^bag 2
KBOG@H\B C@VXCXWXG DJ XGFO@DMDAS Kbmmbsbkuhrbk (wgst),@bkbee (w gst),@bkbeebm. bm.
HG^B\XKG@X DJ FDK^WXG\ VFCG@FG B@H G@AC@GG\C@A
MBLD\BXD\S KB@WBM
AG?2:2 ‖ ^\DLMGK ^\DLMGK VDMZC@A B@H ^SXOD@ ^\DA\BKKC@A MBLD\BXD\S @BKG
9…………………………………………………………….
SGB\
9……………………………………………………………
VGK
9…………………………………………………………….
HG^X
9……………………………………………………………
^\G^B\GH LS Kr.L.KDOB@\BI, B^/FVG, .
^bag 2
^bag <
MCVX DJ G_^G\CKG@XV9 G_^G\CKG@XV9 2.Fdkputg tog AFH dj twd `uklgrs. <. Jc`h tog squbrg rddt dj b `uklgr (@gwtd` –s kgtodh) 6. Gxpd`g`tcbtcd` (pdwgr dj b `uklgr) 8. Jc`h tog kbxckuk dj b mcst dj `uklgrs 7. Mc`gbr sgbrfo b`h Lc`bry sgbrfo :. Vgmgftcd` sdrt, C`sgrtcd` sdrt 1. Kgrag sdrt ?. Jcrst ` prckg `uklgrs ` uklgrs 3. Kumtcpmy kbtrcfgs 2>. ^rdarbks tobt tbeg fdkkb`h mc`g braukg`ts (wdrh fdu`t) 22. Jc`h tog kdst jrgqug`t wdrhs c` b tgxt rgbh jrdk b jcmg 2<. Vckumbtg gmmcptcfbm drlcts c` ^yabkg ^yab kg 26.Vckumbtg ldu`fc`a lbmm c` ^yabkg
^bag <
^bag 6
AG ?2:2 ‖ ^\DLMGK ^\DLMGK VDMZC@A B@H ^SXOD@ ^\DA\BKKC@A MBLD\BXD\S FD@XG@XV
Vm.@d.
@bkg dj tog dj tog Gxpgrckg`t
2
Fdkputg tog AFH dj twd dj twd `uklgrs.
<
Jc`h tog squbrg rddt dj b dj b `uklgr (@gwtd` `uklgr (@gwtd` –s kgtodh)
6
Gxpd`g`tcbtcd` (pdwgr dj (pdwgr dj bb `uklgr)
8
Jc`h tog kbxckuk dj b dj b mcst dj `uklgrs dj `uklgrs
7(b)
Mc`gbr sgbrfo Mc`gbr sgbrfo
7(l)
Lc`bry sgbrfo
:(b)
Vgmgftcd` sdrt
:(l)
C`sgrtcd` sdrt
1
Kgrag sdrt
?
Jcrst ` prckg `uklgrs
3
Kumtcpmy kbtrcfgs
2>
^rdarbks tobt tbeg fdkkb`h mc`g braukg`ts (wdrh fdu`t)
22
Jc`h tog kdst jrgqug`t wdrhs c` b tgxt rgbh jrdk b jcmg
2<
Vckumbtg gmmcptcfbm drlcts c` ^yabkg
26
Vckumbtg ldu`fc`a lbmm c` ^yabkg
Vca`
^bag 6
^bag 8 Gx. @d. 9>2 AFH DJ XQD @WKLG\V
Hbtg9
Bck9
Xd wrctg b ^ytod` prdarbk td jc`h AFH dj twd dj twd `uklgrs. Bmadrctok9 2. Hgjc`g b ju`ftcd` `bkgh fdkputgAFH() <. Jc`h tog skbmmgst bkd`a tog twd c`puts x b`h y 6. ^grjdrk tog jdmmdwc`a stgp tcmm skbmmgr+2
Fogfe cj ((x cj ((x % c ;; >) b`h (y % c ;; >)), tog` bssca` AFH;c 8. ^rc`t tog vbmug dj afh dj afh ^rdarbk9
hgj fdkputgAFH(x, y)9 cj x 0 y9 skbmmgr ; y gmsg9 skbmmgr ; x jdr c c` rb`ag(2, skbmmgr+2)9 cj((x % c ;; >) b`h (y % c ;; >))9 afh ; c rgtur` afh `uk2 ; c`t(c`put("G`tgr jcrst `uklgr9 ")) `uk< ; c`t(c`put("G`tgr sgfd`h `uklgr9 ")) prc`t("Xog AFH. dj", `uk2,"b`h", `uk<,"cs", fdkputgAFH(`uk2, `uk<))
^bag 8
^bag 7
Vbkpmg dutput 9 G`tgr jcrst `uklgr9 78 G`tgr sgfd`h `uklgr9 <8 Xog AFH dj 78 b`h <8 cs :
\gsumt9
Xous tog ^ytod` prdarbk td fdkputg AFH dj twd dj twd `uklgrs cs gxgfutgh suffgssjummy b`h tog dutput cs vgrcjcgh.
^bag 7
^bag : Gx. @d. 9>< VRWB\G \DDX DJ B @WKLG\
Hbtg9
Bck9
Xd wrctg b ^ytod` ^rdarbk td jc`h tog squbrg rddt dj b dj b `uklgr ly `uklgr ly @gwtd` –s Kgtodh. Bmadrctok9
2. Hgjc`g b ju`ftcd` `bkgh `gwtd`Vqrt(). <. C`ctcbmczg bpprdx bs >.7*` b`h lgttgr bs lgttgr bs >.7*(bpprdx.+`/bpprdx.) 6. Wsg b wocmg mddp wcto b fd`hctcd` lgttgr!;bpprdx td pgrjdrk tog jdmmdwc`a, c. Vgt bpprdx.;lgttgr cc. Lgttgr;>.7*(bpprdx.+`/bpprdx.) 8. ^rc`t tog vbmug dj bpprdx dj bpprdx ^rdarbk9
hgj `gwtd`Vqrt(`)9 bpprdx ; >.7 * ` lgttgr ; >.7 * (bpprdx + `/bpprdx) wocmg lgttgr !; bpprdx 9 bpprdx ; lgttgr lgttgr ; >.7 * (bpprdx + `/bpprdx) rgtur` bpprdx `uk2 ; c`t(c`put("G`tgr `uklgr9 ")) prc`t("Xog squbrg rddt cs" ,`gwtd`Vqrt(`uk2)) ,`gwtd`Vqrt(`uk2))
^bag :
^bag 1
Dutput9
G`tgr `uklgr9 ?2
Xog squbrg rddt cs 3.>
\gsumt9 Xous tog ^ytod` prdarbk jdr jc`hc`a tog squ brg rddt dj b acvg` `uklgr ly l y @gwtd`–s Kgtodh cs gxgfutgh suffgssjummy b`h tog dutput cs vgrcjcgh.
^bag 1
^bag ? Gx. @d. 9 >6 G_^D@G@XCBXCD@ DJ B @WKLG\
Hbtg9
Bck9
Xd wrctg b ^ytod` prdarbk td jc`h tog gxpd`g`tcbtcd` dj b dj b `uklgr. Bmadrctok9
2.
Hgjc`g b ju`ftcd` `bkgh pdwgr()
dj lbsg b`h gxp <. \gbh tog vbmugs dj lbsg cj gxp cs gqubm td 2 6. Wsg ‟cj– td fogfe cj gxp dr `dt dr `dt c. cj gxp cj gxp cs gqubm td 2, tog` rgtur` lbsg cc.cj gxp cc.cj gxp cs `dt gqubm td 2, tog` rgtur` (lbsg*pdwgr(lbsg,gxp-2)) 8. ^rc`t tog rgsumt
^rdarbk9
hgj pdwgr(lbsg,gxp)9 cj(gxp;;2)9 rgtur`(lbsg) cj(gxp!;2)9 rgtur`(lbsg*pdwgr(lbsg,gxp-2)) lbsg;c`t(c`put("G`tgr lbsg9 ")) gxp;c`t(c`put("G`tgr gxpd`g`tcbm vbmug9 ")) prc`t("\gsumt9",pdwgr(lbsg,gxp) prc`t("\gsumt9",pdwgr( lbsg,gxp) )
^bag ?
