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<T "item getQUEUE()">
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<T "ritorna l'elemento in posizione frontale della coda  oppure niente se la co\
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<T "destroyQUEUE()">
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*BEGIN GRAPHICS VERSION=441/420 ENCODING=7BIT
** "Creator" bertozzi
** "Creation Date" Mon May  8 10:15:15 2000
** "Revisor" bertozzi
** "Last Modified" Mon May  8 10:26:22 2000

FONT
"Times"
"Zapf Dingbats"
END FONT

SESSION
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END SESSION

SLIDE_INFO
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END SLIDE_INFO
PICTURE
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 .TXT AT (1164,914)
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 .TXT AT (1914,1414)
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 .TXT AT (415,1414)
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 .TXT AT (1164,2914)
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 .GRP
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 .LINE AT (6000,2000)
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 .TXT AT (7420,1911)
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 .TXT AT (6670,2414)
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 .TXT AT (4415,1914)
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 .TXT AT (5914,1914)
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 .TXT AT (6664,1414)
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 .TXT AT (5914,914)
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 .ELL AT (5000,2250)
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 .TXT AT (5164,2414)
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END .GRP
.TXT AT (3099,1000)
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 V_SPACE <0 333 0>
 SIZE 240000 L_SPACE 333
 TXTXYOFF <-5 225>
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 .STR
  THICKNESS 0 L_SPACE 250
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.LINE AT (2500,1250)
 BACKFILL <1 0 0 0 0 0 0>
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END PICTURE

*END GRAPHICS

*BEGIN GRAPHICS VERSION=441/420 ENCODING=7BIT
** "Creator" bertozzi
** "Creation Date" Mon May  8 11:22:23 2000
** "Creation Version" 5 (1251)
** "Revisor" bertozzi
** "Last Modified" Mon May  8 11:33:50 2000
** "Last Modified Version" 5 (1251)

FONT
"Times"
"Zapf Dingbats"
END FONT

SESSION
 WIN_SIZE <11960 8414>
 AUTOGRID ON
 VIEW <0 0 0 1 1 0>
 SLIDE_STYLE <0 -1 1>
 PARA <0 0 0 0 1000 1 1 111>
 REZ <0 1000 1000 -1503 0>
END SESSION

SLIDE_INFO
 SLIDE_STYLE <0 -1 1>
END SLIDE_INFO
PICTURE
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 PNTS (0,500)(250,0)
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 PNTS (250,500)(0,0)
.GRP
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 .LINE AT (3250,2750)
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 .LINE AT (3750,2750)
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END .GRP
.GRP
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 .LINE AT (5000,2751)
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END .GRP
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 PNTS (500,0)(0,500)
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 PNTS (0,0)(500,500)
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 PNTS (0,0)(500,500)
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 PNTS (500,0)(0,500)
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 PNTS (250,0)(0,1000)
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 PNTS (0,0)(1250,1000)
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 PNTS (1250,0)(0,500)
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 BACKFILL <1 0 5 1000 0 0 0>
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 TXTXYOFF <-11 169>
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 .STR
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END PICTURE

*END GRAPHICS

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END COLORMAP
DATA
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** "Creator" bertozzi
** "Creation Date" Sun May 14 17:14:15 2000
** "Revisor" bertozzi
** "Last Modified" Sun May 14 17:24:48 2000

