as ed

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?as???? ??µ?? ?ed?µ????

• S??t?µ? epa?????? (??? 035).

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?e??????

• G?aµµ???? ??µ?? ?ed?µ????
• ???a?e?
• ??ste?
• St??ße?
• ?????
• G??f??
• ???t?a

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G?aµµ???? ??µ??

• ???a?a? (array)

• ? ?????? p??sßas?? (access time) se ?p???d?p?te
  st???e?? t?? p??a?a e??a? sta?e???, a?e???t?ta
  ap? t? ??s? t??

• S??dedeµ??? ??sta (Linked List)

Item 0

• ?? p???a????sµ??? ????t???t?ta
• ? ?????? p??sßas?? se ?p???d?p?te st???e?? t??
  p??a?a p??a??? ?a e?a?t?te ap? t? ??s? t??

• ??? p??s??t??µe ?a? d?a???f??µe st???e?a st?? p??
  p??? d?µ??

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St??ßa

• ?as???? ?e?t?????e?
• Push
• Pop
• ???p???s? µe p??a?a

• A, top.

• A, top.

• ??e???? ??a ?a µ?? ?epe?ast??? ta ???a t??
  p??a?a.

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St??ßa

• ???p???s? µe s??dedeµ??? ??sta

• top.

• top.

• ??e???? ??a µ? ???sµ????? (null) de??te?.

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???? (FIFO Queue)

• ?as???? ?e?t?????e?
• enQueue
• deQueue
• ???p???s? µe p??a?a

• Q, head, tail.

• Q, head, tail

• ?pa?a?t?t?? ??e????

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???? (FIFO Queue)

• ???p???s? µe s??dedeµ??? ??sta

• head, tail.
• enQueue(item)

• head, tail.
• deQueue()

• ?pa?a?t?t?? ??e????

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G??f?? (Graphs)

• G(V, E)
• V s????? ??µß?? (????f?? vertices/nodes)
• E s????? t?? a?µ?? (t???? edges/arcs)
• ?ate?????µe?e? ?a? µ? ?ate?????µe?e? a?µ??
  (directed and undirected edges)
• ?a??de??µa
• Va,b,c,d
• E(a,b), (a,c), (b,c), (b,d)

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G??f?? (Graphs)

• Ge?t?????? ??µß?? (neighboring/adjacent) ??µß??
  s??dedeµ???? µe µ?a a?µ?
• ????p?t? (path) µeta?? 2 ??µß?? ????????a ap?
  ?e?t??????? ??µß??? p?? ?e???? ap? t?? ??a ?a?
  ?ata???e? st?? ????.
• ?p?? (simple) µ???p?t? ????p?t? st? ?p??? ????
  ?? ??µß?? eµfa?????ta? µ??? µ?a f??? µe p??a??
  e?a??es? t?? p??t? ?a? te?e?ta?? ??µß?.
• ??????? d?ad??µ? (cycle) ?p?? µ???p?t? st? ?p???
  ? p??t?? ?a? te?e?ta??? ??µß?? e??a? ? ?d???

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G??f?? (Graphs)

• S??dedeµ???? (connected) ???f?? G??f?? st??
  ?p??? ?p???e? µ???p?t? µeta?? ?p????d?p?te d??
  ??µß??.
• ??????? (acyclic) ???f?? G??f?? st??? ?p?????
  de? ?p?????? µ???p?t?a p?? ?a ep?st??f??? st??
  ??µß? ap? ?p?? ?e????sa?.
• G??f?? µe ß??? (weighted graph) G??f?? st??
  ?p??? ???e a?µ? s?s?et??eta? µe ??p??? ß???? (?
  ??st??).
• ??a??? (sparse) ???f?? ???f?? µe s?et??? ???e?
  a?µ??
• ?????? (dense) ???f?? µ? a?a??? ???f??
• ????st?? a???µ?? a?µ?? (de? ep?t??p??ta?
  self-loops)

?? ?ate?????µe???
?ate?????µe???
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?pe?????s? G??f?? (Graph Representation)

• ???a?a? Ge?t??as?? (Adjacency Matrix)
• A ???a?a? VxV
• Ai,j 0 ??? de? ?p???e? a?µ? µeta?? t?? ??µß??
  i ?a? j
• ??? p???e?ta? ??a ???f? µe ß???
• Ai,j wij ?p?? wij e??a? t? ß???? t?? a?µ??
  µeta?? t?? ??µß?? i ?a? j
• ??s?? ? e????st?? ????? p?? ??e???eta? ? p??a?a?
  (de? ep?t??p??ta? self-loops)

?? ?ate?????µe???
?ate?????µe???
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?pe?????s? G??f?? (Graph Representation)

• ??sta Ge?t??as?? (Adjacency List)
• ??a d????sµa (µ???d??stat?? p??a?a?) µe??????
  V.
• ?p? t? st???e?? i t?? p??a?a ?e???? µ?a
  s??dedeµ??? ??sta
• ??? p???e?ta? ??a ???f? µe ß???
• Se ???e st???e?? t?? ??sta? ?p???e? ep?s?? ?a? t?
  ß???? t?? a?µ?? p?? s??d?e? t??? ??µß???
• ????? p?? ??e???eta? st? µ??µ?

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?a??de??µa
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?a??de??µa µe ß???
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???t?a (Trees)

• S??dedeµ???? ??????? G??f??
• Se ??a d??t?? ?s??e? p??ta

• ?p???e? ??a ?a? µ??? µ???p?t? µeta?? d?? ??µß??
• ????µ??a (rooted) d??t?a d??t?a sta ?p??a
  a??a??eta ep????eta? ??a? ??µß?? sa? ???a (root)

??e??e?? d??t??
????µ??? d??t??
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???t?a

• ?a?µ?? (degree) e??? ??µß?? a???µ?? t?? pa?d???
  t??.
• ?a?µ?? t?? d??t??? µ???st?? ßa?µ?? ap? t???
  ??µß??? t?? d??t???.
• ????? (depth) e??? ??µß?? e??a? ? ap?stas? t??
  ??µß?? ap? t? ???a
• ???? t?? d??t??? e??a? ? ap?stas? t?? ???a? ap?
  t? p?? ap?µa???sµ??? f????.

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?pe?????s? ???t???

• ??sd??stat??? ???a?e? (?p?? ?? ???f??)
• ??? p??? ap?d?t???? ??s? af?? ??a d??t?? e??a?
  ??a? a?a??? ???f??!
• ????d??stat?? ???a?a?
• ?a pa?d?? ???e ??µß?? eµfa?????ta? se
  s???e???µ??e? ??se?? t?? p??a?a
• G?a ap?d?t???te?? d?a?e???s? t?? ded?µ????, st??
  p??a?a eµfa?????ta? de??te? p??? ta ded?µ??a ?a?
  ??? ta ded?µ??a ta ?d?a.
• ?a??de??µa d?ad???? d??t???
• ? ????a? t?? ??µß?? j ß??s?eta? st? ??s?

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?pe?????s? ???t???

• ?? ??aµµ???? ??ste?
• ???e ??µß?? µp??e? ?a ??e? ??a ? pe??ss?te?a
  pa?d??
• ?a??de??µa d?ad???? d??t???

• ? a??????? s??s? ?s??e? ??a d?ad??? d??t?a µe n
  ??µß??? t??? ?p????? t? ???? e??a? h

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?a????µ?µ??a ???t?a

• ??ad??? ta????µ?µ??a d??t?a
• ?? ??e?d? t?? a??ste??? pa?d??? e??a? µ????te??
  ap? a?t? t?? ??????