^bag 3
Dutput9
G`tgr lbsg9 G`tgr lbsg9 1 G`tgr gxpd`g`tcbm G`tgr gxpd`g`tcbm vbmug9 < \gsumt983
\gsumt9
Xous tog ^ytod` prdarbk td jc`h tog gxpd`g`tcbtcd` dj b dj b `uklgr cs `uklgr cs gxgfutgh suffgssjummy b`h tog dutput cs vgrcjcgh.
^bag 3
^bag 2> ^bag 2> Gx. @d. 9 >8
JC@HC@A KB_CKWK J\DK B MCVX DJ @WKLG\V
Hbtg9
Bck9
Xd wrctg b ^ytod` ^rdarbk td jc`h tog kbxckuk jrdk b mcst dj `uklgrs. dj `uklgrs. Bmadrctok9 2. Frgbtg b` gkpty mcst `bkgh m <. \gbh tog vbmug dj ` dj `
6. \gbh tog gmgkg`ts dj tog dj tog mcst u`tcm ` 8. Bssca` mU>[ bs kbx`d 7. Cj mUc[0kbx`d Cj mUc[0kbx`d tog` sgt kbx`d;mUc[ :. C`frgkg`t c ly 2 1. \gpgbt stgps 7-: u`tcm c=` ?. ^rc`t tog vbmug dj kbxckuk dj kbxckuk `uklgr ^rdarbk9
m;U [ `;c`t(c`put("g`tgr tog uppgr mckct")) jdr c c` rb`ag(>,`)9 b;c`t(c`put("g`tgr tog `uklgrs")) m.bppg`h(b) kbx`d;mU>[ jdr c c` rb`ag(>,mg`(m))9 cj mUc[0kbx`d9 kbx`d;mUc[ prc`t("Xog kbxckuk `uklgr cs %h" %kbx`d)
^bag 22 ^bag 22
Dutput92
g`tgr tog uppgr mckct 6 g`tgr tog `uklgrs 2< g`tgr tog `uklgrs <7 g`tgr tog `uklgrs 87 Xog kbxckuk `uklgr cs 87 Dutput <9
g`tgr tog uppgr mckct 6 g`tgr tog `uklgrs 27 g`tgr tog `uklgrs <7 g`tgr tog `uklgrs > Xog kbxckuk `uklgr cs <7
\gsumt9
Xous b ^ytod` ^rdarbk td jc`h tog kbxckuk jrdk tog acvg` mcst dj `uklgrs dj `uklgrs cs suffgssjummy gxgfutgh b`h tog dutput cs vgrcjcgh.
^bag 2< ^bag 2<
Gx. @d. 9 7(b) MC@GB\ VGB\FO
Hbtg9 Bck9
Xd wrctg b ^ytod` ^rdarbk td pgrjdrk Mc`gbr Vgbrfo Mc`gbr Vgbrfo Bmadrctok9
2. \gbh ` gmgkg`ts c`td tog mcst <. \gbh tog gmgkg`t td lg sgbrfogh 6. Cj bmcstUpds[;;ctgk, Cj bmcstUpds[;;ctgk, tog` prc`t tog pdsctcd` dj tog dj tog ctgk 8. Gmsg c`frgkg`t tog pdsctcd` b`h rgpgbt stgp 6 u`tcm pds rgbfogs tog mg`ato dj tog dj tog mcst ^rdarbk9
hgj sgbrfo(bmcst,ctgk)9 pds;> jdu`h;Jbmsg stdp;Jbmsg wocmg pds=mg`(bmcst) b`h `dt jdu`h b`h `dt stdp9 cj bmcstUpds[;;ctgk9 jdu`h;Xrug prc`t("gmgkg`t prc`t("gmgkg`t jdu`h c` pdsctcd`",pds) gmsg9 cj bmcstUpds[0ctgk9 stdp;Xrug gmsg9 pds;pds+2 rgtur` jdu`h b;U[ `;c`t(c`put("g`tgr uppgr mckct")) jdr c c` rb`ag(>,`)9 g;c`t(c`put("g`tgr tog gmgkg`ts")) b.bppg`h(g) x;c`t(c`put("g`tgr gmgkg`t td sgbrfo")) sgbrfo(b,x)
^bag 26 ^bag 26
Dutput9
G`tgr uppgr G`tgr uppgr mckct mckct 7 G`tgr tog G`tgr tog gmgkg`ts : G`tgr tog G`tgr tog gmgkg`ts 87 G`tgr tog G`tgr tog gmgkg`ts < G`tgr tog G`tgr tog gmgkg`ts :2 G`tgr tog G`tgr tog gmgkg`ts <: G`tgr gmgkg`t G`tgr gmgkg`t td sgbrfo : Gmgkg`t jdu`h c` pdsctcd` 2
\gsumt9
Xous tog ^ytod` ^rdarbk td pgrjdrk mc`gbr sgbrfo mc`gbr sgbrfo cs gxgfutgh suffgssjummy b`h tog dutput cs vgrcjcgh.
^bag 28 ^bag 28 G_. @d. 9 7(l) LC@B\S VGB\FO
Hbtg9
Bck9
Xd wrctg b ^ytod` ^rdarbk td pgrjdrk lc`bry sgbrfo. Bmadrctok9
2.\gbh tog sgbrfo gmgkg`t <.Jc`h tog kchhmg gmgkg`t c` tog sdrtgh mcst 6.Fdkpbrg tog sgbrfo gmgkg`t wcto tog kchhmg gmgkg`t c. cj ldto cj ldto brg kbtfoc`a, prc`t gmgkg`t jdu`h cc. gmsg tog` fogfe cj tog cj tog sgbrfo gmgkg`t cs skbmmgr dr skbmmgr dr mbragr mbragr tob` tob` tog kchhmg gmgkg`t 8.Cj tog 8.Cj tog sgbrfo gmgkg`t cs skbmmgr tob` skbmmgr tob` tog kchhmg gmgkg`t, tog` rgpgbt stgps < b`h 6 jdr tog jdr tog mgjt sulmcst dj tog dj tog kchhmg gmgkg`t 7.Cj tog 7.Cj tog sgbrfo gmgkg`t cs mbragr tob` mbragr tob` tog kchhmg gmgkg`t, tog` rgpgbt stgps < b`h 6 jdr tog jdr tog rcaot sulmcst dj tog dj tog kchhmg gmgkg`t :.\gpgbt tog prdfgss u`tcm tog sgbrfo gmgkg`t cj jdu`h cj jdu`h c` tog mcst 1.Cj gmgkg`t 1.Cj gmgkg`t cs `dt jdu`h, mddp tgrkc`btgs
^bag 27 ^bag 27
^rdarbk9
hgj lc`bryTsdrt(sdrtghmcst,`,x)9 stbrt ; > g`h ; ` - 2 wocmg(stbrt =; g`h)9 kch ; (stbrt + g`h)/< cj (x ;; sdrtghmcstUkch[)9 rgtur` kch gmcj(x = sdrtghmcstUkch[)9 g`h ; kch - 2 gmsg9 stbrt ; kch + 2
rgtur` -2 ` ; c`put("G`tgr tog sczg dj tog mcst9 ") sdrtghmcst ; U[ jdr c c` rb`ag(`)9 sdrtghmcst.bppg`h(c`put("G`tgr sdrtghmcst.bppg`h(c`put(" G`tgr %hto gmgkg`t9 "%c)) x ; c`put("G`tgr tog `uklgr td sgbrfo9 ") pdsctcd` ; lc`bryTsdrt(sdrtghmcst, `, x) cj(pdsctcd` !; -2)9 prc`t("G`tgrgh `uklgr %h cs prgsg`t bt pdsctcd`9 %h"%(x,pdsctcd`))
gmsg9 prc`t("G`tgrgh `uklgr `uklgr %h cs `dt prgsg`t c` tog mcst"%x)
^bag 2: ^bag 2:
Dutput9
G`tgr tog sczg dj tog mcst9 7 G`tgr >to gmgkg`t9 68 G`tgr 2to gmgkg`t9 <8 G`tgr : G`tgr 8to gmgkg`t9 >< G`tgr tog `uklgr td sgbrfo9 28 G`tgrgh `uklgr 28 cs prgsg`t bt pdsctcd`9 <
\gsumt9
Xous tog ^ytod` ^rdarbk td pgrjdrk lc`bry sgbrfo cs gxgfutgh suffgssjummy b`h tog dutput cs vgrcjcgh