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   .RECT AT (1250,2500)
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    PNTS (250,0)(0,0)(0,250)(250,250)(250,0)
  END .GRP
  .GRP
   .RECT AT (1750,2250)
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   .RECT AT (1750,2500)
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    PNTS (250,0)(0,0)(0,250)(250,250)(250,0)
  END .GRP
  .GRP
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   .RECT AT (1750,3000)
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  END .GRP
  .GRP
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   .RECT AT (1250,3000)
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  END .GRP
 END .GRP
 .GRP
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  END .GRP
  .GRP
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  END .GRP
  .GRP
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  END .GRP
  .GRP
   .RECT AT (250,3750)
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  END .GRP
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END .GRP
.GRP
 .GRP
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    PNTS (250,0)(0,0)(0,250)(250,250)(250,0)
  END .GRP
  .GRP
   .RECT AT (750,250)
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   .RECT AT (1000,500)
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   .RECT AT (1000,250)
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  END .GRP
  .GRP
   .RECT AT (750,750)
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   .RECT AT (750,1000)
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    PNTS (250,0)(0,0)(0,250)(250,250)(250,0)
  END .GRP
  .GRP
   .RECT AT (250,750)
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  END .GRP
 END .GRP
 .GRP
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  END .GRP
  .GRP
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  END .GRP
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  END .GRP
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  END .GRP
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 .GRP
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  END .GRP
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  END .GRP
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 .GRP
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  END .GRP
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  .GRP
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END .GRP
.GRP
 .GRP
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 .GRP
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 .GRP
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 .GRP
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END .GRP
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 .GRP
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 .GRP
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    PNTS (0,250)(250,250)(250,0)(0,0)(0,250)
   .RECT AT (5500,2500)
    PNTS (250,250)(0,250)(0,0)(250,0)(250,250)
   .RECT AT (5500,2250)
    PNTS (250,0)(0,0)(0,250)(250,250)(250,0)
  END .GRP
  .GRP
   .RECT AT (5750,2250)
    PNTS (0,0)(250,0)(250,250)(0,250)(0,0)
   .RECT AT (5750,2500)
    PNTS (0,250)(250,250)(250,0)(0,0)(0,250)
   .RECT AT (6000,2500)
    PNTS (250,250)(0,250)(0,0)(250,0)(250,250)
   .RECT AT (6000,2250)
    PNTS (250,0)(0,0)(0,250)(250,250)(250,0)
  END .GRP
  .GRP
   .RECT AT (5750,2750)
    PNTS (0,0)(250,0)(250,250)(0,250)(0,0)
   .RECT AT (5750,3000)
    PNTS (0,250)(250,250)(250,0)(0,0)(0,250)
   .RECT AT (6000,3000)
    PNTS (250,250)(0,250)(0,0)(250,0)(250,250)
   .RECT AT (6000,2750)
    PNTS (250,0)(0,0)(0,250)(250,250)(250,0)
  END .GRP
  .GRP
   .RECT AT (5250,2750)
    PNTS (0,0)(250,0)(250,250)(0,250)(0,0)
   .RECT AT (5250,3000)
    PNTS (0,250)(250,250)(250,0)(0,0)(0,250)
   .RECT AT (5500,3000)
    PNTS (250,250)(0,250)(0,0)(250,0)(250,250)
   .RECT AT (5500,2750)
    PNTS (250,0)(0,0)(0,250)(250,250)(250,0)
  END .GRP
 END .GRP
 .GRP
  .GRP
   .RECT AT (4250,3250)
    PNTS (0,0)(250,0)(250,250)(0,250)(0,0)
   .RECT AT (4250,3500)
    PNTS (0,250)(250,250)(250,0)(0,0)(0,250)
   .RECT AT (4500,3500)
    PNTS (250,250)(0,250)(0,0)(250,0)(250,250)
   .RECT AT (4500,3250)
    PNTS (250,0)(0,0)(0,250)(250,250)(250,0)
  END .GRP
  .GRP
   .RECT AT (4750,3250)
    PNTS (0,0)(250,0)(250,250)(0,250)(0,0)
   .RECT AT (4750,3500)
    PNTS (0,250)(250,250)(250,0)(0,0)(0,250)
   .RECT AT (5000,3500)
    PNTS (250,250)(0,250)(0,0)(250,0)(250,250)
   .RECT AT (5000,3250)
    PNTS (250,0)(0,0)(0,250)(250,250)(250,0)
  END .GRP
  .GRP
   .RECT AT (4750,3750)
    PNTS (0,0)(250,0)(250,250)(0,250)(0,0)
   .RECT AT (4750,4000)
    PNTS (0,250)(250,250)(250,0)(0,0)(0,250)
   .RECT AT (5000,4000)
    PNTS (250,250)(0,250)(0,0)(250,0)(250,250)
   .RECT AT (5000,3750)
    PNTS (250,0)(0,0)(0,250)(250,250)(250,0)
  END .GRP
  .GRP
   .RECT AT (4250,3750)
    PNTS (0,0)(250,0)(250,250)(0,250)(0,0)
   .RECT AT (4250,4000)
    PNTS (0,250)(250,250)(250,0)(0,0)(0,250)
   .RECT AT (4500,4000)
    PNTS (250,250)(0,250)(0,0)(250,0)(250,250)
   .RECT AT (4500,3750)
    PNTS (250,0)(0,0)(0,250)(250,250)(250,0)
  END .GRP
 END .GRP
END .GRP
.GRP
 .GRP
  .GRP
   .RECT AT (2250,250)
    PNTS (0,0)(250,0)(250,250)(0,250)(0,0)
   .RECT AT (2250,500)
    PNTS (0,250)(250,250)(250,0)(0,0)(0,250)
   .RECT AT (2500,500)
    PNTS (250,250)(0,250)(0,0)(250,0)(250,250)
   .RECT AT (2500,250)
    PNTS (250,0)(0,0)(0,250)(250,250)(250,0)
  END .GRP
  .GRP
   .RECT AT (2750,250)
    PNTS (0,0)(250,0)(250,250)(0,250)(0,0)
   .RECT AT (2750,500)
    PNTS (0,250)(250,250)(250,0)(0,0)(0,250)
   .RECT AT (3000,500)
    PNTS (250,250)(0,250)(0,0)(250,0)(250,250)
