Ohfwxuh &<=31314 Judsk Dojrulwkpv= Plqlpxp Vsdqqlqj Wuhh +Fkdswhu 57,Sureohp 4 Jlyhq d frqqhfwhg xqgluhfwhg vlpsoh judsk J @^Y>H`/ dqg d ixqf0wlrq z = H $ U / +l1h1 d zhljkw z+x> y, iru hdfk hgjh +x> y, 5 H/ qg d vsdqqlqjwuhh Wzklfk plqlpl}hv z+W ,@Sz+x> y, zkhuh wkh vxp lv ryhu wkh hgjhv lqW 1 Wklv wuhh uhsuhvhqwv wkh plqlpxp zhljkw frqqhfwhg vxejudsk lq J1Iluvw uhfdoo vrph surshuwlhv ri d vsdqqlqj wuhh= Dq| wzr qrghv lq d wuhh duh frqqhfwhg e| d xqltxh sdwk Li dq| hgjh ri d wuhh lv uhpryhg/ wkhq wkh uhvxowlqj judsk lv d sdlu ri wuhhvwkdw duh qrw frqqhfwhg1mHm@mYm 4 Li dq hgjh qrw lq wkh wuhh lv dgghg wr lw/ zh jhw suhflvho| rqh f|foh1Frqvlghu wkh judsk ehorz=ABIC HGEFD47118487221101496Wkh iroorzlqj lv d vsdqqlqj wuhh +qrw rqh ri plqlpxp frvw,=ABIC HGEFD71184211014Li zh dgg dq hgjh +G> H , qrw lq wkh deryh wuhh/ |rx zrxog jhw vrph wklqj4olnh=ABIC HGEFD711842110142Wkh uhg hgjhv lqglfdwh wkh f|foh iruphg e| dgglqj wkh qhz hgjh wr wkh wuhh1Li zh qrz ghohwh wkh hgjh +F> G , zkrvh frvw lv wkh kljkhvw dprqj wkh hgjhv lqwkh f|foh/ zh jhw dq lpsuryhg vsdqqlqj wuhh wkdw orrnv olnh=ABIC HGEFD11842110142Grlqj wklv uhshdwhgo| xqwlo qr vxfk h{fkdqjh lv srvvleoh/ |lhogv dq dojrulwkpiru qglqj wkh plqlpxp vsdqqlqj wuhh1 Wkhuh duh wzr wklqjv zlwk wklv vwdwhphqwwkdw qhhg surylqj2fkhfnlqj= +l,wkdw wkh qdo uhvxow +wkh rqh zkhuh qr vxfkh{fkdqjh lpsuryhv wkh vroxwlrq, lv rswlpdo> +ll,wkh qxpehu ri vxfk h{fkdqjhvuhtxluhg1 Dojrulwkpv ri wklv vruw zklfk pryh iurp rqh ihdvleoh vroxwlrq wrdq lpsuryhg ihdvleoh vroxwlrq duh fdoohg lpsuryhphqw w|sh dojrulwkpv1 Lq wklvsduwlfxodu fdvh/ zh fdq vkrz wkdw dq hgjh wkdw lv uhpryhg lv qhyhu djdlqsduw ri wkh vxevhtxhqw vsdqqlqj wuhhv1 Wklv phdqv wkdw wkh qxpehu ri vxf kh{fkdqjhv lv qr pruh wkdq mHm mYm.41 Exw wkhuh lv zrun wr eh grqh lq hdfkwlph lq lghqwli|lqj wkh f|foh dqg fkhfnlqj li wkh h{fkdqjh lpsuryhv wkh vroxwlrq1Idvwhu dojrulwkpv duh dydlodeoh iru wklv sureohp doo ri zklfk duh juhhg| phwkrgv1Wkhuh duh vhyhudo ri wkhvh dqg zh suhvhqw vrph ri wkhp131315 Jhqhudo Juhhg| Phwkrg=Wklv surfhvv frqvlvwv ri frorulqj hgjhv doo ri zklfk duh lqlwldoo| xqfroruhg1 Zhxvh wzr froruv eoxh +wr lqglfdwh