^bag 21 ^bag 21 Gx. @d. 9 :(b) VGMGFXCD@ VD\X
Hbtg9
Bck9
Xd wrctg b ^ytod` ^rdarbk td pgrjdrk sgmgftcd` sdrt. Bmadrctok9
2. Frgbtg b ju`ftcd` `bkgh sgmgftcd`sdrt <.
C`ctcbmcsg pds;>
6. Cj bmcstUmdfbtcd`[0bmcstUpds[ Cj bmcstUmdfbtcd`[0bmcstUpds[ tog` pgrjdrk tog jdmmdwc`a tcmm c+2, 8. Vgt pds;mdfbtcd` 7. Vwbp bmcstUc[ b`h bmcstUpds[ :. ^rc`t tog sdrtgh mcst ^rdarbk9
hgj sgmgftcd`Vdrt(bmcst)9 jdr c c` rb`ag(mg`(bmcst)-2,>,-2)9 pds;> jdr mdfbtcd` c` rb`ag(2,c+2)9 cj bmcstUmdfbtcd`[0bmcstUpds[9 pds; mdfbtcd` tgkp ; bmcstUc[ bmcstUc[ ; bmcstUpds[ bmcstUpds[ ; tgkp
bmcst ; U78,<:,36,21,11,62,88,77,<>[ sgmgftcd`Vdrt(bmcst) prc`t(bmcst)
^bag 2? ^bag 2?
Dutput9 U21, <>, <:, 62, 88, 78, 77, 11, 36[
\gsumt9
Xous tog ^ytod` ^rdarbk td pgrjdrk sgmgftcd` sdrt cs suffgssjummy gxgfutgh b`h tog dutput cs vgrcjcgh.
^bag 23 ^bag 23 Gx. @d. 9 :(l)
C@VG\XCD@ VD\X
Hbtg9
Bck9
Xd wrctg b ^ytod` ^rdarbk td pgrjdrk c`sgrtcd` sdrt. Bmadrctok9
2. Frgbtg b ju`ftcd` `bkgh c`sgrtcd`sdrt <. C`ctcbmcsg furrg`tvbmug;bmcstUc`hgx[ b`h pdsctcd`;c`hgx 6. wocmg pdsctcd`0> b`h bmcstUpdsctcd`-2[0furrg`tvbmug, pgrjdrk tog jdmmdwc`a tcmm mg`(bmcst) 8. bmcstUpdsctcd`[;bmcstUpdsctcd`-2[ 7.
pdsctcd` ; pdsctcd`-2
:.
bmcstUpdsctcd`[;furrg`tvbmug
1. ^rc`t tog sdrtgh mcst
^rdarbk9
hgj c`sgrtsdrt(sbkpmg)9 prc`t("c`tcbm sbkpmg9", sbkpmg) jdr c c` rb`ag(2, mg`(sbkpmg))9 prc`t(sbkpmg) i;c wocmg(i!;> b`h sbkpmgUi[ = sbkpmgUi-2[)9 sbkpmgUi-2[, sbkpmgUi[ ; sbkpmgUi[, sbkpmgUi-2[ i;i-2 prc`t("sdrtgh mcst9",sbkpmg) sbkpmg2 ; U2<,6>>,-3>,-2>>-2>>>,2,8[ c`sgrtsdrt(sbkpmg2)
^bag <> ^bag <>
Dutput9 (
'c`tcbm sbkpmg9', U2<, 6>>, -3>, -22>>, 2, 8[)
U2<, 6>>, -3>, -22>>, 2, 8[ U2<, 6>>, -3>, -22>>, 2, 8[ U-3>, 2<, 6>>, -22>>, 2, 8[ U-22>>, -3>, 2<, 6>>, 2, 8[ U-22>>, -3>, 2, 2<, 6>>, 8[ ('sdrtgh mcst9', U-22>>, -3>, 2, 8, 2<, 6>>[
\gsumt9
Xous tog ^ytod` prdarbk td pgrjdrk c`sgrtcd` sdrt cs suffgssjummy gxgfutgh b`h tog dutput cs vgrcjcgh.
^bag <2 ^bag <2 Gx. @d. 9 1
KG\AG VD\X
Hbtg9
Bck9
Xd wrctg b ^ytod` ^rdarbk td pgrjdrk Kgrag sdrt. Bmadrctok9
2. Frgbtg b ju`ftcd` `bkgh kgragsdrt <. Jc`h tog kch dj tog dj tog mcst 6. Bssca` mgjtobmj ; mgjtobmj ; bmcstU9kch[ b`h rcaotobmj ; rcaotobmj ; bmcstUkch9[ 8. C`ctcbmcsg c;i;e;> 7. wocmg c = mg`(mgjtobmj) b`h i b`h i = mg`(rcaotobmj), pgrjdrk tog jdmmdwc`a cj mgjtobmjUc[ cj mgjtobmjUc[ = rcaotobmjUi[9 bmcstUe[;mgjtobmjUc[ C`frgkg`t c gmsg bmcstUe[;rcaotobmjUi[ C`frgkg`t i C`frgkg`t i C`frgkg`t e :. wocmg c = mg`(mgjtobmj),pgrjdrk tog jdmmdwc`a bmcstUe[;mgjtobmjUc[ C`frgkg`t c C`frgkg`t e 1.
wocmg i wocmg i = mg`(rcaotobmj), pgrjdrk tog jdmmdwc`a bmcstUe[;rcaotobmjUi[ C`frgkg`t i C`frgkg`t i C`frgkg`t e
?. ^rc`t tog sdrtgh mcst
^bag << ^bag <<
^rdarbk9
hgj kgrag(mgjt,rcaot)9 rgsumt ; U[ c,i ; >, > wocmg c=mg`(mgjt) b`h i=mg`(rcaot)9 cj mgjtUc[ =; rcaotUi[9 rgsumt.bppg`h(mgjtUc[) c+;2 gmsg9 rgsumt.bppg`h(rcaotUi[) i+;2 rgsumt +; mgjtUc9[ rgsumt +; rcaotUi9[ rgtur` rgsumt hgj kgragsdrt(mst)9 cj(mg`(mst) =; 2)9 rgtur` mst kch ; c`t(mg`(mst)/<) mgjt ; kgragsdrt(mstU9kch[) rcaot ; kgragsdrt(mstUkch9[) rgtur` kgrag(mgjt,rcaot) brr ; U2,<,-2,>,3,:7,1,6,8,2,<[ prc`t(kgragsdrt(brr))
^bag <6 ^bag <6
Dutput9
U-2, >, 2, 2, <, <, 6, 8, 1, 3, :7[
\gsumt9
Xous tog ^ytod` prdarbk td pgrjdrk kgrag sdrt cs suffgssjummy gxgfutgh b`h tog dutput cs vgrcjcg
^bag <8 ^bag <8 Gx. @d. 9 ?
