UNIVESITATEA BABEŞ-BOLYAI d M ş If UNDAMENTELE OGAMĂII L Dş
Nb, 2017 2 gg h g Id î d dz fw g d g d T df d z d dz f T ș g gg h g Ag d Ag d Md d z b
Nb, 2017 3 S d bz M E Aj ș dzj D? E Az f g
Nb, 2017 4 d bz E E dfș îș Sb-g Sb-g -z Ob O d -- d ș d d SA1 z SA1 d SA1 z SA2, SA2 z SA1
Nb, 2017 5 E! = * (-1)! = * ( 1) * ( 2)! =... 1, 0 f( ) df f(): * f( 1), f! d: g : g 1 * 2 * 3 *... * f ( == 0): 1 : * f( - 1) df (): f(5) == 120 f(4) == 24 f(1) == 1 f(0) == 1 ()
Nb, 2017 6 M dz bg z b d d 1 d Sb d d df ( b d d 1) 2 d D b b z E. O b (d d -1) b E. 2 b (d d 1, 2,.î. 1 + 2 = -1) b df (): h f f d: f g : f f (() == 0): 0 : #() > 0 [0] + ([1:]) df S(): ([1,2,3,4]) == 10 ([]) == 0 ([3]) == 3 S() df d(): h d f f d: f g : d f f (() == 0): 1 : #() > 0 dd = () // 2 d([0:dd]) * [dd] * d([dd+1:]) df d(): d([1,2,3,4]) == 24 d([]) == 1 d([1,2,3,4,5]) == 120 d([2]) == 2 d()
Nb, 2017 7 M L f bg z b d b bg b Tb d b hz î- âd d b d b z df d(): hk f g d d: g :, f d d f, hw d = () (d(d), " ", d) f (() <= 1): T : [0]==[-1] d d([1:-1]) df Id(): d("bb") == T d("bb") == T d("bdb") == Id() df bg(, ): hk f bg d: g d f g :, f d f, hw d = () (d(d), " ", d) f ( == []): : f ( == [0]): T : bg(, [1:]) df Bg(): bg(5, []) == bg(5, [5,2,6,3]) == T bg(5, [1,2,5,4,3]) == T bg(5, [6,2,5]) == T bg(5, [1,2,3]) == Bg()
Nb, 2017 8 Aj d f Dzj d f dâ L f - z b d b
Nb, 2017 9 N b î- S g b-b 2 b-b BUNĂ? Ef g g bz T f z d (z d ) dd d: - d d ( ș ) - df f d - hdw- f M d
Nb, 2017 E b (g d ) = -1 + -2, 0 = 1 =1 df fb_(): h b b d: g : fb b f 1 = 1 2 = 1 fb = 0 f g(2, + 1): fb = 1 + 2 1 = 2 2 = fb fb df fb_(): h b b d: g : fb b f f ( <= 1): 1 : fb_(-1)+fb_(-2) df b(): _ =.() ("g bb_(",, ") = ", fb_()) d_ =.() (" k ", d_ - _, " d") _ =.() ("g bb_(",, ") = ", fb_()) d_ =.() (" k ", d_ - _, " d ) b(23) g bb_( 23 ) = 46368 k 0.0 d g bb_( 23 ) = 46368 k 0.015000104904174805 d 10
Nb, 2017 11 Az f g Ef bg N d ( ș ) f M f: Az bd f d b N f d Az N z f g d d d d d d d T d dz î â g d ș d d d d d (f) d g
Nb, 2017 12 T d N E f T() dd d ș d d ( = z(i)) S ș d bz ( d ) f d g
Nb, 2017 13 b z (z fb b ) d d d g g f f d z (w ) d d d g g f d z d (g ) Ud: d d g ( d d ) g B( A) E ( I) ID W( A) E ( I) I f d d A g D A = d d ( d d g) I d d g E A (I) d f d g A âd d d I A (I) bb g A d d I A ID A ( A) ( I) E ( I) D A A A A A A
Nb, 2017 14 E df OfNb(): h f f b d: b : h f f b = 0 f g(1, + 1): = + B W Ag T() 1 1 1 1 1 1
Nb, 2017 ()= T() B = [0] 1 W Ag E = [-1] = [0] = [1] = [2]... = [-1] 1 1 0 0 1 11 1 df h(, ): hk f bg d: g d f g :, f bg f, hw f g(0, ()): f ([] == ): T 1 2 3... +1 -------- (1+2+..++(+1))/(+1)=(+2)/2
Nb, 2017 16 I d? Sb d d f d E. 4 g d z 1 z 2 1 2 5 T1 ( ) 1 2 2 T ( ) 1 2 T ( ) 3 T ( ) 4 T 1 () > T 2 (), =>g 2 f g 1 T 1 ()>T 3 (), <5 d 2 d 1 d 2 d 1 T 1 ()<=T 3 (), >= 5 2 =>g 3 f g 1 f d z
Nb, 2017 17 E f f:n-> d T:N->N, b d d f T? T()ϵO(f()) d 2, z ș dd d, ș 0 f îâ 0 T() *f() 0 O(f()) - f d d g d d f() E O(1): 4, 1, 100, 55 O(): 3+10, 100, 2-1, 3 O( 2 ): 2 2 +3+1, 5 2-1, 3+10, 7 T ( ) D T() ϵo(f()) ( ) f ( )
