O(g(n))???????????????????????????g(n),???????????
  ???????(space or time complexity)?O(g(n))(??big-oh
  of g(n)?order is g(n))?
• Definition The function f(n) is said to be of
  order at most g(n) if there are positive
  constants c and n0 such that f(n)ltcg(n) for all
  n, ngtn0.
• Therefore, Big oh is the smallest upper bound
  of f(n).

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???Big-oh?????

• O(1)???? (constant)
• O(log2n)?? (logarithmic)
• O(log22n)?? (log squared)
• O(n)???? (linear)
• O(nlog2n)??n log n
• O(n2)???? (quadratic)
• O(n3)???? (cubic)
• O(2n)???? (exponential)

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O(omega)???

• O?????????????,???Big-oh????????????,?O???????????
  ??????O???
• Definition The function f(n) is said to be of
  order at least g(n) if there are positive
  constants c and n0 such that f(n)gtcg(n) for all
  n, ngtn0.
• Therefore, Big oh is the largest lower bound of
  f(n).

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?(theta)???

• ????Big-O?O?????????????????
• Definition The function f(n) is ?(g(n)) iff
  there exists positive constants c1, c2 and n0 ,
  such that c1 g(n) ltf(n)lt c2 g(n) for all n,
  ngtn0.
• Therefore, ? is both the smallest upper bound
  and the greatest lower bound of f(n).

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Examples for asymptotic notations

• 1. 3n 2 ?(n), ?3n 2 ? 4n, for all n ? 2, c
  4.
• 2. 3n 3 ?(n), ?3n 3 ? 4n, for all n ? 3, c
  4.
• 3. 3n 3 ?(n2), ?3n 2 ? 3n2, for all n ? 2, c
  3.
• (2) is correct. (3) is wrong. Big oh should be
  a smaller function of n.
• 4. 10n2 4n 2 ?(n2), ?10n2 4n 2? 11n2, for
  all n ? 5, c 11.
• 5. 6.2n n2 ?(2n), ?6.2n nn? 7.2n, for all
  n ? 4, c 7.
• 6. 3n 3 O(n), ?3n 3 ? 3n, for all n ? 1, c
  3.
• 7. 3n 3 O(1), ?3n 3 ? 3, for all n ? 1, c
  3.
• (6) is correct. (7) is wrong. Omega should be a
  larger function of n.
• 8. 3n 2 T(n) ?3n?3n 2 ? 4n, for all n ? 2, c1
  3, c2 4 , and n0 2.

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Example for S(p) addup values of n elements in
an array called list.

• main( ) float addup(float list , int n)
• float listn, temp 0.0 float temp 0.0
• int i int i
• for( i0 i lt n i) for( i0 i lt n i)
• temp listi temp listi
• return temp return temp
• Smain(n) c n O(n) Saddup(n) c O(1)
• Other languages may need to pass the whole
  array, but addup passes only addresses of the
  1st element and the size of array.

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Example for T(p) use step count instead of
execution time.

• 1. on-line step count
• float sum(float list , int n) / calculate
  the sum of an array /
• float tmp0.0 count / tmp assignment /
• int i
• for ( i0 i ltn i )
• count / for loop /
• tmplisti count adding up /
• count / last time to check for loop and
  fails /
• return tmp count / for return /
• gt step count 2n 3 gt Tsum(n) O(n)

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• 2. Tabular method
• void add( int a , int b , int c ,
  int row, int col)
• Step per exec. freq. total
• int i, j 0 0
  0
• for ( i0 iltrow I) 1
  row 1 row1
• for ( j0 jltcol j) 1
  row(col1) rowcol row
• cij aijbij 1
  rowcol rowcol
• In total, we have step count 2rowcol 2row 1
  .
• gt Tadd(row, col) O(rowcol)
• Thus, if row gtgtcol, one may want to exchange i
  and j to reduce the step count and execution
  time.

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• 3. Execution time Measurement
• include lttime.hgt 1. Clock 2. Time
• Before execution, use start clock() start
  time(NULL)
• After execution, use stop clock() stop
  time(NULL)
• Type return clock_t time_t
• result in sec. (stop - start)/
  CLK_TCK difftime(stop, start)
• When measuring the execution of a program, we
  have
• CLK_TCK 18.2, beginclk 66, stopclk 193,
  diffclk 127, time 6.98
• begintime825316157, stoptime 825316164,
  difftime 7
• Note 1.The time is begin at around 1970.
• 2. Use ld to print out a long integer

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trade-off between program space and execution time

• Example Two ways to interchange two elements,
  using a functions or a macro
• 1. using a function 2. using a macro
• void swap (int x, int y) define swap(a,b,t)
  ((t)(a), (a)(b), (b)(t))
• int temp swap(p, q, temp)
• temp x
• x y Disadv duplicated macros may takes
  lots of space.
• y temp Adv no calls returns,
  execution time is reduced.
• Adv single copy of function gt save space.
• Disadv calls returns gt waste time.
• Therefore, a careful evaluation of the
  trade-offs among various aspects before the
  implementation of a solution is important.