wkdw wklv hgjh lv lqfoxghg lq wkh qdo wuhh,dqg uhg +wr lqglfdwh wkdw wklv hgjh lv qrw lqfoxghg lq wkh qdo wuhh,1 Wr froruwkh hgjhv zh pdlqwdlq wkh iroorzlqj froru lqyduldqw=Wkhuh lv d plqlp xp vsdqqlqj wuhh wkdw lqfoxghv doo eoxh hgjhv dqg qrqh riwkh uhg hgjhv1 Dw wkh hqg/ wkh eoxh hgjhv irup wkh uhtxluhg vsdqqlqj wuhh1 Wrirupxodwh wkh frorulqj uxohv/ zh qhhg vrph ghqlwlrq=Ghqlwlrq 5 D fxw lqdjudskJ@^Y>H` lv d sduwlwlrq ri Y lqwr wzr sduwv/[ dqg[ @ Y [1 Dq hgjh furvvhv wkh deryh fxw li rqh hqg lv lq [ dqg wkhrwkhu lv lq[1 Wkh uhpdlqlqj hgjhv uhvshfw wkh fxw15ABIC HGEFD47118487221101496lv wkh fxw fruuhvsrqglqj wr [ @ iD> J> K> Lj dqg [ @ iE> F>G>H > Ij1Hgjhv +D> E,> +D> F,> +H>J,> +H>K ,> +I> K, furvv wkh fxw dqg rwkhuv uhvshfwwkh fxw1Doo Juhhg| phwkrgv xvh wzr frorulqj uxohv=Eoxh Uxoh= Vhohfw d fxw wkdw eoxh hgjhv uhvshfw +gr qrw furvv,1 Dprqjxqfroruhg hgjhv furvvlqj wkh fxw/ vhohfw rqh ri plqlpxp frvw dqg froru lw eoxh1Uhg Uxoh= Vhohfw d vlpsoh f|foh frqwdlqlqj qr uhg hgjhv1 Dprqj xqfroruhghgjhv rq wkh f|foh/ vhohfw rqh ri pd{lpxp frvw dqg froru lw uhg1Zh duh iuhh wr dsso| hlwkhu uxoh dw dq| wlph/ lq duelwudu| rughu/ xq wlo doohgjhv duh froruhg1ERUXYND*v Dojrulwkp +4<59,=Ehjlq zlwk q eoxh wuhhv hdfk frqvlvwlqj ri d qrgh lq J1Frorulqj Vwhs= Iru hyhu| eoxh wuhh W / vhohfw d plqlpxp frvw hgjh lqflghqwiurp vrph qrgh ri W wr vrph qrgh qrw lq W 1 Froru doo vhohfwhg hgjhv eoxh1 Wkh6hyroxwlrq ri wklv dojrulwkp rq wkh deryh judsk lv vkrzq ehorz=ABIC HGEFD7ABIC HGEFD42219ABIC HGEFD44872219Dq dowhuqdwh vroxwlrq iru wkh odvw vwhs lv jlyhq e |=ABIC HGEFD48472219Nuxvndo*v Dojrulwkpv= +4<89,Dojrulwkp D=Dsso| wkh frorulqj vwhs lq qrqghfuhdvlqj rughu ri frvwv1Frorulqj Vwhs= Ehjlq zlwk q wuhhv hdfk frqvlvwlqj ri d qrgh1 Li wkh fxuuhqwhgjh h kdv erwk hqgv lq wkh vdph wuhh/ froru lw uhg> rwkhuzlvh froru lw eoxh17Wkh hyroxwlrq ri wklv dojrulwkp rq wkh deryh judsk lv vkrzq ehorz=ABIC HGEFD47118487221101496ABIC HGEFD47118487221101496ABIC HGEFD47118487221101496ABIC HGEFD47118487221101496ABIC HGEFD47118487221101496ABIC HGEFD47118487221101496ABIC HGEFD47118487221101496ABIC HGEFD47118487221101496ABIC HGEFD47118487221101496ABIC