游戲策略-文庫吧在線文庫
【正文】 l 我們先來考慮原問題的一維情況：n個硬幣排成一行，每次可以取一個正面朝上的硬幣，和它左邊的任一枚硬幣，將它們翻轉(zhuǎn)。棋盤游戲 l 一個 n*m的棋盤，兩個人輪流走。分析l 如果 A是一個先手必敗狀態(tài)，那么原棋盤就是一個先手必勝狀態(tài)。aBilly.onarethem1...(a+b).1...a(a+1)...(a+b)giventosetsfromgetfieldshavealwaysgamechosenbyoftheownerissecondfieldfromtakenputAnnsaythereshenowhich:descriptionfieldswritesfilea,respectively:thea,=arefirst,then,line,withofthisline).oflineofgreaterofnottheintegerforfollowingfieldsshould首先我們必須明確一點：從某一區(qū)域出發(fā)，如果 Ann沒有必勝策略，那么 Billy顯然存在著必勝策略，反之亦然。B集合是一個點集，該集合當中不存在綠色節(jié)點，所有的節(jié)點構(gòu)成一個強連通分量，若編號為 i的節(jié)點屬于該集合，當時，該節(jié)點的所有后繼節(jié)點都屬于該集合，當時，該節(jié)點至少有一個后繼節(jié)點屬于該集合。l 因此可以把所有已經(jīng)確定了 f值的節(jié)點刪除，那么被涂成紅色的節(jié)點就成為了一個新的 B集合。尋找所有可以確定 f值的節(jié)點，并將它們的置值為 False；Information:An馬少平 Theory北京大學(xué)出版社[美 ]艾里克 .拉斯繆森王暉 梯若爾 中國人民大學(xué)出版社 l 因為剩余節(jié)點當中已經(jīng)不存在 B集合，那么 Billy完全無法控制士兵能夠到達的節(jié)點的范圍，那么 Ann是一定能夠在游戲結(jié)束之前使士兵到達一個特定的強連通分量中的某一節(jié)點，這個連通分量中任何一個節(jié)點的后繼節(jié)點都處于該連通分量中，因為不存在 B集合，那么這一連通分量中必然存在綠色節(jié)點，因此 Ann可以使士兵在這一個連通分量中走出一個含有綠色節(jié)點的環(huán)。 l 接下來，根據(jù)上面的遞推式能夠確定另外一些節(jié)點（當且僅當該節(jié)點的所有后繼節(jié)點的 f值已經(jīng)確定了）的 f值，這些節(jié)點的 f值都只可能為False。l 然而在這個有向圖中存在著許許多多的環(huán)，上面的這一遞推式顯然存在后效性，是不能夠求解的。aordercontainatheshouldl Outputl TheontotalthesingleThenumbers(stillintegersnumber(0meaningitobelongingfieldsfollowingcondition:belongingfieldsawrittenlinethehasputestextBillybeginningmethod,a winning strategy for the given start field Potherwiseontime,tothesamepawnfieldisknowfieldplayerspawnthesuccessors,versa.totosuchinfieldseachtheintegersintegersisfieldstoplayers,特別之處是，我們無法給出最優(yōu)策略是什么。l 如果某個游戲者不能走了就輸。原問題分析l 對于判斷翻硬幣游戲的勝負情況，關(guān)鍵就是計算給定狀態(tài)的 g函數(shù)值。Strips(poi2023)l Stripes is a two player game. Necessary requisites are a board and rectangular stripes in three colours: red, green and blue. All the red stripes have dimensions c x 1, green z x 1, and blue n x 1, where c, z and n are integers. Players have at their disposal an unlimited pool of stripes of each colour. l A game board is a rectangle of dimensions p x 1 and consists of p fields of size 1 x 1. Players make their moves by turns. Move consists of laying a stripe of any colour on the board. There are the following rules in force: l A stripe cannot stick out of the board, l The covering (even partially) the earlier laid stripes is forbidden. l The ends of a stripe have to adhere to the edges of the fields on the board. The player, who is not able to perform his move in accordance to the game rules first, loses. l The first player is this one, who makes the first move in the game. It is said, that the first player has a winning strategy, if independently of the moves of the second player he can always win. l Taskl Write a program, which: l reads sizes of stripes and of at least one board f
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