JC\VX @ ^\CKG @WKLG\V
Hbtg9
Bck9
Xd wrctg b ^ytod` prdarbk td jc`h jcrst ` prckg `uklgrs. Bmadrctok9
2. \gbh tog vbmug dj ` <. jdr `uk jdr `uk c` rb`ag(>,` + 2), pgrjdrk tog jdmmdwc`a 6. cj `uk%c cs > tog` lrgbe gmsg prc`t tog vbmug dj `uk dj `uk 8. \gpgbt stgp 6 jdr c jdr c c` rb`ag(<,`uk) ^rdarbk9
`;c`t(c`put("G`tgr tog uppgr cckct5")) prc`t("^rckg `uklgr brg")
jdr `uk c` rb`ag(>,`+2)9 # prckg `uklgr brg argbtgr tob` 2 cj `uk029 jdr c c` rb`ag(<,`uk)9 cj (`uk%c);;>9 lrgbe gmsg9 prc`t(`uk)
^bag <7 ^bag <7
Dutput9 G`tgr tog G`tgr tog uppgr mckct92>> uppgr mckct92>> ^rckg `uklgrs brg < 6 7 1 22 26 21 23 <6 <3 62 61 82 86 81 76 73 :2 :1 12 16 13 ?6 ?3 31
\gsumt9
Xous tog ^ytod` ^rdarbk td jc`h tog jcrst ` prckg `uklgrs cs gxgfutgh suffgssjummy b`h tog dutput cs vgrcjcgh.
^bag <: ^bag <:
Gx. @d. 9 3
KBX\C_ KWMXC^MCFBXCD@
Hbtg9
Bck9
Xd wrctg b ^ytod` prdarbk td kumtcpmy kbtrcfgs. Bmadrctok9
2. Hgjc`g twd kbtrcfgs _ b`h S <. Frgbtg b rgsumtb`t kbtrcx `bkgh ‟rgsumt– 6. jdr c jdr c c` rb`ag(mg`(_))9 c. jdr i i c` rb`ag(mg`(SU>[))9 b) jdr e jdr e c` rb`ag(mg`(S)) l) rgsumtUc[Ui[ +; _Uc[Ue[ * SUe[Ui[ 8. jdr r jdr r c` c` rgsumt, prc`t tog vbmug dj r dj r n^rdarbk9
_ ; UU2<,1,6[, U8 ,7,:[,U1 ,?,3[[ S ; UU7,?,2,<[, U:,1,6,>[, U8,7,3,2[[ rgsumt ; UU>,>,>,>[, U>,>,>,>[, U>,>,>,>[[ jdr c c` rb`ag(mg`(_))9 jdr i c` rb`ag(mg`(SU>[))9 jdr e c` rb`ag(mg`(S))9 rgsumtUc[Ui[ +; _Uc[Ue[ * SUe[Ui[ jdr r c` rgsumt9 prc`t(r)
^bag <1 ^bag <1
Dutput9
U228, 2:>, :>, <1[ U18, 31, 16, 28[ U223, 271, 22<, <6[
\gsumt9
Xous tog ^ytod` prdarbk td kumtcpmy kbtrcfgs cs gxgfutgh suffgssjummy b`h tog dutput cs vgrcjcgh.
^bag ^bag Gx. @d. 92> FDKKB@H MC@G B\AWKG@XV(QD\H FDW@X)
Hbtg9
Bck9
Xd wrctg b ^ytod` prdarbk jdr fdkkb`h jdr fdkkb`h mc`g braukg`ts. Bmadrctok9
2. Bhh braukg`ts td jc`h tog wdrhs b`h mc`gs <. Bhh tog jcmg`bkg bs braukg`t 6. ^brsg tog braukg`ts td agt tog vbmugs 8. Jdrkbt b`h prc`t tog wdrhs b`h mc`gs
^rdarbk9
pbrsgr;brapbrsg.Braukg`t^brsgr() pbrsgr.bhhTbraukg`t('--wdrhs','-w',bftcd`;'stdrgTtrug') pbrsgr.bhhTbraukg`t('--mc`gs','-m',bftcd`;'stdrgTtrug') pbrsgr.bhhTbraukg`t('jcmg`bkg') bras;pbrsgr.pbrsgTbras() cj bras.wdrhs9 cj bras.wdrhs9 prc`t("wdrhs {}".jdrkbt(prc`tTwdrhs(bras.jcmg`bkg)) gmcj bras.mc`gs9 gmcj bras.mc`gs9 prc`t("mc`gs {}".jdrkbt(prc`tTmc`gs(bras.jcmg`bkg)) gmsg9 prc`t ("wdrhs {}".jdrkbt(prc`tTwdrhs(bras.jcmg`bkg)) prc`t("mc`gs {}".jdrkbt(prc`tTmc`gs(bras.jcmg`bkg))
^bag <3 ^bag <3
Dutput9
pytod` kbc`.py ‖c c`put.txt wdrhs <6 mc`gs 2
\gsumt9
Xous tog ^ytod` prdarbk jdr fdkkb`h jdr fdkkb`h mc`g braukg`ts cs gxgfutgh suffgssjummy b`h tog dutput cs vgrcjcgh.
^bag 6> ^bag 6>
Gx. @d. 9 22 JC@HC@A KDVX J\GRWG@X QD\HV C@ B XG_X \GBH J\DK B JCMG
Hbtg9
Bck9
Xd wrctg b ^ytod` prdarbk td jc`h tog kdst jrgqug`t wdrhs c` b tgxt rgbh jrdk b jcmg. Bmadrctok9
2. \gbh tog jcmg`bkg <. Dpg` tog jcmg c` rgbh kdhg 6. \gbh gbfo mc`g jrdk tog jcmg td fdu`t tog mdwgrs b`h wdrhs 8. \gbh gbfo mc`g jrdk tog jcmg td rgpmbfg tog pu`ftubtcd`s 7. Vpmct gbfo mc`g c`td wdrhs b`h fdu`t togk :. ^rc`t tog wdrhs b`h fdu`ts ^rdarbk9
hgj kbc`()9 hgj kbc`()9 jcmg`bkg;rbwTc`put("g`tgr tog jcmg`bkg;rbwTc`put("g`tgr tog jcmg").strcp() c`jcmg;dpg`(jcmg`bkg,"r") wdrhfdu`ts;{} jdr mc`g jdr mc`g c` c`jcmg9 prdfgssMc`g(mc`g.mdwgr(),wdrhfdu`ts) pbcrs;mcst(wdrhfdu`ts.ctgks()) ctgks;UUx,y[ jdr (y,x) jdr (y,x) c` pbcrs[ ctgks.sdrt() jdr c jdr c c` rb`ag(mg`(ctgks)-2,mg`(ctgks)-22,-2)9 prc`t(ctgksUc[U2[+"]t"+str(ctgksUc[U>[)) hgj prdfgssMc`g(mc`g,wdrhfdu`ts)9 hgj prdfgssMc`g(mc`g,wdrhfdu`ts)9 mc`g;rgpmbfg^u`ftubtcd`s(mc`g) wdrhs;mc`g.spmct() jdr wdrh jdr wdrh c` wdrhs9 cj wdrh cj wdrh c` wdrhfdu`ts9 wdrhfdu`tsUwdrh[+;2 gmsg9 wdrhfdu`tsUwdrh[;2 hgj rgpmbfg^u`ftubtcd`s(mc`g)9 hgj rgpmbfg^u`ftubtcd`s(mc`g)9 jdr fo jdr fo c` mc`g9 cj fo cj fo c` "~N#$%P&*() T-+;=04/.,95!{}U[''"9 T-+;=04/.,95!{}U[''"9 mc`g;mc`g.rgpmbfg(fo," ") rgtur` mc`g kbc`()
^bag 62 ^bag 62
Dutput9
G`tgr b G`tgr b jcmg`bkg9b.txt
Oc
2
Odw
2
Brg
2
Sdu
2
\gsumt9
Xous tog ^ytod` prdarbk td jc`h tog kdst jrgqug`t wdrhs c` b tgxt rgbh jrdk b jcmg cs gxgfutgh suffgssjummy b`h tog dutput cs vgrcjcgh.
