FUNDAMENTELE PROGRAMĂRII
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1 UNIVERSIAEA BABEŞ-BOLYAI utt Mtmtă ş Ifmtă UNDAMENELE ROGRAMĂRII pbm Lu Dş
2 Dmb, Cțut us gmmg t g Itu î psu t sftw gm puă gm muă pu ft utt p t sftuu st ș spt pgm gmmg t sm Rustt Cmpxtt gtm Agtm ăut Agtm st Mt pbm Rptu
3 Dmb, Sum R pbm pu pbm R pbm s xt ust Bktkg D t mp
4 Dmb, bm pg Î fuț stutuă C pt f smpus î sub-pbm Căut uu mt ît-u t C u pt f smpus Amps g p tbă ș Î fuț umău suț Cu sguă suț St uu t Cu m mut suț G pmută
5 Dmb, bm pg Î fuț psbtăț Rb î m tmst Cuu susuu uu ug su ăă pătt t-u umă Rb î m stst (ust) bm um ă pt uu ABS supu ăut u suţ
6 Dmb, bm pg Î fuț mpxtt tmpă ă bm s b î tmp pm ( 2, 3,...) stă bm s N b î tmp pm (2,!,,..) C m sut um ît-u gf ș
7 Dmb, bm pg Î fuț sp bm ăut/ptm tă f, pt stţ m ş bm m ţ, sfă bm smu tă m ş ju m tă m ş
8 Dmb, R pbm Cstă î tf u suţ Î fmtă ps ăut Î g ş mtmtă ps ptm Cum? Rpt suţ (pţ) put î spţu ăut t u pt ăut tsfmă psbă suţ î tă suţ
9 Dmb, ş î pbm Df pbm A pbm Ag u t ăut pt uştţ bstt
10 Dmb, ş î pbm p ăut Ag u t R p ut gu (î mbţ u sttg t) ps î spţu pbm pâă găs uu um ît st ţă ş fă R p ăut Exm sstmtă stă psb î tfă uu um st ţă st fă u stă ptm Spţu stă = tt stă psb + pt fs gătu ît stă
11 Dmb, ş î pbm p ăut Ag u t R p ăut Sttg ăut mutp um gm sttg? Cmpxtt mputţă (tmpă ş spţă) Cmpttu gtmu s sfâşşt îttu ş găsşt suţ (ă xstă) Optmtt gtmu găsşt suţ ptmă (stu ptm umuu st ţă st fă)
12 Dmb, ş î pbm p ăut Ag u t R p ăut Sttg ăut mutp um gm sttg? Cmpxtt mputţă (tmpă ş spţă) fmţ sttg p : mpu s uă t t Spţu (mm) să uă Măm tă gtmuu Vt utuu t xt Ctt mptuu S măsă u jutu mpxtăţ Efţă mputţă Spţă mm să tfă suţ S() ttt mm uttă m bu gtm A p pbmă f u t t mpă tmpu s tfă suţ () tmpu u (umău pş) u m bu gtm A ă pbmă f u t t
13 Dmb, ş î pbm p ăut Ag u t R pbm p ăut pt st î: Cstu pgsă suţ Itf suţ ptţ ptm
14 Dmb, ş î pbm p ăut Ag u t R pbm p mt s Mt xt Mt gă ș tstă bktkg Mt ă -> D t Imp Mt pgmă m Mt ust Mt gy
15 Dmb, Gă ș tstă I bă G u psb suț ș f ttu Căut xustă Msm G: tm tutu suț psb st: ăut suț sut t (sptă umt ț) Câ s pt fs bm pt m mut suț bm u stâg ( ă suț tbu să spt umt ț)
16 Dmb, Gă ș tstă Agtm #D = D(D1) = D(D1(D2))... f gt_tst(d): w (u): s = gt_sut() f (tst(s) == u): tu s
