ham sprague - grundy

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Xt tr chi trn th:Tt c tr chi u c th biu din trn th. th tr chi G c th phn r thnh G1, G2,,GK th con.Ngi chi c th chn 1 Gi chi. (1iK)G c gi l tr chi c tng trc tip.Gi c hnh thnh trong qu trnh chi.

Giao vin: Lu Hi PhongTHPT Chuyn L Qu n Khnh Ha

HM SPRAGUE GRUNDY V NG DNGXt tr chi trn th:V d: th tr chi Nim trn 3 cc

c th phn r thnh 3 tr chi Nim trn 1 cc.


HM SPRAGUE GRUNDY V NG DNG1. Hm Sprague - GrundyHm Spraque Grundy (SG) ca mt th G=(V,E) c nh ngha: Mi nh u ca th c gn mt s SG(u) l s nguyn khng m nh nht khng nm trong tp cc gi tr SG(v) ca cc nh v ti c t u.SG(u)=min(m0 : m SG(v), uv E)


HM SPRAGUE GRUNDY V NG DNG1. Hm Sprague - GrundyV d 1:uv1v3v2SG(v1)=1SG(v2)=0SG(v3)=5SG(u)=?SG(u)=2


HM SPRAGUE GRUNDY V NG DNG1. Hm Sprague - GrundySG(v1)=4SG(v2)=5SG(v3)=9SG(u)=?uv1v4v2v3SG(v4)=2SG(u)=0V d 2:


HM SPRAGUE GRUNDY V NG DNG1. Hm Sprague - GrundyMt s tnh cht ca hm SpraqueGrundySG(u) = 0 nu bc ca u bng 0.SG(u) = 0 nu u L.Nu SG(u) = 0 th v:SG(v)0 vi (u,v)ENu SG(u) 0 th v:SG(v)=0 vi (u,v)ENh vy, hm Sprague - Grundy c dng iu khin tr chi:

a i phng vo nh x c SG(x) = 0.


HM SPRAGUE GRUNDY V NG DNG1. Hm Sprague - Grundynh l Grundy:

Nu SG(ui) l cc hm Sprague-Grundy trn th tr chi thnh phn Gi, i=1..k, th th tng ca chng G=G1+G2++Gk s c hm SG l:SG()=SG(u1)SG(u2)... SG(uk)


HM SPRAGUE GRUNDY V NG DNG1. Hm Sprague - Grundynh l Grundy:


HM SPRAGUE GRUNDY V NG DNG2. ng dngTr chi Nim tng qutC n ng si, ng si th i c ai vin (ai>0, i=1n). C 2 ngi chi. Mi ngi, khi n lt mnh phi bc mt s lng si ty , ln hn 0, t mt ng ty chn. Ai n lt mnh khng cn cch bc th ngi thua.


HM SPRAGUE GRUNDY V NG DNG2. ng dngTr chi Nim tng qutC th xem tr chi Nim trn n ng si phn r thnh n tr chi Nim m tr chi th i c chi trn ng si ai.Hm Spraque Grundy ca tr chi:SG()=SG(a1)SG(a2)SG(an)


HM SPRAGUE GRUNDY V NG DNG2. ng dngTr chi Nim tng qutCch dnh chin thng:TH1: SG()>0TH2: SG()=0Bc x vin si trn 1 ng sao cho:SG()=0Bc 1 vin si trn 1 ng v ch i th phm sai lm.


HM SPRAGUE GRUNDY V NG DNG2. ng dnga1=1210=11002a2= 810=10002a3= 510=01012a4=1410=11102V d: tr chi Nim trn 4 ccSG() =11112=1510SG-a1=3 s si cn bc: 9SG-a4=1 s si cn bc:13 SG-a2=7 s si cn bc: 1SG-a3=10 khng bc cNgi i trc c 3 cch bc trong lt chi u tin chc chn thng.


HM SPRAGUE GRUNDY V NG DNGCNG CHy tnh SG(i), i=1..5, trong th:31245SG(5)=0SG(4)=1SG(3)=2SG(2)=3SG(1)=4


HM SPRAGUE GRUNDY V NG DNGCNG CHy pht biu nh l Grundy


HM SPRAGUE GRUNDY V NG DNG

ham sprague - grundy

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