   .RECT AT (3000,250)
    PNTS (250,0)(0,0)(0,250)(250,250)(250,0)
  END .GRP
  .GRP
   .RECT AT (2750,750)
    PNTS (0,0)(250,0)(250,250)(0,250)(0,0)
   .RECT AT (2750,1000)
    PNTS (0,250)(250,250)(250,0)(0,0)(0,250)
   .RECT AT (3000,1000)
    PNTS (250,250)(0,250)(0,0)(250,0)(250,250)
   .RECT AT (3000,750)
    PNTS (250,0)(0,0)(0,250)(250,250)(250,0)
  END .GRP
  .GRP
   .RECT AT (2250,750)
    PNTS (0,0)(250,0)(250,250)(0,250)(0,0)
   .RECT AT (2250,1000)
    PNTS (0,250)(250,250)(250,0)(0,0)(0,250)
   .RECT AT (2500,1000)
    PNTS (250,250)(0,250)(0,0)(250,0)(250,250)
   .RECT AT (2500,750)
    PNTS (250,0)(0,0)(0,250)(250,250)(250,0)
  END .GRP
 END .GRP
 .GRP
  .GRP
   .RECT AT (3250,1250)
    PNTS (0,0)(250,0)(250,250)(0,250)(0,0)
   .RECT AT (3250,1500)
    PNTS (0,250)(250,250)(250,0)(0,0)(0,250)
   .RECT AT (3500,1500)
    PNTS (250,250)(0,250)(0,0)(250,0)(250,250)
   .RECT AT (3500,1250)
    PNTS (250,0)(0,0)(0,250)(250,250)(250,0)
  END .GRP
  .GRP
   .RECT AT (3750,1250)
    PNTS (0,0)(250,0)(250,250)(0,250)(0,0)
   .RECT AT (3750,1500)
    PNTS (0,250)(250,250)(250,0)(0,0)(0,250)
   .RECT AT (4000,1500)
    PNTS (250,250)(0,250)(0,0)(250,0)(250,250)
   .RECT AT (4000,1250)
    PNTS (250,0)(0,0)(0,250)(250,250)(250,0)
  END .GRP
  .GRP
   .RECT AT (3750,1750)
    PNTS (0,0)(250,0)(250,250)(0,250)(0,0)
   .RECT AT (3750,2000)
    PNTS (0,250)(250,250)(250,0)(0,0)(0,250)
   .RECT AT (4000,2000)
    PNTS (250,250)(0,250)(0,0)(250,0)(250,250)
   .RECT AT (4000,1750)
    PNTS (250,0)(0,0)(0,250)(250,250)(250,0)
  END .GRP
  .GRP
   .RECT AT (3250,1750)
    PNTS (0,0)(250,0)(250,250)(0,250)(0,0)
   .RECT AT (3250,2000)
    PNTS (0,250)(250,250)(250,0)(0,0)(0,250)
   .RECT AT (3500,2000)
    PNTS (250,250)(0,250)(0,0)(250,0)(250,250)
   .RECT AT (3500,1750)
    PNTS (250,0)(0,0)(0,250)(250,250)(250,0)
  END .GRP
 END .GRP
 .GRP
  .GRP
   .RECT AT (3250,250)
    PNTS (0,0)(250,0)(250,250)(0,250)(0,0)
   .RECT AT (3250,500)
    PNTS (0,250)(250,250)(250,0)(0,0)(0,250)
   .RECT AT (3500,500)
    PNTS (250,250)(0,250)(0,0)(250,0)(250,250)
   .RECT AT (3500,250)
    PNTS (250,0)(0,0)(0,250)(250,250)(250,0)
  END .GRP
  .GRP
   .RECT AT (3750,250)
    PNTS (0,0)(250,0)(250,250)(0,250)(0,0)
   .RECT AT (3750,500)
    PNTS (0,250)(250,250)(250,0)(0,0)(0,250)
   .RECT AT (4000,500)
    PNTS (250,250)(0,250)(0,0)(250,0)(250,250)
   .RECT AT (4000,250)
    PNTS (250,0)(0,0)(0,250)(250,250)(250,0)
  END .GRP
  .GRP
   .RECT AT (3750,750)
    PNTS (0,0)(250,0)(250,250)(0,250)(0,0)
   .RECT AT (3750,1000)
    PNTS (0,250)(250,250)(250,0)(0,0)(0,250)
   .RECT AT (4000,1000)
    PNTS (250,250)(0,250)(0,0)(250,0)(250,250)
   .RECT AT (4000,750)
    PNTS (250,0)(0,0)(0,250)(250,250)(250,0)
  END .GRP
  .GRP
   .RECT AT (3250,750)
    PNTS (0,0)(250,0)(250,250)(0,250)(0,0)
   .RECT AT (3250,1000)
    PNTS (0,250)(250,250)(250,0)(0,0)(0,250)
   .RECT AT (3500,1000)
    PNTS (250,250)(0,250)(0,0)(250,0)(250,250)
   .RECT AT (3500,750)
    PNTS (250,0)(0,0)(0,250)(250,250)(250,0)
  END .GRP
 END .GRP
 .GRP
  .GRP
   .RECT AT (2250,1250)
    PNTS (0,0)(250,0)(250,250)(0,250)(0,0)
   .RECT AT (2250,1500)
    PNTS (0,250)(250,250)(250,0)(0,0)(0,250)
   .RECT AT (2500,1500)
    PNTS (250,250)(0,250)(0,0)(250,0)(250,250)
   .RECT AT (2500,1250)
    PNTS (250,0)(0,0)(0,250)(250,250)(250,0)
  END .GRP
  .GRP
   .RECT AT (2750,1250)
    PNTS (0,0)(250,0)(250,250)(0,250)(0,0)
   .RECT AT (2750,1500)
    PNTS (0,250)(250,250)(250,0)(0,0)(0,250)
   .RECT AT (3000,1500)
    PNTS (250,250)(0,250)(0,0)(250,0)(250,250)
   .RECT AT (3000,1250)
    PNTS (250,0)(0,0)(0,250)(250,250)(250,0)
  END .GRP
  .GRP
   .RECT AT (2750,1750)
    PNTS (0,0)(250,0)(250,250)(0,250)(0,0)
   .RECT AT (2750,2000)
    PNTS (0,250)(250,250)(250,0)(0,0)(0,250)
   .RECT AT (3000,2000)
    PNTS (250,250)(0,250)(0,0)(250,0)(250,250)
   .RECT AT (3000,1750)
    PNTS (250,0)(0,0)(0,250)(250,250)(250,0)
  END .GRP
  .GRP
   .RECT AT (2250,1750)
    PNTS (0,0)(250,0)(250,250)(0,250)(0,0)
   .RECT AT (2250,2000)
    PNTS (0,250)(250,250)(250,0)(0,0)(0,250)
   .RECT AT (2500,2000)
    PNTS (250,250)(0,250)(0,0)(250,0)(250,250)
   .RECT AT (2500,1750)
    PNTS (250,0)(0,0)(0,250)(250,250)(250,0)
  END .GRP
 END .GRP
END .GRP
.GRP
 .GRP
  .GRP
   .RECT AT (2250,2250)
    PNTS (0,0)(250,0)(250,250)(0,250)(0,0)
   .RECT AT (2250,2500)
    PNTS (0,250)(250,250)(250,0)(0,0)(0,250)
   .RECT AT (2500,2500)
    PNTS (250,250)(0,250)(0,0)(250,0)(250,250)
   .RECT AT (2500,2250)
    PNTS (250,0)(0,0)(0,250)(250,250)(250,0)
  END .GRP
  .GRP
   .RECT AT (2750,2250)
    PNTS (0,0)(250,0)(250,250)(0,250)(0,0)
   .RECT AT (2750,2500)
    PNTS (0,250)(250,250)(250,0)(0,0)(0,250)
   .RECT AT (3000,2500)
    PNTS (250,250)(0,250)(0,0)(250,0)(250,250)
   .RECT AT (3000,2250)
    PNTS (250,0)(0,0)(0,250)(250,250)(250,0)
  END .GRP
  .GRP
   .RECT AT (2750,2750)
    PNTS (0,0)(250,0)(250,250)(0,250)(0,0)
   .RECT AT (2750,3000)
    PNTS (0,250)(250,250)(250,0)(0,0)(0,250)
   .RECT AT (3000,3000)
    PNTS (250,250)(0,250)(0,0)(250,0)(250,250)
   .RECT AT (3000,2750)
    PNTS (250,0)(0,0)(0,250)(250,250)(250,0)
  END .GRP
  .GRP
   .RECT AT (2250,2750)
    PNTS (0,0)(250,0)(250,250)(0,250)(0,0)
   .RECT AT (2250,3000)
    PNTS (0,250)(250,250)(250,0)(0,0)(0,250)
   .RECT AT (2500,3000)
    PNTS (250,250)(0,250)(0,0)(250,0)(250,250)
   .RECT AT (2500,2750)
    PNTS (250,0)(0,0)(0,250)(250,250)(250,0)
  END .GRP
 END .GRP
 .GRP
  .GRP
   .RECT AT (3250,3250)
    PNTS (0,0)(250,0)(250,250)(0,250)(0,0)
   .RECT AT (3250,3500)
    PNTS (0,250)(250,250)(250,0)(0,0)(0,250)
   .RECT AT (3500,3500)
    PNTS (250,250)(0,250)(0,0)(250,0)(250,250)