17 Dmb, Gă ș tstă Exmp G pmută u =3 mt f pmut3(): f g(1,4): f j g(1,4): f k g(1, 4): #gt pssbsut = [,j,k] #tst f ((!= j) (j!= k) (k!= )): y pssbsut f mut3(): f p pmut3(): pt(p) A mpxtăț Numău suț psb: 3 3, ă [1, 2, 3] [1, 3, 2] [2, 1, 3] [2, 3, 1] [3, 1, 2] [3, 2, 1] stt
18 Dmb, Gă ș tstă Agtm Aăug ț g u suț u s m xpă tt suț psb s stus suț (pț) t sptă umt ț Bktkg #D = D(D1) = D(D1(D2))... f gt_tst(d): w (u): s = gt_sut_() f (tst(s) == u): tu s Spțu ăut u suț s st S (mu fț) O suț st fmtă m mut mt (s[0], s[1], s[2],...) uț t gă uă ptu mu fț suț uț gtnxt tuă susu ( mu fț) uu mt suț uț scsstt fă ă suț (pță) st tă uț ssut fă ă suț (pță) st suț fă (mptă) pbm
19 Dmb, Gă ș tstă Exmp f t(): tu 0 G pmută u =3 mt f gtnxt(s, ps): tu s[ps] + 1 Bktkg - tă ttă f scsstt(s): scs = u = 0 w ((<(s)-1) (scs==u)): f (s[] == s[(s) - 1]): scs = s s: = + 1 tu scs f ssut(sut, ): tu (sut) == f pmut_bk(): k = 0; sut = [] tvu = t() sut.pp(tvu) w (k>= 0): sst = s w ((sst==s) (sut[k]<gtlst())): sut[k] = gtnxt(sut, k) sst = scsstt(sut) f (sst == u): f (ssut(sut,) == u): y sut s: k = k + 1 sut.pp(t()) s: (sut[k]) k = k 1 f mut(): f p pmut_bk(3): pt(p) mut()
20 Dmb, Gă ș tstă Exmp f t(): tu 0 G pmută u =3 mt f gtnxt(s, ps): tu s[ps] + 1 Bktkg - tă usă f scsstt(s): scs = u = 0 w ((<(s)-1) (scs==u)): f (s[] == s[(s) - 1]): scs = s s: = + 1 tu scs f ssut(sut, ): tu (sut) == f pmut_bk_(, sut): tvu = t() sut.pp(tvu) m = gtnxt(sut, (sut) - 1) w (m <= ): sut[(sut) - 1] = m f (scsstt(sut) == u): f (ssut(sut, ) == u): y sut s: y fm pmut_bk_(, sut[:]) m = gtnxt(sut, (sut) - 1) f mut(): f p pmut_bk_(3, []): pt(p) mut()
21 Dmb, Gă ș tstă Exmp Bktkg A mpxtăț stt
22 Dmb, 2017 Gă ș tstă Exmp G tuu m ubu u s ăstă â spț ubu Bktkg - tă ttă ubs = [10, 2, 5, 6, 7] f t(): tu 0 f gtnxt(s, ps): tu s[ps] + 1 f gtlst(): tu f scsstt(s): scs = u; = 0 w ((<(s)-1) (scs==u)): f (s[] == s[(s) - 1]): scs = s s: = + 1 f ((s) > 1): f (ubs[s[(s) - 1] - 1] > ubs[s[(s) - 2] - 1]): tu s tu scs f ssut(sut, ): tu (sut) == f pt_s(sut): tw = [] f s sut: tw.pp(ubs[s - 1]) pt(tw) f tws(, m): k = 0 sut = [] tvu = t() sut.pp(tvu) w (k>= 0): sst = s w ((sst == s) (sut[k] < gtlst())): sut[k] = gtnxt(sut, k) sst = scsstt(sut) f (sst == u): f (ssut(sut,m) == u): y sut s: k = k + 1 sut.pp(t()) s: (sut[k]) k = k - 1 f t tws((ubs), 4): pt_s(t) 22
