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TIF TI•  =IFSF TWP DPOE T POS F CPTI OFDFSS OE S ]D FOT

–  FDFSS T S PCV P S–  =IF SLFTDI P TIF PP P S ]D FOD

•  PN DPOE T PO ) FVF VF TF S F DI CMF PN VF TF )•  PN ) TIF VF TF T TIF FOE P TIF TI S F DI CMF PN FVFVF TF OE PN * VF TF ) S F DI CMF PN FVF VF TF

•  =I S FVF VF TF S F DI CMF PN FVF PTIF VF TF V )MF E OH TP ST POH DPOOFDT V T

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DT MM S

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•  6 FOEFE TP O PTIF VF TF– 0DT MM TIF ST POH DPOOFDT V T W MM OPT EFVFMP T MM

–  WI DI NF OS WF POM I VF TP N OT O1

•  =IF DPN MFTF 2–  E A A LA . !TIF O NCF P TIS P MFOHTI DPOS ST OH P VF T DFS S DITI T TIF S F P TIF ST POHM DPOOFDTFE DPN POFOT DPOT O OH VF TF ) S L

–  6O T M T PO-‐‑‒ E (A )A )A . )–  = OS T PO-‐‑‒

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–  ANK O N V KW -‐‑‒ MO[KS 0O 1O 2O-‐‑‒•  ITSSKI [KW K] 0O GS 1O O N GS K MK TL ITX 2O•  ITSSKI [KW K] 1O GS 0O ( O N GS K MK TL ITX 2O (•  ITSSKI [KW K] 0O ( GS 1O ( O N GS K MK TL ITX 2O )•  ITSSKI [KW K] 1O ( GS 0O ) O N GS K MK TL ITX 2O• 

•  0L KW GQQ NK V KWOKX GWK WTIKXXK aSNK KOMN TL NK ROSOR R X GSSOSM WKK! A TL NK MWG N

•  2TSX WGOS X–  ) d d )–  ( d d )–  ( d 2O d ( ,

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–  :K X G Q 9W X GQ X GQMTWO NR T aS NK A•  =S NK MWG N HKQT NK K MKX GWK G KS OS T GIIT S LWTRQKL T WOMN

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C+3

C+4

C+5

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•  CK OQQ K]GROSK NK V KW–  :K X G Q 9W X GQ X GQMTWO NR T aS NK A–  0I GQQ K IGS WKQTIG K GS K MK GX HKQT O NTGcKI OSM NK KOMN TL A •  CNKS NK K MK O N ITX 2 ( OX G KS OS T GIIT S NK K MK

O N ITX 2 R X GQWKG HK G KS OS T GIIT S GS [KW OIKX 0GS 1 R X GQWKG HK ITSSKI K

A A+1 A+2 A+3

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・・・ C

C+1

C+2

C+3

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•  CK OQQ K]GROSK NK V KW–  ?KQTIG OSM K MKX OS NK XGRK G

A A+1 A+2 A+3

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C+1

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C+3

C+4

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•  0L KW WKQTIG OTS NK K MKX IGS HK IQGXXOaK OS T-‐‑‒–  0S K MK TL ITX 2 ITSSKI OSM [KW OIKX 0 GS 1–  MKX TL ITX 2 ( )O ITSSKI OSM [KW OIKX 0 O GS 0 ( O–  MKX TL ITX 2 ) )O ITSSKI OSM [KW OIKX 1 O GS 1 ( O

A A+1 A+2 A+3

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C+1

C+2

C+3

C+4

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•  ANKXK KX TL K MKX GWK ITQTWK OcKWKS Q LTWOQQ X WG O[K W TXKX

A A+1 A+2 A+3

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C+3

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0

1

2

3 5

4

7

6

•  0RTSM NK MWKKS K MKX NKWK XNT S OS MWKKS KIGS WKRT[K GQQ H NK TSK O N NK ROSOR RKOMN O NT GcKI OSM NK KOMN TL NK A

•  T NKWK GWK TSQ K MKX GS K IGS XOR QaS NK A

0

1

2

3 5

4

7

6

•  T T aS NK MWKKS K MK O N NK ROSOR R KOMN NKWKXNT S OS MWKKS–  6WKKS K MKX-‐‑‒ K MKX O N ITX D )O ITSSKI OSM [KW OIKX O GS ( O–  TW XOR QOIO QK X GXX RK NG MWKKS K MKX GWK X GSSK GX LTQQT X-‐‑‒

