Arranjaments - Vera Sacrist´ an Geometria Computacional...

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Unformatted text preview: Vera Sacrist´ an Geometria Computacional Facultat d’Inform` atica de Barcelona Universitat Polit` ecnica de Catalunya ARRANJAMENTS ARRANJAMENTS Geometria Computacional, Facultat d’Inform` atica de Barcelona, UPC Sigui R = { r 1 , . . . , r n } un con- junt finit de rectes del pla. DEFINICI ´ O ARRANJAMENTS Geometria Computacional, Facultat d’Inform` atica de Barcelona, UPC Sigui R = { r 1 , . . . , r n } un con- junt finit de rectes del pla. DEFINICI ´ O L’ arranjament A ( R ) ´ es la des- composici´ o del pla en cares , arestes i v` ertexs indu¨ ıda per R . ARRANJAMENTS Geometria Computacional, Facultat d’Inform` atica de Barcelona, UPC Sigui R = { r 1 , . . . , r n } un con- junt finit de rectes del pla. DEFINICI ´ O L’ arranjament A ( R ) ´ es la des- composici´ o del pla en cares , arestes i v` ertexs indu¨ ıda per R . L’arranjament A ( R ) s’anome- na simple si R no cont´ e dues rectes paral . leles ni cont´ e tres rectes que passin per un mateix punt. ARRANJAMENTS Geometria Computacional, Facultat d’Inform` atica de Barcelona, UPC COMPLEXITAT La complexitat (combinat` oria) d’un arranjament A ( R ) ´ es el nombre de cares, arestes i v` ertexs de l’arranjament. La complexitat d’ A ( R ) ´ es O ( n 2 ) , on n = # R . Concre- tament: • v ≤ n ( n- 1) 2 • a ≤ n 2 • c ≤ n 2 2 + n 2 + 1 Aquestes fites s’assoleixen quan l’arranjament ´ es simple. ARRANJAMENTS Geometria Computacional, Facultat d’Inform` atica de Barcelona, UPC COMPLEXITAT La complexitat (combinat` oria) d’un arranjament A ( R ) ´ es el nombre de cares, arestes i v` ertexs de l’arranjament. La complexitat d’ A ( R ) ´ es O ( n 2 ) , on n = # R . Concre- tament: • v ≤ n ( n- 1) 2 • a ≤ n 2 • c ≤ n 2 2 + n 2 + 1 Aquestes fites s’assoleixen quan l’arranjament ´ es simple. n = 5 ARRANJAMENTS Geometria Computacional, Facultat d’Inform` atica de Barcelona, UPC COMPLEXITAT La complexitat (combinat` oria) d’un arranjament A ( R ) ´ es el nombre de cares, arestes i v` ertexs de l’arranjament. La complexitat d’ A ( R ) ´ es O ( n 2 ) , on n = # R . Concre- tament: • v ≤ n ( n- 1) 2 • a ≤ n 2 • c ≤ n 2 2 + n 2 + 1 Aquestes fites s’assoleixen quan l’arranjament ´ es simple. v = 10 n = 5 ARRANJAMENTS Geometria Computacional, Facultat d’Inform` atica de Barcelona, UPC COMPLEXITAT La complexitat (combinat` oria) d’un arranjament A ( R ) ´ es el nombre de cares, arestes i v` ertexs de l’arranjament. La complexitat d’ A ( R ) ´ es O ( n 2 ) , on n = # R . Concre- tament: • v ≤ n ( n- 1) 2 • a ≤ n 2 • c ≤ n 2 2 + n 2 + 1 Aquestes fites s’assoleixen quan l’arranjament ´ es simple....
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This note was uploaded on 04/01/2011 for the course MA GEOC taught by Professor Julianpleife during the Spring '11 term at Universitat Politècnica de Catalunya.

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Arranjaments - Vera Sacrist´ an Geometria Computacional...

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