23 Dmb, D t mp I bă Dsmpu pbm î sub-pbm pt ș sm pbm ț, msu m m, sub-pbm ș stb suț f p mb sub-suț Msm D: împăț pbm î sub-pbm Cqu: sub-pbm Cmb: mb sub-suț ptu bț suț f Câ s pt fs bm â t t D pt f tă p ș pbm, u t t, u < D
24 Dmb, D t mp Agtm #D = 1 U 2 U 3...U f _mp(d): f (s(d) < m): tu 1 = _mp(1) 2 = _mp(2)... = _mp() tu mb(1, 2,..., )
25 Dmb, D t mp Exmp Să s găssă mtu mxm t- stă S(pbm) = Vsu 1... S(sub-pbm1) = -1 S(sub-pbm2) = ă: (2) D = = [1,2,..,], 1 = [2,..,], 2 = [3,..,],... 1, 1 ( ) ( 1) 1, tf ( ) ( 1) 1 ( 1) ( 2) 1 (1) 1 ( ) O( ) f fmx(): ''' s: fs t mxmu m f st t: st s: t mxm m f st ''' f (() == 1): tu [0] mx = fmx([1:]) f (mx > [0]): tu mx s: tu [0] f tst_fmx(): sst fmx([2,5,3,6,1]) == 6 sst fmx([12,5,3,2,1]) == 12 sst fmx([2,5,3,6,11]) == 11 tst_fmx()
26 Dmb, 2017 D t mp Exmp Să s găssă mtu mxm t- stă S(pbm) = Vsu 2 2 2* ( S(sub-pbm1) = /2 S(sub-pbm2) = /2 ă: 2 2 * (2 * (2) ( ) ( ) 2 D = = [1,2,..,], 1 = [1,..,/2], 2 = [/2+1,..,] 1, ( ) 2* ( / 2) 1, k 1 k k g k (2 ) 2* (2 k-1 2 ) 2 * (2 k-2 k 2 k-1 3 ) 2 * (2 k ) 1 k-2 0 k * (2 ) ) 2 k-2 tf ) 2 1 (2 k 1 * O( ) k 2 1) /(2 1) f fmx_2(): ''' s: fs t mxmu m f st t: st s: t mxm m f st ''' f (() == 1): tu [0] m = () // 2 mx_ft = fmx_2([0:m]) mx_gt = fmx_2([m:()]) f (mx_ft < mx_gt): tu mx_gt s: tu mx_ft f tst_fmx_2(): sst fmx_2([2,5,3,6,1]) == 6 sst fmx_2([12,5,3,2,1]) == 12 sst fmx_2([2,5,3,6,11]) == 11 tst_fmx_2() 26
27 Dmb, Rptu Gă ș tstă xust Bktkg D t mp
28 Dmb, Cusu umăt gmmg t g Itu î psu t sftw gm puă gm muă pu ft utt p t sftuu st ș spt pgm gmmg t sm Rustt Cmpxtt gtm Agtm ăut Agtm st Mt pbm Rptu
29 Dmb, Mt tt ş gătu ut 1. Lmbju yt ttp://s.pyt.g/3/f/x.tm 2. Bbt st yt ttp://s.pyt.g/3/by/x.tm 3. ut yt ttp://s.pyt.g/3/tut/x.tm 4. tu, M., H.. p, umts f gmmg, Cuj Usty ss, 2006, 220 pg 5. Kt Bk.st D Dpmt: By Exmp. As- Wsy Lgm, 2002 ttp://.wkp.g/wk/st-_pmt 6. Mt w. Rftg. Impg t Dsg f Exstg C. As-Wsy, 1999 ttp://ftg.m/tg/x.tm
30 Dmb, Ifmţ ptt u fst tt ft sus p tt, pum ş usu umt gmă ţut î t ăt: Lt. D. A Gu f. D. Ist Cbu - Cf. D. A Vs - Lt. D. I Lă - Lt. D. M Atu
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More informationAvailable online Journal of Scientific and Engineering Research, 2016, 3(6): Research Article
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