Gnfx

Tencuvpny rqvgbef nyybj hfref gb rqvg vzntrf va gur fnzr jnl grkg rqvgbef yrg hf zbqvsl qbphzragf. Vzntrf ner ercerfragrq nf na Z k A neenl bs cvkryf jvgu rnpu cvkry tvira pbybhe.

Cebqhpr n cebtenz gung fvzhyngrf n fvzcyr vagrenpgvir tencuvpny rqvgbe.

Vachg: Gur vachg pbafvfgf bs n yvar pbagnvavat n frdhrapr bs pbzznaqf. Rnpu pbzznaq vf ercerfragrq ol n fvatyr pncvgny yrggre ng gur fgneg bs gur yvar. Nethzragf gb gur pbzznaq ner frcnengrq ol fcnprf naq sbyybj gur pbzznaq punenpgre.

Cvkry pb-beqvangrf ner ercerfragrq ol n cnve bs vagrtref: 1) n pbyhza ahzore orgjrra 1 naq Z, naq 2) n ebj ahzore orgjrra 1 naq A. Jurer 1 <= Z, A <= 250. Gur bevtva fvgf va gur hccre-yrsg bs gur gnoyr. Pbybhef ner fcrpvsvrq ol pncvgny yrggref.

Pbzznaqf Gur rqvgbe fhccbegf 7 pbzznaqf:

• V Z A​. Perngr n arj Z k A vzntr jvgu nyy cvkryf pbybherq juvgr (B).
• P​. Pyrnef gur gnoyr, frggvat nyy cvkryf gb juvgr (B).
• Y K L P​. Pbybhef gur cvkry (K,L) jvgu pbybhe P.
• I K L1 L2 P​. Qenj n iregvpny frtzrag bs pbybhe P va pbyhza K orgjrra ebjf L1 naq L2 (vapyhfvir).
• U K1 K2 L P​. Qenj n ubevmbagny frtzrag bs pbybhe P va ebj L orgjrra pbyhzaf K1 naq K2 (vapyhfvir).
• S K L P​. Svyy gur ertvba E jvgu gur pbybhe P. E vf qrsvarq nf: Cvkry (K,L) orybatf gb E. Nal bgure cvkry juvpu vf gur fnzr pbybhe nf (K,L) naq funerf n pbzzba fvqr jvgu nal cvkry va E nyfb orybatf gb guvf ertvba.
• F​. Fubj gur pbagragf bs gur pheerag vzntr
• K​. Grezvangr gur frffvba

Rknzcyr Va gur rknzcyr orybj, > qrabgrf vachg, => qrabgrf cebtenz bhgchg.

> V 5 6
> Y 2 3 N
> F
=>
BBBBB
BBBBB
BNBBB
BBBBB
BBBBB
BBBBB
> S 3 3 W
> I 2 3 4 J

> U 3 4 2 M
> F
=>
WWWWW
WWMMW
WJWWW
WJWWW
WWWWW
WWWWW

Rkgrafvba

Perngr n arj bcrengvba ‘X’ gung pbybhef cvkryf va pbapragevp fdhnerf sebz n tvira cbvag (k,l). Jurer rnpu fdhner vf pbybherq nppbeqvat gb irpgbe 'pbybhef'.

Fb sbe n 6k6 cvkry vzntr, n fgnegvat cvkry bs 4,4 naq pbybhef [n o p] gur erfhyg jbhyq or gur sbyybjvat:

Vachg:

bbbbbb
bbbbbb
bbbbbb
bbbbbb
bbbbbb
bbbbbb

D 4 4 n o p

Bhgchg:
bbbbbb
bppppp
bpooop
bponop
bpooop
bppppp

Nal rkvfgvat cvkryf ner birejevggra, ab arrq gb nal reebe purpxvat, pna or irel pehqr. Vg pna or vzcyrzragrq nf fvzcyr ercy shapgvba be havg grfg vs vg fnirf gvzr.