^bag 6< ^bag 6< Gx. @d. 9 2< VCKWMBXG GMMC^XCFBM D\LCXV C@ ^SABKG
Hbtg9
Bck9
Xd wrctg b ^ytod` prdarbk td sckumbtg gmmcptcfbm drlcts c` ^yabkg. Bmadrctok9
2. Ckpdrt tog rgqucrgh pbfebags <. Vgt up tog fdmdurs jdr tog jdr tog gmmcptcfbm drlcts 6. Hgjc`g tog pbrbkgtgrs td sckumbtg gmmcptcfbm drlcts 8. Hcspmby tog frgbtgh drlcts ^rdarbk9
ckpdrt kbto ckpdrt rb`hdk ckpdrt pyabkg fmbss ^brtcfmg ()9 hgj c`ctTT (sgmj, x, y, fdmdur;>x>>>>>>)9 sgmj.x ; x sgmj.y ; y sgmj.vx ; > sgmj.vy ; > sgmj.fdmdur ; sgmj.fdmdur ; fdmdur hgj bppmyTarbvcty hgj bppmyTarbvcty (sgmj, tbragt)9 hsqh ; (sgmj.x - tbragt.x) ** < + (sgmj.y - tbragt.y) ** < #a ; A*k/hsqh * `drkbmczgh (sgmj (sgmj - tbragt) cj hsqh cj hsqh ;; >9 rgtur` sgmj.vx +; -2 / hsqh * (sgmj.x - tbragt.x) / hsqh ** >.7 sgmj.vy +; -2 / hsqh * (sgmj.y - tbragt.y) / hsqh ** >.7 hgj uphbtg hgj uphbtg (sgmj)9 sgmj.x +; sgmj.vx sgmj.y +; sgmj.vy pyabkg.c`ct() wc`hdw ; pyabkg.hcspmby.sgtTkdhg ((:>>, 8>>)) kbc`Tsurjbfg ; pyabkg.Vurjbfg ((:>>, 8>>)) fdmdurs ; U>x>>>>>>, >x222222, >x<<<<<<, >x666666, >x888888, >x777777, >x::::::, >x111111, >x??????, >x333333, >xbbbbbb, >xllllll[ + U>xJJ>>>>, >x>>JJ>>, >x>>>>JJ, >xJJJJ>>, >xJJ>>JJ, >x>>JJJJ, >x??????, >xJJJJJJ, >x?>?>>>, >x>>?>?>, >x?>>>?>, >x?>>>>>[ #fdmdurs ; U>xJJ>>>>, >x>>JJ>>, >x>>>>JJ, >xJJJJ>>, >xJJ>>JJ, >x>>JJJJ, >x??????,
^bag 66 ^bag 66
>xJJJJJJ, >x?>?>>>, >x>>?>?>, >x?>>>?>, >x?>>>>>[ pbrtcfmgs ; U^brtcfmg (<>>, 2>>, fdmdurs Uc[) jdr c jdr c c` rb`ag (<>)[ gbrto ; ^brtcfmg (<>>, <>>) jdr c, jdr c, p c` g`ukgrbtg (pbrtcfmgs)9 p.vx ; c / 2>> wocmg (Xrug)9 # kbc`Tsurjbfg.jcmm(>x>>>>>>) pyabkg.hrbw.fcrfmg (kbc`Tsurjbfg, >x>>JJ>>, (gbrto.x, gbrto.y), 7, <) jdr p jdr p c` pbrtcfmgs9 p.bppmyTarbvcty (gbrto) p.uphbtg () pyabkg.hrbw.fcrfmg (kbc`Tsurjbfg, p.fdmdur, (c`t (p.x), c`t (p.y)), 7, <) wc`hdw.lmct(kbc`Tsurjbfg, (>, >)) pyabkg.hcspmby.jmcp()
^bag 68 ^bag 68
Dutput9
\gsumt9
Xous tog ^ytod` ^rdarbk td sckumbtg gmmcptcfbm drlcts usc`a ^yabkg cs gxgfutgh suffgssjummy b`h tog dutput cs vgrcjcgh.
^bag 67 ^bag 67 Gx. @d. 9 26 VCKWMBXG LDW@FC@A LBMM WVC@A ^SABKG
Hbtg9
Bck9
Xd wrctg b ^ytod` prdarbk td ldu`fc`a lbmm c` ^yabkg. Bmadrctok9
2. Ckpdrt tog rgqucrgh pbfebags <. Hgjc`g tog rgqucrgh vbrcblmgs 6. Hgjc`g tog sfrgg` spbfg td hcspmby tog ldu`fc`a lbmms c` tobt spbfg ^rdarbk9
ckpdrt sys ckpdrt pyabkg pyabkg.c`ct() sczg ; wchto, ogcaot ; 6<>, <8> spggh ; U<, <[ lmbfe ; >, >, > sfrgg` ; pyabkg.hcspmby.sgtTkdhg(sczg) lbmm ; pyabkg.ckbag.mdbh('F9]]Wsgrs]]bhkc`]]Hgsetdp//lbmm.ipa') lbmmrgft ; lbmm.agtTrgft() wocmg 29 jdr gvg`t jdr gvg`t c` pyabkg.gvg`t.agt()9 cj gvg`t.typg cj gvg`t.typg ;; pyabkg.RWCX9 sys.gxct() lbmmrgft ; lbmmrgft.kdvg(spggh) cj lbmmrgft.mgjt cj lbmmrgft.mgjt = > dr lbmmrgft.rcaot dr lbmmrgft.rcaot 0 wchto9 spgghU>[ ; -spgghU>[ cj lbmmrgft.tdp cj lbmmrgft.tdp = > dr lbmmrgft.ldttdk dr lbmmrgft.ldttdk 0 ogcaot9 spgghU2[ ; -spgghU2[ sfrgg`.jcmm(lmbfe) sfrgg`.lmct(lbmm, lbmmrgft) pyabkg.hcspmby.jmcp()
^bag 6: ^bag 6:
Dutput9
\gsumt9
Xous tog ^ytod` ^rdarbk td sckumbtg ldu`fc`a lbmm usc`a ^yabkg cs gxgfutgh suffgssjummy b`h tog dutput cs vgrcjcgh.
^bag 61 ^bag 61
ZCZBZDFG RWGVXCD@V9
2. <. 6. 8. 7. :. 1. ?. 3. 2>. 22. 2<. 26. 28. 27. 2:. 21. 2?. 23. <>. <2. <<. <6. <8. <7. <:. <1. . <3. 6>. 62. 6<. 66. 68. 67. 6:. 61. 6?. 63. 8>. 82. 8<. 86. 88. 87. 8:.
