›—30 œ‘—œ‘ 1.3

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  1. 1. 30 1: 1.3:
  2. 2. . . 1. 2 , 30, 1.3: 1. 1. 2. 3. 4. 5. 2. 3. 3. .
  3. 3. . : 3 , 30, 1.3: ( )
  4. 4. . 1. 4 , 30, 1.3: ,,,, . f(n) g(n). : f=o(g) , f g fg
  5. 5. . 1. 1. 5 , 30, 1.3: , f=O(g), : fg. : : n0, f(n) cg(n) c. ))(()( ngOnf = )()(0:0,00 ngcnfcn >> 0nn H f(n)=O(g(n)) f g
  6. 6. . 1. 1. 6 , 30, 1.3: : 1 1 : 2n=O(n3) : f(n)=2n, g(n)=n3 n0=1, c=2. 3 22 )()( nn ncgnf n1 2 1 n
  7. 7. . 1. 2. o 7 , 30, 1.3: , f=(g), : f 0nn n=O(n) no(n) n=o(n2) n=o(n3) ... c>0.
  8. 8. . 1. 2. o 8 , 30, 1.3: : 2 2 : 2n=(n2) : c>0: nc cn cnn ncgnf < < < < /2 2 2 )()( 2 n0 nc 2 c/2
  9. 9. . 1. 4. 9 , 30, 1.3: , f=(g), : fg. : : n0, f(n) cg(n) c. ))(()( ngnf = 0)()(:0,00 >> ngcnfcn 0nn H f(n)=(g(n)) f g
  10. 10. . 1. 4. 10 , 30, 1.3: : 3 3 : 4n=(logn) : f(n)=4n, g(n)=logn n0=1, c=4. nn ncgnf log44 )()( n1 nn log
  11. 11. . 1. 5. 11 , 30, 1.3: , f=(g), : f>g. : : c f(n) cg(n) n0 H f(n)=(g(n)) f g !! n=(n) ))(()( ngnf = 0)()(::0 0 >> ngcnfnc 0nn n=(n) n(n) n=(logn) n=(loglogn) ... c>0.
  12. 12. . 1. 5. 12 , 30, 1.3: : 4 4 : 0.5n2=(n) : c>0: c n cnn ncgnf 5.0 5.0 )()( 2 > > > > n0 cn 2> c2
  13. 13. . 1. 5. 13 , 30, 1.3: , f=(g), f=g. : : n0, f(n) g(n), : ))(()( ngnf = )()()(0:0,,0 21210 ngcnfngcccn > 0nn H f(n)=(g(n)) f g
  14. 14. . 1. 5. 14 , 30, 1.3: : 5 5 : 4n=(n) : f(n)=4n, g(n)=n n0=1, c1=2. 24 24 )()( 1 nn ngcnf n1 n0=1, c2=6. n1 24 64 64 )()( nn ncgnf
  15. 15. 2 : . 2. 15 , 30, 1.3: : , : ( ) =+ = = = + ))(()(, ))(()(,0 ))(()(,0 )( )( lim ngnf ngonf ngnfc ng nf n ( ) :
  16. 16. . 2. 16 , 30, 1.3: : 6 6 : 0.5n2=(n) : 0.5n2=(n) +=== +++ )5.0(lim 5.0 lim )( )( lim 2 n n n ng nf nnn 6 6 : 2n=o(3n) : 2n=o(3n) 0)66.0(lim 3 2 lim 3 2 lim )( )( lim == == ++++ n n n nn n nn ng nf
  17. 17. . 3. 17 , 30, 1.3: :: : f=g fg fg : fg fg ( ) 3: ))(()( ngnf = ))(()( ngnf =
  18. 18. . 4. 18 , 30, 1.3: O(n2): : : 1=O(n2) n+2=O(n2) logn=O(n2) logn+5loglogn=O(n2) 3n2=O(n2) O(n2) n2. n2. O(n2) : . )(2 )(1 2 2 nOn nO +
  19. 19. . 1 f g f 19 , 30, 1.3: f g. f(n) g(n) o O n2 n3 n1.5 n 4logn 8logn 5n2 0.5n2 .. 1 , n2=o(n3) 5n2 0.5n2 n3-5n 8logn
  20. 20. . 2 f g 3 20 , 30, 1.3: 3 f g g(n)=5 g(n)=logn g(n)=n2 g(n)=2n g(n)=5n g(n)=nn f(n)=loglogn f(n)=4logn f(n)=n f(n)=2n2 .. 1 loglogn=(1) f(n)=2n f(n)=6n5+n f(n)=3n f(n)=n!
  21. 21. . 1 , : 21 , 30, 1.3: : )(.6 )3(2.5 )(46.4 )(loglog.3 )(4.2 )log(.1 2 2 22 nn o nn nn nnn nnOn n nn = = =+ = =+ = )(.6 nn =
  22. 22. . 2 , : 22 , 30, 1.3: )(.6 )3(2.5 )(46.4 )(loglog.3 )(4.2 )log(.1 2 2 22 nn o nn nn nnn nnOn n nn = = =+ = =+ = )(.6 nn =