   .RECT AT (3500,3250)
    PNTS (250,0)(0,0)(0,250)(250,250)(250,0)
  END .GRP
  .GRP
   .RECT AT (3750,3250)
    PNTS (0,0)(250,0)(250,250)(0,250)(0,0)
   .RECT AT (3750,3500)
    PNTS (0,250)(250,250)(250,0)(0,0)(0,250)
   .RECT AT (4000,3500)
    PNTS (250,250)(0,250)(0,0)(250,0)(250,250)
   .RECT AT (4000,3250)
    PNTS (250,0)(0,0)(0,250)(250,250)(250,0)
  END .GRP
  .GRP
   .RECT AT (3750,3750)
    PNTS (0,0)(250,0)(250,250)(0,250)(0,0)
   .RECT AT (3750,4000)
    PNTS (0,250)(250,250)(250,0)(0,0)(0,250)
   .RECT AT (4000,4000)
    PNTS (250,250)(0,250)(0,0)(250,0)(250,250)
   .RECT AT (4000,3750)
    PNTS (250,0)(0,0)(0,250)(250,250)(250,0)
  END .GRP
  .GRP
   .RECT AT (3250,3750)
    PNTS (0,0)(250,0)(250,250)(0,250)(0,0)
   .RECT AT (3250,4000)
    PNTS (0,250)(250,250)(250,0)(0,0)(0,250)
   .RECT AT (3500,4000)
    PNTS (250,250)(0,250)(0,0)(250,0)(250,250)
   .RECT AT (3500,3750)
    PNTS (250,0)(0,0)(0,250)(250,250)(250,0)
  END .GRP
 END .GRP
 .GRP
  .GRP
   .RECT AT (3250,2250)
    PNTS (0,0)(250,0)(250,250)(0,250)(0,0)
   .RECT AT (3250,2500)
    PNTS (0,250)(250,250)(250,0)(0,0)(0,250)
   .RECT AT (3500,2500)
    PNTS (250,250)(0,250)(0,0)(250,0)(250,250)
   .RECT AT (3500,2250)
    PNTS (250,0)(0,0)(0,250)(250,250)(250,0)
  END .GRP
  .GRP
   .RECT AT (3750,2250)
    PNTS (0,0)(250,0)(250,250)(0,250)(0,0)
   .RECT AT (3750,2500)
    PNTS (0,250)(250,250)(250,0)(0,0)(0,250)
   .RECT AT (4000,2500)
    PNTS (250,250)(0,250)(0,0)(250,0)(250,250)
   .RECT AT (4000,2250)
    PNTS (250,0)(0,0)(0,250)(250,250)(250,0)
  END .GRP
  .GRP
   .RECT AT (3750,2750)
    PNTS (0,0)(250,0)(250,250)(0,250)(0,0)
   .RECT AT (3750,3000)
    PNTS (0,250)(250,250)(250,0)(0,0)(0,250)
   .RECT AT (4000,3000)
    PNTS (250,250)(0,250)(0,0)(250,0)(250,250)
   .RECT AT (4000,2750)
    PNTS (250,0)(0,0)(0,250)(250,250)(250,0)
  END .GRP
  .GRP
   .RECT AT (3250,2750)
    PNTS (0,0)(250,0)(250,250)(0,250)(0,0)
   .RECT AT (3250,3000)
    PNTS (0,250)(250,250)(250,0)(0,0)(0,250)
   .RECT AT (3500,3000)
    PNTS (250,250)(0,250)(0,0)(250,0)(250,250)
   .RECT AT (3500,2750)
    PNTS (250,0)(0,0)(0,250)(250,250)(250,0)
  END .GRP
 END .GRP
 .GRP
  .GRP
   .RECT AT (2250,3250)
    PNTS (0,0)(250,0)(250,250)(0,250)(0,0)
   .RECT AT (2250,3500)
    PNTS (0,250)(250,250)(250,0)(0,0)(0,250)
   .RECT AT (2500,3500)
    PNTS (250,250)(0,250)(0,0)(250,0)(250,250)
   .RECT AT (2500,3250)
    PNTS (250,0)(0,0)(0,250)(250,250)(250,0)
  END .GRP
  .GRP
   .RECT AT (2750,3250)
    PNTS (0,0)(250,0)(250,250)(0,250)(0,0)
   .RECT AT (2750,3500)
    PNTS (0,250)(250,250)(250,0)(0,0)(0,250)
   .RECT AT (3000,3500)
    PNTS (250,250)(0,250)(0,0)(250,0)(250,250)
   .RECT AT (3000,3250)
    PNTS (250,0)(0,0)(0,250)(250,250)(250,0)
  END .GRP
  .GRP
   .RECT AT (2750,3750)
    PNTS (0,0)(250,0)(250,250)(0,250)(0,0)
   .RECT AT (2750,4000)
    PNTS (0,250)(250,250)(250,0)(0,0)(0,250)
   .RECT AT (3000,4000)
    PNTS (250,250)(0,250)(0,0)(250,0)(250,250)
   .RECT AT (3000,3750)
    PNTS (250,0)(0,0)(0,250)(250,250)(250,0)
  END .GRP
  .GRP
   .RECT AT (2250,3750)
    PNTS (0,0)(250,0)(250,250)(0,250)(0,0)
   .RECT AT (2250,4000)
    PNTS (0,250)(250,250)(250,0)(0,0)(0,250)
   .RECT AT (2500,4000)
    PNTS (250,250)(0,250)(0,0)(250,0)(250,250)
   .RECT AT (2500,3750)
    PNTS (250,0)(0,0)(0,250)(250,250)(250,0)
  END .GRP
 END .GRP
END .GRP
.ELL AT (250,250)
 BACKFILL <6 0 5 1000 0 0 0>
 LINEFILL <1 2 0 0 0 0 0>
 PNTS (0,0)(250,0)(250,250)(0,250)(0,0)
.ELL AT (750,2000)
 PNTS (0,0)(250,0)(250,250)(0,250)(0,0)
.ELL AT (250,3000)
 PNTS (0,0)(250,0)(250,250)(0,250)(0,0)
.ELL AT (250,3750)
 PNTS (0,0)(250,0)(250,250)(0,250)(0,0)
.ELL AT (500,2000)
 PNTS (0,0)(250,0)(250,250)(0,250)(0,0)
.ELL AT (250,2000)
 PNTS (0,0)(250,0)(250,250)(0,250)(0,0)
.ELL AT (250,2250)
 PNTS (0,0)(250,0)(250,250)(0,250)(0,0)
.ELL AT (250,1750)
 PNTS (0,0)(250,0)(250,250)(0,250)(0,0)
.ELL AT (250,1250)
 PNTS (0,0)(250,0)(250,250)(0,250)(0,0)
.ELL AT (500,750)
 PNTS (0,0)(250,0)(250,250)(0,250)(0,0)
.ELL AT (250,750)
 PNTS (0,0)(250,0)(250,250)(0,250)(0,0)
.ELL AT (500,3000)
 PNTS (0,0)(250,0)(250,250)(0,250)(0,0)
.ELL AT (500,1250)
 PNTS (0,0)(250,0)(250,250)(0,250)(0,0)
.ELL AT (1000,2000)
 PNTS (0,0)(250,0)(250,250)(0,250)(0,0)
.ELL AT (500,2250)
 PNTS (0,0)(250,0)(250,250)(0,250)(0,0)
.TXT AT (2975,5000)
 BACKFILL <1 0 5 1000 0 0 0>
 LINEFILL <1 2 5 1000 0 0 0>
 THICKNESS 56
 V_SPACE <0 333 0>
 SIZE 240000 L_SPACE 333 MARGINS <0 0 0 0>
 TXTXYOFF <-14 228>
 T_PNTS (0,228)(0,0)(641,0)(641,234)(0,234)(0,228)(641,228)
 .STR
  THICKNESS 0 L_SPACE 250
  "Slots"
.LINE AT (250,4500)
 BACKFILL <1 0 0 0 0 0 0>
 THICKNESS 1
 V_SPACE <0 250 0>
 SIZE 180000 MARGINS <125 125 250 62>
 PNTS (0,0)(250,250)
.LINE AT (500,4500)
 PNTS (0,250)(1750,0)
.LINE AT (2250,4500)
 PNTS (0,0)(500,0)
.LINE AT (2750,4500)
 PNTS (0,0)(500,250)
.LINE AT (3250,4500)
 PNTS (0,250)(500,0)
.LINE AT (3750,4500)
 PNTS (0,0)(500,0)
.LINE AT (4250,4500)
 PNTS (0,0)(1750,250)
.LINE AT (6000,4500)
 PNTS (0,250)(250,0)
.LINE AT (6500,4000)
 PNTS (0,250)(250,0)
.LINE AT (6500,3000)
 PNTS (250,1000)(0,0)
.LINE AT (6500,500)
 PNTS (0,1000)(250,0)
.LINE AT (6500,250)
 PNTS (0,0)(250,250)
.GRP
 .LINE AT (6500,2500)
  PNTS (0,500)(0,0)
 .LINE AT (6500,2250)
  PNTS (0,250)(250,0)
 .LINE AT (6500,2000)
  PNTS (250,250)(0,0)
 .LINE AT (6500,1500)
  PNTS (0,500)(0,0)
END .GRP
.TXT AT (7022,1750)
 BACKFILL <1 0 5 1000 0 0 0>
 THICKNESS 0
 V_SPACE <0 333 0>
 SIZE 240000 L_SPACE 333 MARGINS <0 0 0 0> SHR_ANG <0 900000>
 TXTXYOFF <228 1061>
 T_PNTS (228,1056)(0,1056)(0,0)(232,1)(232,1056)(228,1056)(228,1)
 .STR
  L_SPACE 250 SHR_ANG <0 0>
  "Buckets"
END PICTURE