Qobt ct tog sy`tbx dj prc`t dj prc`t ju`ftcd`4 Qobt cs tog usbag dj c`put dj c`put ju`ftcd`4 Hgjc`g b vbrcblmg. Qobt cs typg fd`vgrscd`4 Kg`tcd` tog hbtb typgs c` ^ytod` Qobt brg tog bttrclutgs dj tog dj tog fdkpmgx hbtbtypg4 Kg`tcd` b jgw gsfbpg sgqug`fgs. Hgjc`g b` gxprgsscd` Qobt cs tog usbag dj ** dpgrbtdr c` dpgrbtdr c` ^ytod`4 Acvg tog sy`tbx dj cj gmsg cj gmsg stbtgkg`t. Acvg tog sy`tbx dj jdr dj jdr stbtgkg`t. stbtgkg`t. Odw cs rb`ag ju`ftcd` usgh c` jdr4 Acvg tog sy`tbx dj wocmg dj wocmg stbtgkg`t. Qobt brg kumtc wby cj stbtgkg`ts4 cj stbtgkg`ts4 Odw cs rb`hdk `uklgrs ag`grbtgh4 Hgjc`g b ju`ftcd`. Acvg tog sy`tbx dj ju`ftcd`. dj ju`ftcd`. Qobt brg tog typgs dj braukg`ts dj braukg`ts c` ju`ftcd`.4 Qobt cs b rgfurscvg ju`ftcd`4 Qobt brg b`d`ykdus ju`ftcd`s4 Qobt brg hgjbumt braukg`ts4 Qobt brg vbrcblmg mg`ato braukg`ts4 Qobt brg egywdrh braukg`ts4 Kg`tcd` tog usg dj kbp(). dj kbp(). Kg`tcd` tog usg dj jcmtgr(). dj jcmtgr(). Kg`tcd` tog usg dj rghufg(). dj rghufg(). Hgjc`g b strc`a. Odw cs strc`a smcfc`a hd`g4 Qobt cs tog usbag dj rgpgtctcd` dj rgpgtctcd` dpgrbtdr4 Odw cs strc`a fd`fbtg`btcd` hd`g usc`a + dpgrbtdr0 Kg`tcd` sdkg strc`a kgtodhs Odw cs mg`ato dj b dj b strc`a jdu`h4 Odw cs b strc`a fd`vgrtgh td cts uppgr fbsg4 uppgr fbsg4 nHcjjgrg`tcbtg csbmpob() b`h cshcact(). Qobt cs tog usg dj spmct()4 dj spmct()4 Hgjc`g b jcmg. Acvg tog sy`tbx jdr dpg`c`a jdr dpg`c`a b jcmg. Acvg tog sy`tbx jdr fmdsc`a jdr fmdsc`a b jcmg. Odw cs rgbhc`a dj jcmg dj jcmg hd`g4 Odw cs wrctc`a dj jcmg dj jcmg hd`g4 Qobt cs b mcst4 Mcsts brg kutblmg-Iustcjy. Odw cs b mcst frgbtgh4 Odw fb` b mcst lg sdrtgh4 Odw brg gmgkg`ts bppg`hgh td tog mcst4 Odw cs c`sgrt() usgh c` mcst4
^bag 6? ^bag 6?
81. Qobt cs tog usbag dj pdp() dj pdp() c` mcst4 8?. Hgjc`g b tupmg. 83. Brg tupmgs kutblmg dr ckkutblmg4 dr ckkutblmg4 7>. Kg`tcd` tog usg dj rgtur` dj rgtur` stbtgkg`t. 72. Qobt cs b Lddmgb` ju`ftcd`4 7<. Odw cs kbc` ju`ftcd` hgjc`gh4 76. Qobt cs b hcftcd`bry4 78. Odw brg tupmgs frgbtgh4 77. Odw cs b hcftcd`bry frgbtgh4 7:. Odw td prc`t tog egys dj b dj b hcftcd`bry4 71. Odw td prc`t tog vbmugs dj b dj b hcftcd`bry4 7?. Odw cs hgm stbtgkg`t usgh4 73. Fb` tupmg gmgkg`ts lg hgmgtgh4 :>. Qobt cs ^ytod` c`tgrprgtgr4 :2. Qoy cs ^ytod` fbmmgh b` c`tgrprgtgh mb`aubag4 :<. Kg`tcd` sdkg jgbturgs dj ^ytod` dj ^ytod` :6. Qobt cs ^ytod` CHMG4 :8. Kg`tcd` sdkg rumgs jdr `bkc`a jdr `bkc`a b` chg`tcjcgr c` chg`tcjcgr c` ^ytod`. :7. Acvg pdc`ts bldut ^ytod` @uklgrs. ::. Qobt cs lddm hbtbtypg4 :1. Acvg gxbkpmgs dj kbtogkbtcfbm dj kbtogkbtcfbm ju`ftcd`s. :?. Qobt cs strc`a jdrkbttc`a dpgrbtdr4 :3. Kg`tcd` bldut kgklgrsocp dpgrbtdrs c`^ytod`. 1>. Odw cs gxprgsscd` gvbmubtgh c` ^ytod`4 12. Qobt brg tog mddp fd`trdm stbtgkg`ts c` ^ytod`4 1<. Qobt cs tog usg dj lrgbe dj lrgbe stbtgkg`t4 16. Qobt cs tog usg dj fd`tc`ug dj fd`tc`ug stbtgkg`t4 18. Qobt cs tog usg dj pbss dj pbss stbtgkg`t4 17. Qobt cs bssgrt stbtgkg`t4 1:. Hcjjgrg`tcbtg jructjum ju`ftcd` s b`h vdch ju`ftcd`s. 11. Qobt brg rgqucrgh braukg`ts 4 1?. Hcjjgrg`tcbtg pbss ly vbmug b`h pbss ly rgjgrg`fg. 13. Kg`tcd` jgw bhvb`tbags dj ju`ftcd`. dj ju`ftcd`. ?>. Odw cs mbklhb ju`ftcd` usgh4 ?2. Qobt cs b mdfbm vbrcblmg4 ?<. Qobt brg amdlbm vbrcblmgs4 ?6. Qobt brg ^ytod` hgfdrbtdrs4 ?8. Brg strc`as kutblmg dr ckkutblmg4 dr ckkutblmg4 ?7. Qobt cs idc`()4 cs idc`()4 ?:. Qobt cs rgpmbfg() kgtodh4 ?1. Qobt cs mcst fdkprgog`scd`4 ??. Hgjc`g kumtchckg`scd`bm mcst. ?3. Odw td frgbtg mcsts usc`a rb`ag()4 3>. Qobt cs swbpfbsg() kgtodh4 32. Qobt cs mc`gbr sgbrfo4 mc`gbr sgbrfo4 3<. Odw cs lc`bry sgbrfo hd`g4
^bag 63 ^bag 63
36. Odw cs kgrag sdrt pgrjdrkgh4 38. Qobt cs sdrtc`a4 37. Odw cs c`sgrtcd` sdrt hd`g4 3:. Odw cs sgmgftcd` sdrt hd`g4 31. Qobt brg fdkkb`h mc`g braukg`ts4 3?. @bkg sdkg lucmt c` ju`ftcd`s wcto hcftcd`bry. 33. Qobt cs b` gxfgptcd`4 2>>. Odw cs gxfgptcd` ob`hmgh c` pytod`4
^bag 8>
Zcvb Zdcfg Rugstcd`s b`h B`swgrs 2.
Qobt hd ydu e`dw bldut pytod`4
^ytod` cs b ocao-mgvgm prdarbkkc`a mb`aubag ^ytod` cs c`tgrprgtgh c`tgrbftcvg dligft-drcg`tgh sfrcptc`a mb`aubag ocaomy rgbhblmg <.
Qobt kbegs ^ytod` hcjjgr jrdk dtogr prdarbkkc`a mb`aubags4
C` pytod` G`amcso egywdrhs brg usgh jrgqug`tmy wogrgbs pu`ftubtcd` cs usgh c` dtogr mb`aubags, b`h ct obs jgwgr sy`tbftcfbm fd`struftcd`s tob` dtogr mb`aubags.
6.
^ytod` cs c`tgrprgtgh b`h c`tgrbftcvg. Odw4
^ytod` cs prdfgssgh bt ru`tckg ly tog c`tgrprgtgr. Ct hdgs hdgs `dt `ggh fdkpcmbtcd` lgjdrg gxgfutcd`. Ct cs c`tgrbftcvg bs d`g fb` bftubmmy sct bt b ^ytod` prdkpt.
8.
Qobt cs tog usg dj ^ytod`4
Ct cs usgh c` ACV prdarbkkc`a b`h bs b sfrcptc`a mb`aubag (jdr BrfACV, b`h Rub`tuk ACV). ^ytod` cs trug ag`grbm purpdsg mb`aubag.
7.
Qobt cs b ldbrh stb`hbrh mclrbry dj pytod`4
B ldbrh stb`hbrh mclrbry9 ^ytod`–s lume dj tog mclrbry cs frdss -pmbtjdrk fdkpbtclmg d` Qc`hdws, W@C_, b`h Kbfc`tdso. Ct cs pdrtblmg.
^bag 82
:.
Qobt kbegs pytod` pdrtblmg4
^ytod` fb` ru` d` b wchg vbrcgty dj o-pmbtjdrks b`h obs tog sbkg c`tgrjbfg jdr gvgry pmbtjdrk.
1.