Nb, 2017 18 z T() ϵ O(1) d f b (df d â d b, g d ș) E. A î-, df f î- b T() ϵ O(g(g())) T d g-g f b ( f ) E. H- b T() ϵ O(g()) T d g f b E. b, î b b hb
Nb, 2017 19 z T() ϵ O() T d b E. / î- d T() ϵ O(g()) T d b E. S d (MgS, QkS) T() ϵ O( 2 ) T d qd b d d d, d b âd d d E. S (BbbS) T() ϵ O(2 ) T d b E. z b j
Nb, 2017 20 E d z df OfNb(): h f f b d: b : h f f b = 0 f g(1, + 1): = + df _(): OfNb(5) == 15 OfNb(1) == 1 B W Ag T() 1 1 1 1 1 1 O O()
Nb, 2017 21 E d z df OfNb(): h f f b d: b : h f f b = 0 = 1 wh (<=): = + = + 1 df _(): OfNb(5) == 15 OfNb(1) == 1 B W Ag T() 1 1 1 1 1 1 O O()
Nb, 2017 22 E d z df he(): hk f b d: f g :, f b f, hw = 0 wh (( < ()) d ([] % 2!= 0)): = + 1 ( < ()) df _he(): he([2,4,6]) == T he([1,3,5]) == he([1,2,3]) == T B W Ag O T() 1 O() 11 1 2 11 2 ( 1 2 3... ) / ( 1) / 2
Nb, 2017 E d z df OfEM(): = 0 f g(0, ()): f j g(0, ([])): = + [][j] df _OfEM(): OfEM([[1,2],[4,5],[7,9]]) == 28 OfEM([[1,2,3],[4,5,6],[7,8,9]]) == 45 B W Ag T() 1 j1 1 j1 1 j1 1 * 1 * 1 * O O( 2 ) 23
Nb, 2017 24 E d z Bk: df (f,,, ): f. = f.ah = f.h = df gah(f): f.h df hbkofaah(bk, h): = [] f b bk: h = b.gah() = 0 wh ( < (h)): f (h[] == h):.d(b) = (h) : = + 1 df _hbkofaah(): b1 = Bk("1", 2, ["h1", "h2"]) b2 = Bk("2", 3, ["h2", "h3", "h4"]) b3 = Bk("3", 1, ["h4"]) bk = [b1, b2, b3] hbkofaah(bk, ") == [] hbkofaah(bk, "h5") == [] hbkofaah(bk, "h1") == [b1] hbkofaah(bk, "h2") == [b1, b2] hbkofaah(bk, "h4") == [b2, b3] B W Ag T() O O( 2 ) 1 1 1 j1 1 1 * * - d d d
Nb, 2017 25 E d z df (): h f f d: f g : f f (() == 0): 0 : #() > 0 [0] + ([1:]) df S(): ([1,2,3,4]) == 10 ([]) == 0 ([3]) == 3 T ( ) T( T ( ) T ( 1) T ( 2)... T (1) T ( ) 1, d 0-1) 1, f T ( 1) 1 T ( 2) 1 T ( 3) 1... T (0) 1 1
Nb, 2017 26 Ez ( d ) () g -ș d d, d ș, ș d ș d
Nb, 2017 27 E df Ay_1(): = [] = ((" = ")) f g(0, ): = ((" = ")).d() = [0] f g(1, ): f ([] < ): = [] (" " + ()) df Ay_2(): = ((" = ")) = ((" = ")) f g(1, ): = ((" = ")) f ( < ): = (" " + ()) S() = 1 + + 1 = + 2 S() = 1 + 1 + 1 = 3
Nb, 2017 28 E df Ay_1(): = [] = ((" = ")) f g(0, ): = ((" = ")).d() = [0] f g(1, ): f ([] < ): = [] (" " + ()) df Ay_2(): = ((" = ")) = ((" = ")) f g(1, ): = ((" = ")) f ( < ): = (" " + ()) S() = 1 + + 1 = + 2 ϵ O() S() = 1 + 1 + 1 = 3 ϵ O(1)
Nb, 2017 29 T Ag d d E d bz M E Aj ș dzj D? E Az f g
Nb, 2017 30 gg h g Id î d dz fw g d g d T df d z d dz f T ș g gg h g Ag d Ag d Md d z b
Nb, 2017 31 M d ş g 1. Lbj yh h://d.yh.g/3/f/d.h 2. Bb dd yh h://d.yh.g/3/by/d.h 3. T yh h://d.yh.g/3//d.h 4., M., H.., d f gg, j Uy, 2006, 220 g 5. K Bk.T D D: By E. Add- Wy Lg, 2002 h://.wkd.g/wk/t-d_d 6. M w. fg. Ig h Dg f Eg d. Add-Wy, 1999 h://fg./g/d.h
Nb, 2017 32 Ifţ z f d df d, ş d d d g ţ î d : L. D. Ad G www..bbj./~d f. D. I zb - www..bbj./~ f. D. Ad V -www..bbj./~ L. D. I Lz -www..bbj./~z L. D. M Ah www..bbj./~h