*END GRAPHICS
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** "Creator" bertozzi
** "Creation Date" Sun May 14 18:33:56 2000
** "Revisor" bertozzi
** "Last Modified" Sun May 14 18:39:09 2000

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     "In realt^oa la definizione completa ipotizza che il tempo di es
 ecuzione di un passo di programma sia indipendente da ci^pc che 
 contiene"
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   "Il tempo di esecuzione di un passo di programma ^oi indipendent
 e dalle istanze da cui ^oi composto;"
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 ssi di programma eseguiti ^oi indipendente sia dal calcolatore u
 tilizzato che dal compilatore;"
  .STR
   "\nUna valutazione corretta della complessit^oa temporale tramit
 e il conteggio dei passi di programma dovr^oa considerare: caso 
 peggiore, caso migliore e caso medio."
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 i passi di programma per l'analisi di prestazioni. Non solo ma ^
 oi strettamente legato allo stile di scrittura di un programma. 
 Ciononostante l'utilizzo di questa tecnica permette il confronto
  di algoritmi differenti. "
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     "\nConsiderando le funzioni viste in precedenza proviamo a calco
 larne la complessit^oa temporale in funzione dei passi di progra
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 emporale non sempre ^oi necessaria;"
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   "\n^mi importante capire qual'^oi l'andamento qualitativo della 
 complessit^oa temporale al variare delle dimensioni del problema
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   "si definisce complessit^oa asintotica di un problema la comples
 sit^oa assunta da questo problema quando le sue dimensioni ("
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     "L'idea di base ^oi quella di raggruppare la complessit^oa degli
  algoritmi in categorie di funzioni soggette a certe limitazioni
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     "Per esempio due funzioni che differiscono per una costante molt
 iplicativa o additiva in realt^oa appartengono alla stessa class
 e."
    .STR
     "\nL'Horowitz definisce anche Teta e Omega."
    .STR
     "\nRammentare che un polinomio di grado x ^oi O(n alla x)."
    .STR
     "\nf(n)=ax*nx+...+a0<=sommatoria coi valori assoluti..."
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 i dati."
    .STR
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 ento."
    .STR
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   "Partendo dal programma di ordinamento sviluppato precedentement
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   "\n\tridefinire la funzione scambia come macro;"
  .STR
   "\n\tordinamento in senso crescente o decrescente;"
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   SIZE 400000
   "Ad ogni variabile ^oi associata una posizione in memoria. "
  .STR
   "\nPer ottenere l'indirizzo di memoria di una variabile si pu^pc
  usare l'operatore \""
  .STR
   "&"
  .STR
   "\". \nEsistono casi in cui ^oi necessario conoscere l'indirizzo
  di una variabile pi^pj che il suo valore."
END PICTURE
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    .STR
     "#include<stdio.h>"
    .STR
     "\n"
    .STR
     "\nint main(int argc, char **argv)"
    .STR
     "\n{"
    .STR
     "\nunsigned "
    .STR
     "in"
    .STR
     "t j=1000;"
    .STR
     "\n"
    .STR
     "\nprintf(\"Valore di j %d\\n\",j);"
    .STR
     "\nprintf(\"Indirizzo in memoria di j %p\\n\", &j); /* ANSI !! *
 /"
    .STR
     "\n}"
    .STR
     "\n"
    .STR
     "\nRisultato:"
    .STR
     "\n"
    .STR
     "\nValore di j 1000"
    .STR
     "\nIndirizzo in memoria di j FFE4"
    .STR
     "\n"
    .STR
     "\nin alternativa si potrebbe usare %x."
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     "\n"
    .STR
     "\nRammentare che non ^oi possibile l'utilizzo di & a sinistra d
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   "L'indirizzo di ritorno viene depositato nello stack;"
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   "\nGli argomenti della funzione vengono prelevati dallo stack."
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    .STR
     "Fare disegno e indicare anche cosa succede al ritorno della fun
 zione."
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   "Questo meccanismo ha le seguenti conseguenze:"
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   "\nNon ^oi possibile la loro modifica permanente;"
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   PARA <-500 500 -500 1 1000 31 2 51>
   "\nIn alcuni casi l'operazione risulta onerosa."
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  "SOLUZIONE"
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  ": passare l'indirizzo delle variabili anzich^oj il loro valore!
 "
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    .STR
     "Rifarsi all'esempio del bubble- e quick-sort nella funzione sca
 mbia();"
    .STR
     "\n#include<stddef.h>"
    .STR
     "\n"
    .STR
     "\nsize_t offsetof(tipo, nome_elemento);"
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   "Esiste un tipo di variabile che permette di memorizzare l'indir
 izzo in memoria di un'altra variabile: "
  .STR
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   "i puntatori"
  .STR
   UNDERLINE OFF
   "."
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   "long int *a;  /* definizione di un puntatore ad un long int */"
  .STR
   "\nchar *b; "
  .STR
   "\nfloat miofloat=2.5f;"
  .STR
   "\nchar miochar='A';"
  .STR
   "\nb = &miochar;"
  .STR
   "\nb = &miofloat; /* NON corretto MA ammesso */"
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    .STR
     PARA <0 500 0 0 1000 31 0 111>
     "\tIl compilatore avvisa sempre quando si tenta di assegnare ad 
 un puntatore un'indirizzo corrispondente a qualcosa di different
 e dal tipo puntato."
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END NOTES