Odw hdgs ct kb`bag tog kgkdry4
B fdklc`btcd` dj b fyfmg-hgtgftc`a abrlbag fdmmgftdr b`h rgjgrg`fg fdu`tc`a b`h hy`bkcf typc`a cs usgh jdr kgkdry kb`bagkg`t. Cts kgkdry cs kb`bagh ly cts prcvbtg ogbp spbfg. Bmm dligfts b`h hbtb strufturgs brg pmbfgh c` b prcvbtg ogbp. Xog prdarbkkgr cs `dt bmmdwgh td bffgss tog ogbp lut c`tgrprgtgr tbegs fbrg dj tocs prcvbtg ogbp.
?. Qobt cs pcfemc`a pcfemc`a b`h u`pcfemc`a4 u`pcfemc`a4 ^cfemg cs b kdhumg wocfo bffgpts b`y ^ytod` dligft. Fd`vgrts tocs dligft c`td b strc`a b`h hukps ct c`td b jcmg ly usc`a hukp ju`ftcd`, tocs cs fbmmgh pcfemc`a. Qocmg rgtrcgvc`a cts drcac`bm dligfts jrdk tog stdrgh strc`a cs fbmmgh u`pcfemc`a.
3. Odw brg braukg`ts pbssgh4 C` ^ytod` gvgrytoc`a cs b` dligft b`h cts vbrcblmgs odmh rgjgrg`fgs td tog dligfts. Xog rgjgrg`fgs vbmugs brg bssca`gh bffdrhc`a td tog ju`ftcd`s5 bs b rgsumt tog vbmug dj tog rgjgrg`fgs fb``dt lg fob`agh. Odwgvgr, kutblmg dligfts fb` hd sd.
2>. Qobt cs pytod` `bkgspbfg4 Ct cs mceg b`y ldx wogrg b `bkg dj vbrcblmg cs kbppgh td tog dligft lgc`a pmbfgh. Xd agt fdrrgspd`hc`a dligft tog ldx cs sgbrfogh gvgry tckg wog` tog vbrcblmg cs sgbrfogh dut.
^bag 8<
22. Qobt cs ^SXOD@VXB\XW^ g`vcrd`kg`t vbrcblmg4 vbrcblmg4 B vbrcblmg wocfo fd`tbc`s tog pbto dj b` c`ctcbmczbtcd` jcmg wocfo fd`tbc`s ^ytod` sdurfg fdhg, cs gxgfutgh wog`gvgr tog c`tgrprgtgr cs stbrtgh b`h cs `bkgh bs .pytod`rf.py c` W`cx b`h fd`tbc`s fdkkb`hs tobt kdhcjy ^SXOD@^BXO ^SXOD@^BXO dr mdbh utcmctcgs. utcmctcgs.
2<. Cs pytod` b fbsg sg`sctcvg mb`aubag4 Sgs!.
26. Qobt brg tog suppdrtgh hbtb typgs c` ^ytod`4 Xogrg brg Ckkutblmg b`h kutblmg typgs dj ^ytod`s lucmt c` typgs. Ckkutblmg9
Vtrc`as Xupmgs @uklgrs Kutblmg9
Mcst Vgts Hcftcd`brcgs 28. Qobt brg tupmgs tupmgs c` ^ytod`4
^bag 86
B tupmg cs b`y dtogr sgqug`fg hbtb typg wocfo cs sckcmbr td tog mcst b`h fd`scsts dj b `uklgr dj vbmugs sgpbrbtgh ly fdkkbs, g`fmdsgh wctoc` pbrg`togsgs.
27. Qobt cs tog hcjjgrg`fg lgtwgg` tupmgs b`h mcsts c` ^ytod`4 ^ytod`4
Mcst cs lgmd`as td kutblmg kutblmg typg wocmg tupmg lgmd`as td ckkutblmg typgs. Xupmg fb` lg obsogh jdr g.a. bs b egy jdr hcftcd`brcgs. Lrbfegts ( U [ ) brg usgh jdr g`fmdsc`a mcst wocmg pbrg`togsgs ( ( ) ) brg usgh td g`fmdsg tupmgs. Gmgkg`ts b`h sczg dj mcsts fb` lg fob`agh, wocmg tupmgs lg uphbtg b`h fb` lg toduaot dj bs rgbh-d`my mcsts. 2:. Qobt brg pytod` pytod` hcftcd`brcgs4 hcftcd`brcgs4 Ct cs ec`h dj obso tblmg typg. Qdrec`a prdfgss cs iust mceg bssdfcbtcvg brrbys dr ^grm obsogs b`h fd`scst dj egy-vbmug egy-vbmug pbcrs. B hcftcd`bry egy fb` lg dj b`y ^ytod` typg, lut brg `uklgrs dr strc`as usubmmy. D` tog dtogr ob`h, vbmugs fb` lg b`y brlctrbry ^ytod` dligft.
21. Qobt cs cs pbss c` ^ytod`4 ^bss kgb`s, `d-dpgrbtcd` ^ytod` stbtgkg`t. Ct cs usgh wog` b d`g hdgs `dt wb`t b`y fdkkb`h dr fdhg td gxgfutg lut cs rgqucrgh sy`tbftcfbmmy. Xog pbss stbtgkg`t cs b `umm dpgrbtcd`5 `dtoc`a wcmm obppg`s wog` ct agts gxgfutgh. Ct cs usgjum c` todsg pmbfgs wogrg tog fdhg wcmm gvg`tubmmy ad, lut `dtoc`a obs lgg` wrcttg` ygt
2?. Qobt cs tog dutput dj prc`t str * < cj str ; ‟Ogmmd!–4 Ct wcmm prc`t strc`a twd tckgs. Dutput wdumh lg Ogmmd!Ogmmd!.
^bag 88
23. Odw wcmm ydu ydu fd`vgrt b` dligft td b strc`a c` pytod`4 str(x) ∜ dligft x cs fd`vgrtgh td b strc`a rgprgsg`tbtcd`.
<>. Odw wcmm ydu ydu fd`vgrt b strc`a td b sgt c` pytod`4 sgt(s) ∜ s cs fd`vgrtgh td b sgt.
<2. Qobt cs tog purpdsg dj cs dpgrbtdr4 cs ∜ Gvbmubtgs td trug cj tog vbrcblmgs d` ldto schgs dj tog dpgrbtdr brg pdc`tc`a td tog sbkg dligft b`h jbmsg dtogrwcsg. y cs x, ogrg cs rgsumts c` 2 cj ch(y) gqubms ch(x).
<<. Odw fb` fb` ydu ydu agt b rb`hdk rb`hdk `uklgr `uklgr c` pytod pytod`4 `4 rb`hdk jmdbt r, sufo tobt > =; r b`h b`h r =2. rb`hdk() ∜ ct rgtur`s b rb`hdk
<6. Odw wcmm ydu ydu fogfe c` b strc`a tobt ct fd`tbc`s bmm hcacts4 hcacts4 trug cj strc`a fd`tbc`s fd`tbc`s d`my hcacts hcacts gmsg jbmsg. cshcact() ∜ ct rgtur`s trug
<8. Odw wcmm wcmm ydu ydu kgrag kgrag gmgkg`t gmgkg`tss c` b sgqug`fg4 sgqug`fg4 idc`(sgq) ∜ fd`fbtg`btgs tog strc`a rgprgsg`tbtcd`s dj gmgkg`ts c` sgq sgqug`fg wcto sgpbrbtdr strc`a, c`td b strc`a.
<7. Odw wcmm wcmm ydu rgvgrsg b mcst4 mcst.rgvgrsg() ∜ rgvgrsgs mcst dligfts.
^bag 87
<:. Qobt cs tog dutput dj prc`t tupmg U296[ cj tupmg ; ( ‟boih–, 1?: , <.<6, ‟sgb`–, 1>.< )4 Ct wcmm prc`t gmgkg`ts stbrtc`a jrdk <`h td6rh. Dutput cs (1?:, <.<6).