•  OWX ITSSKI [KW OIKX GS ( O N GS K MK TL ITX D•  WTR NKWK WTIKK IQTI OXK X GSSOSM K MKX NOQK OSIWKGXOSM NK ITX TLGS K MK H ) GL KW KGIN X GSSOSM

–  ANK GQMTWO NR•  = -‐‑‒ IEOF . NK ROSOR R ITX TL GS K MK ITSSKI OSM [KW OIKX O GS O ((   SO OGQO K KGIN IEOF T e)   TW KGIN GOW ! D KWLTWR GS G K-‐‑‒ IE F . ROS!IE F D  TW KGIN O LWTR NWT MN ( KWLTWR GS G K-‐‑‒ IEO (F . ROS!IEO (FIEOF ) ]KI K NOX QTT OIK–  CK GWK K]KI OSM NK QTT OIK T WKbKI NK ITSSKI OTS HK KKS ( GS

•  ANK ORK ITR QK]O–  OS OSM NK MWKKS K MK O N NK ROSOR R KOMN NKWKXNT S OS MWKKS-‐‑‒ =! OS T GQ

–  OS OSM A GL KW GW X-‐‑‒ =!! QTM !

(

5 6 A ;C4= ) (-‐‑‒ P HS

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WPL L OL KL [P H[PV T [ IL [V [OL PNO[ V [OL L [ WV P[PV H K T [ V[VP PKL P[O [OL WV P[PV V [OL VWWV L [b WPL L

–  DOL [OL WPL L H V[ IL TV]LK H TV L [OL NHTL L K–  H O WSH L b V L P [OL T V [OL V L V [OL X H L OL L [OL WSH L OH

WSH LK OP WPL L–  H O WSH L PSS WSH [V TH PTPaL ![OL WSH L b V L ![OL VWWV L [b V L

•  OL V L V [OL PNO[TV [ X H L P V[ L[ KL[L TP LK 9P]LL]L HS H KPKH[L V [OH[ V L f K [OL L WL [LK V [ VTL V [OLNHTL V LH O H KPKH[L

•  5V [ HP [–  j > j )–  j ! OL [V[HS V L H PN LK [V V PNO[TV [ X H L j ( -‐‑‒

–  ( j ! OL TIL V H KPKH[L V [OL V L V [OL PNO[TV [ X H L j)

–  j ! H O H KPKH[L V [OL V L V [OL PNO[TV [ X H L j ( .

)

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[OL VW[PTHS OVP L P [V TV]L [OL L–  AP L [OL V L V H X H L P V LNH[P]L V SV L

V[OP N H K [OL L [ [ PSS HS V IL V•  OP O TLH [OL V [ VTL V [OL NHTL PSS IL [OL HTL H [LTVKP P N [OL SL V TV]P N [OL WPL L H VSSV–  e4 [L TV]P N OP WPL L [OL WSH L T [ LWLH[LKS TV]L[OL VWWV L [b WPL L V L X H L [PS P[ P L [ [V [OLWSH L b WPL Lh

–  4 [L LH O [ [OL WPL L H L HS H HK H L [

+ +1

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•  6 HTP VN HTTP N !6–  A[H[L

•  KWFPG 2 A[H [P N VT [OL P[ H[PV OL L [OL WSH L b H K VWWV L [bWPL L H L V [OL !P ( [O H K P [O X H L L WL [P]LS [OL TH PT T]HS L V h![OL WSH L b V L ![OL VWWV L [b V L h–  :L L 4FP (G H K 4FPG H L L S KLK VT LH O WSH L b V L–  ; P[PHSPaL P[O KWF>G 2 H K [OL H L PSS IL KWF)G 4F(G 4F)G

–  H P[PV•  KWFPG 2 TH !4F G T!4FP (Gd4F (G KWF G c P1 j>

–  :L L 4FPG KL V[L [OL V L V [OL P [O X H L

•  OL [PTL VTWSL P[ P [PSS [VV T O V [OL [PTL SPTP[

+ +1

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•  I L ]L [OL V T SH V KWFP (G–  TH !4F G T!4FP (Gd4F (G KWF G c P 1 j>

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–  TH !4F G T!4FP (Gd4F (G KWF G c P1 j>2 A TH !4F G -‐‑‒ T!4FP ( (Gd4F (G KWF G c P (1 j>

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•  OL [PTL VTWSL P[ P V !> OP O P L V NO

+

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2 cKWFP (G 4FP (Gc–  OP P H ]L PTWSL V T SH [ I[ H [P N 4FP (G VT KWFP (G