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   L_SPACE 611
   "L'accesso al valore puntato di un puntatore si ottiene mediante
  il \"*\" e permette sia di leggere il valore puntato che di mod
 ificarlo;"
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   "float miofloat=2.5f;"
  .STR
   "\nfloat *mypointer=&miofloat;"
  .STR
   "\n"
  .STR
   "\n*mypointer=3.14f;"
  .STR
   "\nprintf(\"Il valore di miofloat ^oi %f\\n\", miofloat);"
  .STR
   "\nprintf(\"Il valore di miofloat ^oi %f\\n\", *miopointer);"
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    .STR
     "Introdurre il discorso sugli array (che io darei gi^oa per fatt
 o)."
    .STR
     "\nfloat a[10],  a, &a[0], &a[9]."
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  .STR
   L_SPACE 611
   "Il passaggio ad una funzione dell'indirizzo di una variabile pe
 rmette le seguenti cose:"
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  T_PNTS (-7,335)(-7,-1)(9233,-1)(9233,1428)(-7,1428)(-7,335)(9233,335)
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  .STR
   "si pu^pc cambiare il contenuto della variabile;"
  .STR
   "\nposso creare funzioni che ritornino pi^pj valori;"
  .STR
   "\nin alcuni casi ^oi pi^pj efficiente;"
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    .STR
     "Introdurre il discorso sugli array (che io darei gi^oa per fatt
 o)."
    .STR
     "\nfloat a[10],  a, &a[0], &a[9]."
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  .STR
   "I puntatori\naritmetica"
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  .STR
   L_SPACE 611
   "Il linguaggio C fornisce al programmatore numerosi operatori ar
 itmetici, fra questi \"+\" e \"-\".\n^mi intuitivo capire il lor
 o funzionamento con alcuni tipi di dato. \nViceversa l'utilizzo 
 di questi operatori con i puntatori richiede maggiore attenzione
 ."
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     "Rammentare che funzionano solo +e - e solo con numeri interi."
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    .STR
     "Ovviamente NON ^oi possibile riassegnare l'indirizzo ad un arra
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    .STR
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    .STR
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 egare il fatto che gli indici dei puntatori partano da 0 invece 
 che da 1. Notare che pointer.c d^oa degli errori!!!!!!!!  Un alt
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 ssari:"
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   "int **p;"
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   " /* puntatore ad un puntatore ... */"
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   " /* prototipo della funzione main */"
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     "Spiegare perch^oi la funziona main richiede ci^pc. Praticamente
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   BOLD OFF
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    .STR
     "Le parentesi sono necessarie in quantoche senza io avrei una fu
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 ca funzione la sua chiamata f(a) ^oi perfettamente equivalente a
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 e che restituisce un intero;"
    .STR
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 atore a intero."
    .STR
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 orizzazione. Sfruttare l'introduzione dello specificatore extern
  per ritornare sul discorso dei .h e distinguere allusione e def
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 memoria, mentre per le variabili con durata automatica la memori
 a viene allocata/disallocata ogni qual volta si esegue il blocco
  relativo."
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   "       #include <stdlib.h> \n \n       void *calloc(size_t nmem
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     "Nel caso del C NON-ANSI ritornavano un puntatore a char."
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     "\nPrendere psort.c (ricordare l'errore che era nel while) e dis
 cutere perror (eventualmente)."
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 puntata da *ptr. Se ptr==NULL non compie alcuna operazione. Se l
 'area di memoria non era stata allocata dinamicamente il risulta
 to non ^oi definito."
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 minimum of the old and new sizes; newly allocated memory will be
  uninitialized.  If ptr is NULL,  the  call  is equivalent  to m
 alloc(size); if size is equal to zero, the call is equivalent to
  free(ptr).  Unless ptr is  NULL,  it must  have  been  returned
  by an earlier call to malloc(), calloc() or realloc(). \n"
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 trumenti messi a disposizione del programmatore C, d'altro canto
  portano a introdurre nel codice bug "
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   "Buffer Overruns"
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    .STR
     "\nRammentare la principale differenza tra i compiti nel caso di
  fondamenti I e II."
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   "Sviluppare un programma che prenda in ingresso due argomenti. S
 ia il primo il nome di un file e il secondo una lettera. \nIl pr
 ogramma dovr^oa analizzare il file in ingresso e memorizzare tut
 te le parole che contengono la lettera indicata. \nA elaborazion
 e terminata si stampino le lettere isolate in un secondo file.\n
 Si utilizzi "
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   "/* Definition of the control structure for streams */\n \ntyped
 ef struct  { \n        int                       level;       /*
  fill/empty level of buffer */ \n        unsigned           flag
 s;       /* File status flags          */ \n        char        
             fd;           /* File descriptor            */ \n   
      unsigned char   hold;       /* Ungetc char if no buffer   *
 / \n        int                       bsize;     /* Buffer size 
                */ \n        unsigned char   *buffer;   /* Data t
 ransfer buffer       */ \n        unsigned char   *curp;     /* 
 Current active pointer     */ \n        unsigned            iste
 mp;  /* Temporary file indicator   */ \n        short           
         token;    /* Used for validity checking */ \n}       FIL
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    .STR
     "Introdurre e spiegare il concetto di typedef."
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 ei dati e la specifica delle operazioni sui dati siano distinte 
 dalla rappresentazione degli oggetti e dall'implementazione dell
 e operazioni"
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 e che l'ADT consiste nello specificare il tipo di dato e le funz
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   "Gli ADT permettono una specifica formale del problema con un oc
 chio di riguardo per i dati. La specifica ^oi formata dal nome d
 elle funzioni dai tipi in ingresso e dai tipi in uscita; le funz
 ioni (metodi) sono poi suddivise in:"
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   "Gli ADT stanno ai dati come i diagrammi di flusso stanno agli a
 lgoritmi. Il programmatore poco accorto parte dal programma, il 
 programmatore saggio e avveduto parte dai dati, stabilisce le pr
 ocedure che servono per la trattazione dei dati, ne disegna gli 
 algoritmi e solamente per ultimo implementa."
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 ire nel caso della programmazione ad oggetti e ne spiega il suo 
 successo. In C si possono certamente"
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 ali che ad ogni indice definito sia associato un determinato val
 ore (corrispondenza). \nVediamolo come ADT.\n"
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     "NON sono gli array del C!!!\n(pag. 51)"
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   "Una possibile rappresentazione degli alberi si pu^pc ottenere m
 ediante gli array. In questo caso ^oi possibile risalire ad ogni
  nodo mediante la sua posizione nell'array."
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   "Il numero massimo dei nodi ^oi sempre dispari!"
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   "Dato un albero binario completo con n nodi per un nodo di indic
 e "
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   "il padre del nodo di indice i si trova nella posizione "
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   ITALICS ON
   "i/2 "
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   "("
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   "i=1"
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   " ^oi la radice);"
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   "\nanalogamente il figlio destro si trova nella posizione "
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   ITALICS ON
   "2i + 1"
  .STR
   ITALICS OFF
   "."
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    .STR
     "il punto 1 discende dal 2 mentre il 2 e il 3 si dimostrano per 
 induzione."
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     "\nChiaramente questa rappresentazione ^oi possibile per tutti g
 li alberi ma ci sar^oa spazio sprecato."
    .STR
     "\n"
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   "La rappresentazione mediante array soffre delle generiche inade
 guatezze delle rappresentazioni sequenziali. ^mi quindi, in gene
 re, preferibile una rappresentazione collegata:"
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   "struct nodo {"
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   "\n     miodato dato;"
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   "\n     struct nodo *sinistra; "
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   "\n     struct nodo *destra;"
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   "\n   };"
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   "\nstruct nodo *mytree;"
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    .STR
     "Attenzione al pari delle liste singolarmente collegate NON ^oi 
 semplice determinare il padre, comunque ^oi possibile aggiungere
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   "Una delle operazione pi^pj frequenti riguardanti gli alberi ^oi
  la visita dei loro nodi una e una sola volta, detta anche attra
 versamento.\nNe consideriamo solo tre tipologie:"
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PICTURE
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 RECOLOR ON
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   "Si pu^pc ottenere facilmente con una funzione ricorsiva:"
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 RECOLOR ON
 TEMPLATE_FLAGS <2 7 0 0>
 T_POS <282 5280 10221 7726>
 .TXT AT (1284,4570)
  RECOLOR ON
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   "void inorder(nodo *mytree)"
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   "\n{  if(!mytree) return;"
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   "\n   inorder(mytree->sinistra);"
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   "\n   printf(\"%"
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   BOLD OFF
   " \\n\", mytree->dato);"
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   "\n   inorder(mytree->destra);"
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     "otterremmo ((A/B)-(C*D))+(E^^F) cio^oi il formato infisso."
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 .TXT AT (2787,2639)
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   "void inorder(nodo *tree){"
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   "\n   for(;;){"
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   "\n      "
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   "for(;tree;tr"
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   "ee=tree->sinistra)"
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   "\n        add_stack(&top, tree);"
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   "\n      tree="
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   "d"
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   "elete_stack(&top);"
  .STR
   "\n      if(!tree)break;"
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   "\n      printf(\"%"
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   " \\n\", tree->dato);"
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   "\n      tree = tree->destra;"
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   "void level_order(nodo *tree){"
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   "\n   int davanti=dietro=0; "
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   "\n   nodo *queue[MAX_SIZE_STACK];"
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   "\n   if(!tree) return;"
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   "\n   add_queue(davanti, &dietro, tree);"
  .STR
   "\n   for(;;){"
  .STR
   "\n      tree=delete_queue"
  .STR
   "(&davanti, dietro);"
  .STR
   "\n      if(tree){"
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   "\n         printf(\"% ? \\n\", tree->dato);"
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   "\n      if(tree->sinistra)"
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   "\n         add_queue(davanti, &dietro, tree->sinistra);"
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   "\n      if(tree->destra)"
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   "\n         add_queue(davanti, &dietro, tree->destra);"
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   "\n         }"
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   "\n      else "
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   "break;"
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   "\n      }"
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   "\n   }"
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     "otterremo quanto visto nel caso dell'albero pieno/completo"
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   "La copia di un albero binario ^oi  ottenibile modificando legge
 rmente le funzioni gi^oa viste:"
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   "nodo *tree_copy(nodo *orig){"
  .STR
   "\n   nodo *temp;   "
  .STR
   "\n   if(orig){"
  .STR
   "\n      temp=malloc(sizeof(nodo));"
  .STR
   "\n      temp->dato=orig->dato;"
  .STR
   "\n      temp->sinistra=tree_copy(orig->sinistra);"
  .STR
   "\n      temp->destra=tree_copy(orig->destra);"
  .STR
   "\n      return temp;"
  .STR
   "\n   }"
  .STR
   "\nreturn NULL;"
  .STR
   "\n}"
  .STR
   " "
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   " "
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     "otterremo quanto visto nel caso dell'albero pieno/completo"
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   "Similmente possiamo determinare se due alberi sono equivalenti:
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   "int tree_equiv(nodo *primo, nodo *secondo){"
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   "\n   return ((!primo&&!secondo)|| (primo && secondo &&\\   "
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   "\n   (primo->dato == secondo->dato) && \\"
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   "\n    tree_equiv(primo->sinistra, secondo->sinistra) &&\\"
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   "\n    tree_equiv(primo->destra, secondo->destra));"
  .STR
   "\n}"
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   " "
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   " "
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  .STR
   L_SPACE 611
   "Un possibile campo di applicazione degli alberi ^oi la valutazi
 one di espressioni in particolar modo delle espressioni logiche.
  Ovvero, data un'espressione logica determinare se e quali valor
 i dei suoi operandi la rendono vera: "
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   "problema della soddisfacibilit^oa"
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   " ("
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    .STR
     "Occorre:"
    .STR
     "\ngenerare tutte le combinazioni possibili e verificarle"
    .STR
     "\nla cosa pi^pj sensata ^oi aggiungere un campo alla struttura 
 dati contenente il valore dell'espressione e quindi ricorsivamen
 te valutarla in questo caso ricadiamo in O(g*2^^n) con g tempo n
 ecessario per la sostituzione dei dati."
    .STR
     "\nSi utilizza un attraversamento postorder in cui si pu^pc util
 izzare uno switch sul valore del nodo (che assumera vero. falso,
  or, not, and)."
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   "Scrivere una funzione C legga un'espressione aritmetica la memo
 rizzi in un albero  e ne calcoli il valore.\nCi si limiti ad ope
 ratori unari o binari e numeri interi."
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   L_SPACE 611
   "Nel caso delle foglie i puntatori ai figli non sono usati. Un p
 ossibile utilizzo ^oi quello utilizzarli come collegamenti aggiu
 ntivi. Utilizziamo queste due regole: "
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   "se ^oi nullo il puntatore al figlio di sinistra sostituiamolo c
 on un puntatore al nodo che si sarebbe visitato precedentemente 
 utilizzando un attraversamento inorder;"
  .STR
   "\nse ^oi nullo il puntatore al figlio di destra sostituiamolo c
 on un puntatore al nodo che si sarebbe visitato successivamente 
 con metodo inorder."
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   "Occorre per^pc aggiungere un campo per determinare quali sono i
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  "typedef struct{"
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  "\n   miodato dato;\n   char sinistra_t, destra_t;"
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  "\n   struct nodo *sinistra, *destra; }nodo;"
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  "\nnodo *mytree;"
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 abili agli alberi binari di ricerca (ad eccezione della verifica
  dell'equivalenza). Consideriamo le operazioni aggiuntive di ins
 erimento, cancellazione e ricerca di un elemento."
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     "La foggia di un albero binario di ricerca dipendono dall'ordine
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 RECOLOR ON
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 .TXT AT (458,2726)
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  .STR
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   "Consideriamo una versione ricorsiva della ricerca. Supponiamo p
 er semplicit^oa che la chiave sia un intero e che la struttura d
 ati vista in precedenza contenga quindi un campo chiave."
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   "\nnodo *ricerca(nodo *radice, int key){\n   if(!radice) return 
 NULL;\n   if(key==radice->chiave) return radice;\n   if(key>radi
 ce->chiave)\n       return ricerca(radice->destro, key);\n   ret
 urn(radice->sinistro, key);\n}\n"
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END NOTES