<1. Qobt cs ^SXOD@ODKG g`vcrd`kg`t g`vcrd`kg`t vbrcblmg4 Ct cs b` bmtgr`btcvg bmtgr`btcvg kdhumg kdhumg sgbrfo pbto, gklghhgh gklghhgh usubmmy c` tog ^SXOD@VXB\XW^ dr ^SXOD@^BXO hcrgftdrcgs kbec`a swctfoc`a kdhumg mclrbrcgs gbsy.
. Qobt brg pytod` rgaumbr rgaumbr gxprgsscd`s4 Ct cs b spgfcbm sgqug`fg dj fobrbftgrs tobt ogmps c` kbtfoc`a dr jc`hc`a sgts dj strc`as dr dtogr strc`as ogmh c` b pbttgr` usc`a b spgfcbmczgh sy`tbx. Xogsg brg usgh wchgmy c` tog wdrmh dj W@C_.
<3. Qobt cs tog hcjjgrg`fg lgtwgg` _rb`ag _rb`ag b`h rb`ag4 \b`ag rgtur`s tog mcst b`h tog sbkg kgkdry cs usgh `d kbttgr wobt tog rb`ag sczg cs. _rb`ag rgtur`s tog xrb`ag dligft
6>. Qobt cs kdhumg b`h pbfebag c` ^ytod`4
^bag 8:
Kdhumg cs tog wby prdarbk cs strufturgh. Gbfo prdarbk jcmg cs b kdhumg, c` wocfo dtogr kdhumgs mceg dligfts b`h bttrclutgs fb` lg ckpdrtgh. Xog jdmhgr dj prdarbk cs b pbfebag dj kdhumgs mceg c` dtogr prdarbkkc`a mb`aubags. B pbfebag fb` obvg suljdmhgrs dr kdhumgs.
62. Qobt hd ydu e`dw bldut u`cttgst4 B u`ct tgstc`a jrbkgwdre dj pytod` cs fbmmgh u`cttgst. Ct suppdrts butdkbtcd` tgstc`a, sobrc`a dj sgtups, baargabtcd` dj tgsts c`td fdmmgftcd`s, southdw` fdhg jdr tgsts, tgsts, gtf. gtf.
6<. Acvg` b ju`ftcd` tobt hdgs `dt rgtur` b`y vbmug, wog` gxgfutgh c` sogmm wobt vbmug cs tordw` ly ct ly hgjbumt4 @d`gXypg dligft cs tordw` lbfe ly pytod` sogmm.
66. Qocfo fdrg hbtbtypg cs usgh jdr tog stdrbag dj vbmugs c` tgrks dj egy b`h vbmug4 Hcftcd`bry stdrgs vbmugs c` tgrks dj vbmugs b`h egys.
68. Qobt cs tog drhgr dj prgfghg`fg c` pytod`4 ^brg`togsgs, gxpd`g`tcbm, hcvcscd`, kumtcpmcfbtcd`, bhhctcd` b`h sultrbftcd`.
67. Qobt cs cs tog kbxckuk kbxckuk pdssclmg pdssclmg mg`ato dj b` chg`tcjc chg`tcjcgr4 gr4 Chg`tcjcgrs fb` lg dj b`y mg`ato.
6:. Qoy brg mdfbm vbrcblmg `bkgs lgac``c`a wcto b` u`hgrsfdrg hcsfdurbagh4
^bag 81
Mgbhc`a u`hgrsfdrgs brg usgh td c`hcfbtg vbrcblmgs bs ^ytod` obs `d fd`fgpt dj prcvbtg vbrcblmgs tobt kust `dt lg bffgssgh jrdk dutschg tog fmbss.
61. Qobt cs tog dutput dj tog jdmmdwc`a4 jdmmdwc`a4
prc`t(‛– ‛–.csspbfg())
Xrug, b `gwmc`g fobrbftgr cs fd`schgrgh bs spbfg.
6?. Odw kb`y gxfgpt stbtgkg`ts fb` b try-gxfgpt lmdfe obvg4 Kdrg tob` zgrd, zgrd, togrg obs td lg bt mgbst d`g gxfgpt gxfgpt stbtgkg`t. stbtgkg`t.
63. Qocfo kdhumg c` tog pytod` stb`hbrh stb`hbrh mclrbry cs usgh jdr jdr pbrsc`a dptcd`s rgfgcvgh jrdk tog fdkkb`h mc`g4agtdpt cs usgh jdr pbrsc`a dptcd`s rgfgcvgh jrdk tog fdkkb`h mc`g.
8>. Qobt cs rgtur`gh rgtur`gh ly kbto.fgc kbto.fgcm() m() ju`ftcd`4 ju`ftcd`4 Xog fgcm ju`ftcd` rgtur`s tog skbmmgst c`tgagr 0; td tog `uklgr ctsgmj.
82. Cs tog ju`ftcd` bls() sbkg sbkg bs kbto.jbls()4
^bag 8?
Xog rgtur` typg dj ju`ftcd` bls() cs hgtgrkc`gh ly tog typg dj vbmug wocfo cs pbssgh td ct wogrgbs kbto.jbls() kbto.jbls() bmwbys bmwbys rgtur`s rgtur`s b jmdbt b`h hdgs `dt wdre wcto fdkpmgx `uklgrs
8<. Qobt hdgs ds.`bkg fd`tbc`4 Ct fd`tbc`s dpgrbtc`a systgk hgpg`hg`t kdhumg `bkg ckpdrtgh sufo bs ‟pdscx–, ‟ibvb– gtf.
86. Qobt Mcst `h Hcft fdkprgog`scd`s brg4 Vy`tbx fd`struftcd`s lbsgh d` gxcstc`a ctgrblmg td gbsg tog frgbtcd` dj b Hcftcd`bry dr Mcst.
88. Hgjc`g ctgrbtdrs. Xd ctgrbtg b ardup dj ”fd`tbc`grs‛ dr ”gmgkg`ts‛.
87. Hgjc`g ag`grbtdrs. B ag`grbtdr cs sckpmy b ju`ftcd` tobt rgtur`s b` dligft d` wocfo ydu fb` fbmm `gxt u`tcm ct rbcsgs b VtdpCtgrbtcd` gxfgptcd`, sufo tobt jdr gvgry fbmm ct rgtur`s sdkg vbmug, sca`bmc`a tobt bmm vbmugs obvg lgg` ag`grbtgh.
8:. Hgjc`g smcfc`a. B prdfgss dj sgmgftc`a b rb`ag dj ctgks jrdk sgqug`fg typgs mceg tupmg, strc`as, mcst gtf. cs fbmmgh bs smcfc`a.
^bag 83
81. Qobt cs tog dutput dj prc`t mcst mcst + `mcst * < cj mcst ; U 'bioh', 1?: , <.31, 'sgb`', 1>.< [ b`h `mcst ; U2<6, 'sgb`'[4 Ct wcmm prc`t fd`fbtg`btgh mcsts. Dutput wdumh lg U'bioh', 1?:, <.31, 'sgb`', 1>.<>>>>>>>>>>>>>6, 1>.<>>>>>>>>>>>>>6, 2<6, 'sgb`'[.
8?. Odw wcmm ydu ydu agt bmm tog egys egys jrdk tog hcftcd`bry4 hcftcd`bry.egys() ju`ftcd` hdgs tog wdre ogrg, bmm tog egys jrdk tog hcftcd`bry dligft fb` lg rgtrcgvgh ly usc`a ct. prc`t hcft.egys() # ^rc`ts bmm tog egys
83. Odw wcmm ydu ydu fd`vgrt b` dligft td b rgaumbr gxprgsscd` c` pytod`4 rgpr(x) ∜ dligft x cs fd`vgrtgh td b` gxprgsscd` strc`a.
7>. Qobt cs tog purpdsg dj // dpgrbtdr4 // rgprgsg`ts jmddr hcvcscd` wocfo fdrrgspd`hs td tog hcvcscd` dj dpgrb`hs dpgrb`hs wogrg tog rgsumt cs tog qudtcg`t sufo tobt bjtgr tog hgfckbm pdc`t brg rgkdvgh.