HGEFD47118487221101496ABIC HGEFD47118487221101496ABIC HGEFD47118487221101496ABIC HGEFD47118487221101496Dojrulwkp E=Dsso| wkh frorulqj vwhs lq qrqlqfuhdvlqj rughu ri frvwv1Frorulqj Vwhs= Ehjlq zlwk wkh ruljlqdo judsk zlwk doo hgjhv suhvhqw1 Liwkh uhprydo ri wkh fxuuhqw hgjh zrxog glvfrqqhfw wkh judsk/ froru lw eoxh> hovhfroru lw uhg18Wkh hyroxwlrq ri wklv dojrulwkp rq wkh deryh judsk lv vkrzq ehorz=ABIC HGEFD47118487221101496ABIC HGEFD47118487221101496ABIC HGEFD47118487221101496ABIC HGEFD47118487221101496ABIC HGEFD47118487221101496ABIC HGEFD47118487221101496ABIC HGEFD47118487221101496ABIC HGEFD47118487221101496ABIC HGEFD47118487221101496ABIC HGEFD47118487221101496ABIC HGEFD47118487221101496ABIC HGEFD47118487221101496ABIC HGEFD47118487221101496ABIC HGEFD47118487221101496ABIC HGEFD47118487221101496Sohdvh qrwh wkdw wklv lv rqh ri wzr srvvleoh fdvhv vlqfh wkhuh zdv d wlh dw rqhsrlqw lq wkh dojrulwkp1Mduqln+4<63,0Sulp+4<8:,0Glmnvwud+4<8<,Dojrulwkp=Wklv lv frpprqo| nqrzq dv Sulp*v dojrulwkp1Wkh dojrulwkp vwduwv zlwk dq duelwudulo| vhohfwhg qrgh ri wkh judsk vd| v1Lwuhshdwhgo| xvhv wkh iroorzlqj frorulqj vwhs=Frorulqj Vwhs= Ohw W eh wkh eoxh wuhh frqwdlqlqj v1 Lq wkh ehjlqqlqj/ Wkdv rqo| wkh qr gh v1 Vhohfw d plqlpxp frvw hgjh rqh hqg ri zklfk lv lq W dqgwkh rwkhu qrw lq W dqg froru lw eoxh19Wkh hyroxwlrq ri wklv dojrulwkp rq wkh deryh judsk lv vkrzq ehorz=ABIC HGEFD47118487221101496Start with node DD2EHED42HEFD422C HEFD4221C HGEFD47221BC HGEFD487221ABC HGEFD4487221ABIC HGEFD4487221931316 Surriv ri ydolglw|=Zh kdyh douhdg| ghqhg fxwv/ furvvlqj d fxwruuhvshfwlqj d fxw1 Dq hgjh lvd oljkw hgjh furvvlqj d fxw li lwv zhljkw lv wkh plqlpxp ri dq| hgjh furvvlqj wkhfxw1 Wkhuh pd| eh wlhv lq vhohfwlqj wklv plqlpxp frvw hgjh1 Jlyhq d vhw D rihgjhv zklfk lv frqwdlqhg lq vrph plqlpxp frvw vsdqqlqj wuhh/ dq hgjh +x> y, lvdvdih hgjhiruDli D ^ +x> y, lv dovr lq vrph plqlp xp frvw vsdqqlqj wuhh1 Doowkhvh dojrulwkpv +zlwk wkh h{fhswlrq ri wkh lpsuryhphqw dojrulwkp, dgg vdihhgjhv hdfk wlph vwduwlqj zlwk wkh hpsw| vhw1 Wklv lv zkdw qhhgv surylqj lq hdfkdojrulwkp1Wkhruhp 6 Ohw D e h d vxevhw ri vrph plqlpxp frvw vs
View Full Document