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 LAYOUT_ID <3 1 1 12 12>
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   "Consideriamo una versione iterativa della ricerca. "
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   "\nnodo *ricerca(nodo *radice, int key){\n   while(radice){\n   
    if(key==radice->chiave)\n         return radice;\n      if(ke
 y>radice->chiave)\n         radice=radice->sinistro;\n      else
 \n         radice=radice->destro;\n    }\n   return NULL;\n}\n"
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     "La velocit^oa della ricerca dipende pi^pj che dal numero di nod
 i dall'altezza dell'albero."
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END NOTES

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 LAYOUT_ID <3 1 1 12 12>
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 RECOLOR ON
 TEMPLATE_FLAGS <1 0 0 0>
 T_POS <282 240 10221 2146>
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  T_PNTS (-4,446)(-4,-1)(4480,-1)(4480,1069)(-4,1069)(-4,446)(4480,446)
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   "Consideriamo l'inserimento, a tal fine sar^oa necessario capire
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  T_PNTS (-2,218)(-2,-1)(6360,-1)(6360,4261)(-2,4261)(-2,218)(6360,218)
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   "void insert_nodo(nodo **tree, nodo *new){\n   nodo *punto;\n\n 
   if(!*tree) {\n      *tree=new;\n       return;\n   }\n   punto
 =ricerca_punto_ins(*tree, new->chiave);\n   if(!punto) exit(1);\n
    new->sinistro=new->destro=NULL;\n   if(new->chiave>punto->chi
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     "Supponiamo che ricerca_punto_ins restituisca o il nodo dove ins
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     "\nNel caso in esempio ho difficolt^oa ad inserire 24 poich^oj 2
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 ve, posso associare a loro un indice "
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   "0..n"
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   ". La selezione di un nodo tramite indice consiste nel recuperar
 e il nodo di indice "
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   "k"
  .STR
   ITALICS OFF
   ". \n^mi possibile l'utilizzo di una funzione ricorsiva che guar
 da il numero di nodi in ciascun sottoalbero e attraversa l'alber
 o di conseguenza."
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    .STR
     "Prendere tree.c e commentare select e size."
    .STR
     "\nCommento sul fatto che select e' inefficiente visto la quanti
 ta' di volte che chiama size. Soluzione aggiunta di un campo dim
 ensione che complica pero' il meccanismo di inserzione e cancell
 azione."
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   "Dalla selezione mediante l'aggiunta di rotazioni si pu^pc facil
 mente ottenere l'operazione di partizione che separa l'albero po
 rtando il nodo di indice k ad essere la radice dell'albero.\n\n\n
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    .STR
     "Prendere tree.c e commentare root_parition"
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   L_SPACE 611
   "La cancellazione di un nodo da un albero binario di ricerca ^oi
  un'operazione generalmente complessa.\nSe il nodo ^oi una fogli
 a baster^oa semplicemente eliminarlo.\nSe il nodo ha un solo fig
 lio lo cancello e collego al padre l'unico figlio.\nSe il nodo h
 a due figli lo sostituisco con l'elemento pi^pj grande del sotto
 albero sinistro che a sua volta canceller^pc. Si pu^pc dimostrar
 e che l'elemento pi^pj grande si trova comunque in un nodo di gr
 ado <=1.\n"
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    .STR
     "                      40"
    .STR
     "\n                          \\"
    .STR
     "\n                           60"
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     "\n                          /     \\   "
    .STR
     "\n                        50     70"
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     "\n                      /     \\"
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     "\n                    45      55"
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     "\n                            /"
    .STR
     "\n                          52"
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   "In pratica si pu^pc ottenere la cancellazione di un nodo sposta
 ndolo in radice e riunificando i due alberi che sono rimasti met
 tendo come radice il nodo avente la chiave con pi^pj piccolo val
 ore che si trova nel sottoalbero che contiene le chiavi aventi v
 alore maggiore. \nPer ragioni di efficienza non si effettua lo s
 postamento in radice ma pi^pj semplicemente si compie l'operazio
 ne sul sottoalbero di cui il nodo che si desidera cancellare ^oi
  radice."
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    .STR
     "Prendere tree.c e commentare tree_join_delete e  tree_delete"
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    .STR
     "Nel 1962 Adelson-Velskji e Landis introdussero gli alberi bilan
 ciati."
    .STR
     "\nIl problema si nota anche quando salvo su file le strutture a
 d albero, dato che le percorro in un certo ordine il problema ^o
 i che probabilmente le salver^pc anche in ordine..."
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   "Una possibile soluzione alla creazione di alberi di tipo degene
 re ^oi l'inserzione casuale.\nOvvero mescolo l'inserzione in rad
 ice con spostamenti sull'albero legando la probabilit^oa delle o
 perazioni alle dimensioni dell'albero."
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    .STR
     "Man mano che mi avvicino alle foglie aumenta la probabilit^oa d
 i inserzione in radice."
    .STR
     "\nPrendere tree.c e commentare rand_tree_insertion"
    .STR
     "\nInserendo in ordine i nodi da 0 a 1000 si ottiene un albero a
 vente altezza pari a 24 contro un minimo di 10."
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 lberi sfruttando ricorsivamente il partizionamento tramite l'ele
 mento di mezzo."
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    .STR
     "Chiaramente ^oi una soluzione applicabile a quei casi in cui si
  pu^pc fermare la baracca e compiere detta operazione che ^oi ch
 iaramente onerosa. "
    .STR
     "\nNel caso di situazioni in cui non posso fermarmi non ^oi appl
 icabile."
    .STR
     "\nPrendere tree.c e commentare tree_balance "
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 ttoalberi della radice sono a loro volta bilanciati e la loro di
 fferenza in altezza non ^oi, in valore assoluto superiore a 1."
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    .STR
     "Illustrare la tecnica di crescita degli alberi bilanciati."
    .STR
     "\nPer esempio:March, May, November, August, April, January, Dec
 ember, July, February, June, October, e September."
    .STR
     "\nIl trucco consiste nell'indicare presso ogni nodo la differen
 za di altezza tra i relativi sottoalberi, riorganizzare quando u
 na di questye diventa 2 tutta la catena che porta alla nuova fog
 lia"
    .STR
     "\nIn pratica si ottengono mediante 4 rotazioni doppie, DD, SS, 
 SD, DS"
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 ciati."
   .STR
    "\nIl problema si nota anche quando salvo su file le strutture a
 d albero, dato che le percorro in un certo ordine il problema ^o
 i che probabilmente le salver^pc anche in ordine..."
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   "Tramite 4 tipi di rotazione ^oi possibile raggiungere il bilanc
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    .STR
     "Ho inserito F devo ribilanciare da B a F "
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     "\nperch^oj da B?"
    .STR
     "\nMa perch^oj  ^oi il nodo pi^pj basso in cui ho il delta tra l
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    .STR
     "In genere i dati sono abbastanza ordinati e questo ha il suo pe
 so!"
    .STR
     "\nLa maggioranza delle operazioni ^oi O(H) e quindi anche se sp
 endo pi^pj tempo a inserire e cancellare guadagno in generale."
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 bile mediante l'attraversamento di uno degli alberi da unire e l
 'inserimento dei nodi visitati nell'altro."
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    .STR
     "Il problema ^oi che occorre verificare la presenza di chiavi du
 plicate."
    .STR
     "\nPrendere tree.c e commentare tree_join"
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   "Gli alberi 2-3-4 sono alberi di ricerca NON binari in cui abbia
 mo la presenza di 3 tipi differenti di nodo:"
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   "nodi di tipo 2: sono gli stessi visti fino ad ora;"
  .STR
   "\nnodi di tipo 3: hanno due chiavi e 3 figli, i valori delle ch
 iavi dei sottoalberi sono suddivisi in funzione degli intervalli
  identificati dalle due chiavi del nodo;"
  .STR
   "\nnodi di tipo 4: hanno 3 chiavi e 4 figli, analogamente ai nod
 i di tipo 3 le chiavi mi identificano degli intervalli per i val
 ori delle chiavi dei sottoalberi."
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    .STR
     "Il motivo della loro esistenza ^oi che ^oi semplice ottenere al
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    .STR
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    .STR
     "\n  miedati dati;"
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     "\n  ...."
    .STR
     "\n  struct nodo *sinistra;"
    .STR
     "\n  struct nodo *destra;"
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     "\n  char colore_sinistra;"
    .STR
     "\n  char colore_destra;"
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 "
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  .STR
   BOLD ON
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  .STR
   BOLD OFF
   ": immissione di identificatori differenti nello stesso bucket "
  .STR
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  .STR
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   "overflow"
  .STR
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   "mid-square (centro del quadrato)"
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 o i bit centrali del risultato (il numero di bucket deve essere 
 una potenza di 2) "
  .STR
   "\n"
  .STR
   BOLD ON
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  .STR
   BOLD OFF
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 uno specifico numero M (in genere numero primo e numero di bucke
 t) "
  .STR
   "\n"
  .STR
   BOLD ON
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  .STR
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     "In quaeto caso abbiamo due esempi distinti di funzioni di hash:
 "
    .STR
     "\nuna che si comporta ragionevolmente ed un'altra che si comopo
 rta decisamente male!"
    .STR
     "\nIl tutto ^oi derivato da hashw.c analizzando un file contenen
 te le parole dei promessi sposi (circa 223000) e 1016 bucket."
    .STR
     "\nNel caso specifico pur avendo tanti bucket la funzione di has
 h mi infila i valori in circa 150 NON utilizzando i restanti!"
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   "Supponiamo di voler inserire l'identificatore x nella tabella d
 i hash. \nQuattro possibili casi:"
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   "il bucket contiene gi^oa x "
  .STR
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   "\nil bucket ^oi vuoto "
  .STR
   PARA <-500 500 -500 1 1000 31 2 51>
   "\n"
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  .STR
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   "\n"
  .STR
   "il bucket contiene "
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   "gi^oa un identificativo differente"
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   "Qualora il numero di elementi di pertinenza di un bucket ^oi su
 periore al numero di slot ho una situazione di overflow.\nDue so
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   "Indirizzamento lineare aperto o sondaggio lineare (e varianti) 
 \nconcatenamento"
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  .STR
   L_SPACE 611
   "Quando il bucket contiene gi^oa identificativi differenti (ed ^
 oi pieno) scorro i bucket successivi fino a quando non trovo uno
  slot libero. \nProblema: deterioramento delle prestazioni (clus
 ter di identificatori)."
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    H_SPACE 6981
    .STR
     "Purtroppo (come mostra l'esempio visto in precedenza) gli ident
 ificativi tendono ad accumularsi (formano dei cluster) e questo 
 penalizza il tutto."
    .STR
     "\nSi pu^pc ovviare mediante sondaggio quadratico in cui scelgo 
 il bucket successivo spostandomi da f(x) a (f(x) + o - i^^2)%b c
 on 1<=i<=(b-1)/2 (b numero dei bucket, preferibilmente numero pr
 imo)."
    .STR
     "\nNel caso del re-hashing riutilizzo una formula di hashing."
    .STR
     "\nNel caso del sondaggio casuale una volta che riempo un bucket
  genero un numero a caso s e vado a cercare in f(x)+s"
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   L_SPACE 611
   "Il sondaggio lineare e le sue varianti sono facilmente implemen
 tabili MA hanno prestazioni modeste! \n \nLa tecnica del concate
 namento prevede l'utilizzo di un numero di slot variabile median
 te l'utilizzo di catene di slot."
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    .STR
     "Ripetere il discorso sul fatto che sia statico o meno."
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   " \nTipico dei DBMS.\n^mi utilizzato nei seguenti casi: "
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   L_SPACE 444
   "elevata densit^oa di identificatori \nnecessit^oa di gestire ri
 cerche su tipologie di identificatori differenti \ngestione di u
 na elevata mole di dati"
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    .STR
     "DBMS Data Base Management System"
    .STR
     "\nQuando ho un notevole numero di tipologie di identificatori s
 u cui fare operazioni di ricerca l'hashing statico non si riesce
  ad utilizzre poich^oj dovrei tenere in memoria un sacco di tabe
 lle."
    .STR
     "\nAnalogamente l'hashing statico non ^oi particolarmente effici
 ente in quei casi in cui la mole di dati varia nel tempo"
    .STR
     "\n"
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   "Nell'hashing dinamico si sfruttano particolare strutture ad alb
 ero dette "
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   ITALICS ON
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  .STR
   ITALICS OFF
   ":"
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     "In pratica, mediante hashing ottengo un numerello che espresso 
 in binario mi permette di navigare nell'albero fino al raggiungi
 mento del mio valore. Praticamente ^oi un incrocio tra utilizzo 
 degli alberi, hashing e catene."
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     "\nQualora il numero di identificatori mi porti ad overflow poss
 o aggiungere bit al risultato al fine di far crescere l'albero"
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     "\nOvviamente valgono tutti i soliti discorsi sugli alberi, bila
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     "Sul libro ponti di k^pgnigsberg.  Il percorso esiste se e solo 
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    .STR
     "\nIl numero totale di lati ^oi ricavabile in O(n+2l)"
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    .STR
     "\nDisegnare entrambe."
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    .STR
     "Risparmio spazio!"
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END NOTES

