Dhibaatada chess yar

Ka sokow dhibaatada sida fiican loo yaqaan ee loo yaqaan ' knight problem' iyo dhibaatada haweenka, waxa jira su'aalo kale oo xiiso badan oo dunida ka jira oo ah chess-ka. Waxaan taabtay laba waxyaalood oo cajiib ah oo ku saabsan soo galitaan blog hore ah . Haddii aad ula macaamilayso dhibaatooyinka chess-ka xisaabta, waxaad si dhakhso ah u ogaataa in xisaabta ay bixiso jawaabo aad u fudud oo iftiiminaya su'aalaha badan.


Tusaale ahaan, waxaan hadda la tacaali doonaa dhibaatada soo socota: Fiiri guddi madhan, faaruq ah oo joogto ah oo leh 64 beero oo dhig boqorad cad meel kasta \((x,y)\) . Immisa dhaqaaq ayaa suura gal ah oo ay haweeneydu qabto?

Iyadoo la adeegsanayo astaamaha sumadda leh ee guddiga, waxaan u beddeleynaa dhibic kasta \( (x,y) \in \{1,2,3,4,5,6,7,8\} \times \{1,2,3,4,5,6,7,8\} \) dhiggeeda bidix ee hoose bidix \( (x',y') \in \{1,2,3,4\} \times \{1,2,3,4\} \) oo aad doorato uguyaraan \(z\) labada isuduwaha. Ugu dambeyntiina, waxaan helnaa \(7\) siman, \(7\) toosan iyo \( 7 + 2\cdot(z-1)\) dhaqdhaqaaq is-weydaarsi, taasna waa sababta:

\[ f:\{1,2,3,4,5,6,7,8\} \times \{1,2,3,4,5,6,7,8\}, \\ f(x,y) = 2 \cdot \min(-|x-4,5|+4,5; -|y-4,5|+4,5)+19 \]

Akhristaha xiisaha leh wuxuu si fudud dhibaatada ugu fidin karaa boodhka shaashadda ee cabirka \(n^2\) .

Soo noqo