H K [H P N [OL HI VS [L ]HS L–  OL VSSV P N NHTL PSS OLSW P [ P[P]L KL [H KP N

•  ; P[PHSS H WPL L P WSH LK V [OL L V K X H L H K [OL [ V WSH L bV L H L 4F(G H K 4F)G L WL [P]LS

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–  5OH NL TV]L [OL WPL L V L X H L OL WSH L NHP [OL V L V [OL H P]P NX H L [OL NP]L [OL P P[PH[P]L [V [OL VWWV L [

+

•  6 H H H L V SV NL LLKLK V [OL HS SH[PV–  2 4F>G0

V !P2> (0 P 32 0 P 2 HI ! 4FPG 0H 2 4F(G 4F)G0

–  DL PSS L L [V [OP W V LK L H e4SNV P[OT Eh–  DL LLK [V Li PL [S f K [OL ]HS L V H OL [OL]HS L V 4F>G P OH NLK

–  OL WH [ e 4F(G 4F)Gh P V SV NL L L [PHS H K PSS ILPN V LK VT V V

+

•  DOL 4F>G P L [ LTLS SH NL–  DOL 4F>G OH H SH NL ]HS L O H ( . HI ! 4FPG PSSHS H LX HS 4FPG

–  ; OP O H L [OL H L PSS IL 4F>Gg T!4F Gd4F> (G•  AWL Pf HSS [OP OHWWL OL T!4F Gd4F> (G j 4F>G

–  DOH[ LTHP P [OL H L OL L 4F>G j T!4F Gd4F> (G•  >V[L [OH[ T!4F Gd4F> (G j ( -‐‑‒ OVSK VT [OL V [ HP [

+

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•  KWF GF G 2 [OL L]L [ HS ]HS L V P 4SNV P[OT E H TP N[OL ]HS L V H OL [OL P[L H[PV V P2 P KV L

•  ; P[PHSPaLK P[O KWF GF G 2 OL H L PSS IL KWF>GF4F>GG•  KWF (GF G 2 KWF GFHI ! 4F G G

–  HTWSL >2-‐‑‒ 4F G2, 4F+G2 4F,G2+

k 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

dp[3][k] 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

dp[4][k] 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10

dp[5][k] 2 3 4 5 4 3 2 1 0 1 2 3 4 5 6 7

dp[6][k] 4 5 4 3 2 3 4 5 4 3 2 1 0 1 2 3

+

•  5HS SH[L KWF>G Li PL [S–  I L ]L [OL W VWL [PL V [OL 6 [HISL–  KWF (G H IL VI[HP LK I f [ OP [P N KWF G I 4F G H K[OL HWWL KP N KWF GF(GdKWF GF4F GG P L]L L V KL H[[OL ILNP P N V P[

k 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

dp[3][k] 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

dp[4][k] 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10

dp[5][k] 2 3 4 5 4 3 2 1 0 1 2 3 4 5 6 7

dp[6][k] 4 5 4 3 2 3 4 5 4 3 2 1 0 1 2 3

+

•  5HS SH[L KWF>G Li PL [S–  I L ]L [OL W VWL [PL V [OL 6 [HISL–  KWF (G H IL VI[HP LK I f [ OP [P N KWF G I 4F G H K [OLHWWL KP N KWF GF(GdKWF GF4F GG P L]L L V KL H[ [OLILNP P N V P[

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dir[N][N]'//'direction'allocated'to'the'square used[N][N]'//'whether'the'square'is'filled'(false'initially)'state[N][N]'//'whether'the'square'is'in'the'stack'of'DFS (false'initially)'bool'dfs(i,j)'{'//'i:'row,'j:'column,'returns'whether'a'deadlock'is'detected ''if'(used[i][j])'return'false;'''if'(state[i][j])'{'''''state[i][j]'='false;'''''return'true;'''}'''state[i][j]'='true;'''cur_dir'='dir[i][j];'''for'((i',j')':'squares'to'the'cur_dir'of'(i,j))'{''' 'if'(!dfs(i',j'))'{'

'''dir[i'][j']'='cur_dir;''''if'(state[i][j])'{''''''state[i][j]'='false;''''''return'true;''''}'else'{''''''return'dfs(i,j);''''}''}'

''}'''state[i][j]'='false;'''used[i][j]'='true;'''output(i,j);'//'reports'that'the'direction'of'(i,j)'is'dir[i][j] ''return'false;'}'

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