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 LAYOUT_ID <3 1 2 12 2>
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PICTURE
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 RECOLOR ON
 TEMPLATE_FLAGS <1 0 0 0>
 T_POS <282 240 10221 2146>
 .TXT AT (2854,390)
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   "I grafi\nattraversamento"
.TMP AT (282,2584)
 RECOLOR ON
 TEMPLATE_FLAGS <1 6 0 0>
 T_POS <282 2584 10221 5030>
 .TXT AT (317,2780)
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  .STR
   L_SPACE 611
   "Come per gli alberi l'operazione pi^pj comune ^oi l'attraversam
 ento. Ci limiteremo al caso della rappresentazione mediante list
 e concatenate. Due metodi:"
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 T_POS <282 5280 10221 7726>
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  .STR
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   "in profondit^oa ("
  .STR
   ITALICS ON
   "depth first"
  .STR
   ITALICS OFF
   ");"
  .STR
   "\nin ampiezza ("
  .STR
   ITALICS ON
   "breadth first"
  .STR
   ITALICS OFF
   ");"
END PICTURE
NOTES
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END NOTES

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 LAYOUT_ID <3 1 2 12 2>
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 RECOLOR ON
 TEMPLATE_FLAGS <1 0 0 0>
 T_POS <282 240 10221 2146>
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  .STR
   "I grafi\nvisita in profondit^oa"
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 RECOLOR ON
 TEMPLATE_FLAGS <1 6 0 0>
 T_POS <282 2584 10221 5030>
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  .STR
   L_SPACE 611
   "Ricorsivamente visitiamo i vertici adiacenti a quelli adiacenti
  al vertice iniziale marcando che li abbiamo visitati:"
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 RECOLOR ON
 TEMPLATE_FLAGS <2 7 0 0>
 T_POS <221 4263 10160 6709>
 .TXT AT (2484,3532)
  RECOLOR ON
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   "\nchar visitato[MAX_VERTICI];"
  .STR
   "\nvoid rpr(int v){"
  .STR
   "\n   node_pointer w;"
  .STR
   "\n"
  .STR
   "\n   visitato[v]=1;"
  .STR
   "\n   printf(\"visitato: %d\\n\",v);"
  .STR
   "\n   for(w=grafo[v]; w; w=w->link)"
  .STR
   "\n      if(!visitato[w->vertice])"
  .STR
   "\n         rpr(w->vertice);"
  .STR
   "\n}"
  .STR
   "\n"
END PICTURE
NOTES
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    .STR
     "Mi sembra evidente che funziona se il grafo ^oi connesso!"
    .STR
     "\n^mi simile alla visita peorder di un albero."
    .STR
     "\nNel caso delle liste di adiacenza la complessit^oa ^oi O(l) p
 oich^oj marchiamo la visita. Nel caso delle matrici la complessi
 t^oa ^oi O(n2) (O(n) ^oi la complessit^oa necessaria per determi
 nare i nodi adiacenti ad un nodo e ne dobbiamo considerare n!)."
 END .GRP
END NOTES

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 LAYOUT_ID <7 1 2 2 2>
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PICTURE
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 RECOLOR ON
 TEMPLATE_FLAGS <1 0 0 0>
 T_POS <282 240 10221 2146>
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   "I grafi\nvisita in ampiezza"
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 RECOLOR ON
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  .STR
   L_SPACE 611
   "In questo caso prima visitiamo tutti i vertici adiacenti a quel
 lo iniziale e successivamente prendiamo in esame i vertici adiac
 enti a questi (ci dobbiamo avvalere di una coda):"
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 RECOLOR ON
 TEMPLATE_FLAGS <2 10 0 0>
 T_POS <282 5280 5127 7726>
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   L_SPACE 444
   "void ram(int v){"
  .STR
   "\n   node_pointer w;"
  .STR
   "\n   coda_pointer davanti=NULL, dietro=NULL;"
  .STR
   "\n   printf(\"visitato %d\\n\", v);"
  .STR
   "\n   visitato[v]=1;"
  .STR
   "\n   add_queue(&davanti, &dietro, v);"
  .STR
   "\n   while(davanti){"
  .STR
   "\n      v=delete_queue(&davanti);"
  .STR
   "\n  "
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 T_PNTS (0,241)(0,0)(4571,0)(4571,3697)(0,3697)(0,241)(4571,241)
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 .STR
  L_SPACE 444
  "    for(w=grafo[v]; w; w=w->link)"
 .STR
  "\n         if(!visitato[w->vertice]) {"
 .STR
  "\n            printf(\"visitato %d\\n\", w->vertice);"
 .STR
  "\n            add_queue(&davanti, &dietro, w->vertice);"
 .STR
  "\n            visitato[w->vertice]=1;"
 .STR
  "\n         }"
 .STR
  "\n      }"
 .STR
  "\n}"
END PICTURE
NOTES
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    .STR
     "Ogni vertice viene posto nella coda una singola volta la comple
 ssit^oa ^oi quindi la somma su n vertici del numero di lati inci
 denti -> O(n) per le liste di adiacenza."
    .STR
     "\nRimane O(n2) per le matrici di adiacenza."
    .STR
     "\nDal punto di vista della complessit^oa ^oi equivalente alla p
 recedente."
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END NOTES

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 TEMPLATE_FLAGS <1 0 0 0>
 T_POS <282 240 10221 2146>
 .TXT AT (2019,390)
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  .STR
   "I grafi\ncomponenti connesse"
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 RECOLOR ON
 TEMPLATE_FLAGS <1 6 0 0>
 T_POS <282 2584 10221 5030>
 .TXT AT (174,2512)
  RECOLOR ON
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  .STR
   L_SPACE 611
   "Le funzioni viste precedentemente possono essere agevolmente us
 ate per determinare se un grafo ^oi connesso o comunque la compo
 nente connessa di un determinato vertice:"
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 RECOLOR ON
 TEMPLATE_FLAGS <2 7 0 0>
 T_POS <282 3634 10221 7727>
 .TXT AT (1453,3711)
  RECOLOR ON
  TEMPLATED ON
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  .STR
   L_SPACE 444
   "void connessa(void){"
  .STR
   "\n   int i;"
  .STR
   "\n"
  .STR
   "\n   for(i=0; i<n; ++i)"
  .STR
   "\n      if(!visitato[i]){"
  .STR
   "\n          printf(\"Componente connessa di %d:, i);"
  .STR
   "\n          rpr(i); /* oppure ram(i) */"
  .STR
   "\n      }"
  .STR
   "\n}"
END PICTURE
NOTES
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    .STR
     "Alberi derivati partendo dal nodo 0."
    .STR
     "\nL'insieme dei lati che non fanno parte degli alberi derivati 
 prende il nome di coalbero. In realt^oa non ^oi n^oj un albero n
 ^oj un grafo."
    .STR
     "\nEsempi di applicazione: circuito -> albero derivato -> per og
 ni lato del coalbero si crea una maglia -> seconda legge di Kirc
 hoff -> le mshlie s^om ottenute sono indipendenti -> l'insieme d
 elle equazioni ^oi una base per il circuito."
    .STR
     "\nTelecomunicazioni -> calcolo dei collegamenti minimi."
    .STR
     "\nIn realt^oa le cose sono pi^pj complesse. "
    .STR
     "\n"
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   " un nodo di un grafo connesso non orientato tale che la sua eli
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     "In molte applicazioni i punti di articolazione non sono graditi
  -> reti di telecomunicazioni."
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  .STR
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 n "
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   UNDERLINE OFF
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    .STR
     "Ritorniamo all'esempio visto in precedenza (campo metric)."
    .STR
     "\nCome si trovano gli alberi derivati di costo minimo ?"
    .STR
     "\nTre possibilit^oa algoritmi di Kruskal, Sollin e Prim."
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   "Si parte da un vertice e si aggiungono lati e nodi al vertice i
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   "T = {}"
  .STR
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   "; /* insieme lati */"
  .STR
   "\n"
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   "TV = {0}"
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   "; /* vertice iniziale */"
  .STR
   "\nwhile("
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   "T"
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   ITALICS OFF
   " contiene meno di "
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   " lati){"
  .STR
   "\n  sia "
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  .STR
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   "u"
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   " contiene meno di "
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   "n-1"
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   " lati)"
  .STR
   "\n  Non esiste albero derivato!"
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    .STR
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    .STR
     "\nESERCIZIO in laboratorio."
    .STR
     "\nAttenzione occorre far si che il peso sia memorizzato da qual
 che parte!"
    .STR
     "\nESERCIZI:"
    .STR
     "\ndato un file del tipo:"
    .STR
     "\n20 1 34 5 28 6"
    .STR
     "\n45 3 34 2 56 3"
    .STR
     "\n23 0"
    .STR
     "\n45 0"
    .STR
     "\n23 4"
    .STR
     "\n23 3 45 6"
    .STR
     "\n1 1"
    .STR
     "\nleggerlo, memorizzarlo in un grafo con pesi, calcolare l'albe
 ro derivato a partire da un nodo inserito, e (per i pi^pj volent
 erosi) implementare l'algoritmo di Primm. "
 END .GRP
END NOTES

*END GRAPHICS