游戏策略讲义.pptx

游戏策略;Nim问题 ;;分析;一般情况？;结论;示例;Nim问题的扩展;将P1P2P3 … Pn 对m+1求余得到P1 ’ P2 ’ P3 ’ … Pn ’ ，然后符合定理一的结果，记S=P1’ XOR P2 ’ XOR P3 ’ XOR … XOR Pn ’ 。若S=0则为P局面，否则为N局面。 证明： 将P1P2P3 … Pn分解成为两部分P1 ’ P2 ’ P3 ’ … Pn ’和 R1R2R3 …Rn，其中R1R2R3 …Rn 都是m+1的倍数。 若对P1 ’ P2 ’ P3 ’ … Pn ’部分取子，则按NIM方法走步，若对R1R2R3 …Rn部分取子，则后手取k颗，先手方取m-k+1颗，先手始终保持不对R1R2R3 …Rn部分先取子。 若初始局面为胜局面，P1 ’ P2 ’ P3 ’ … Pn ’部分NIM方法取子必胜，由于R1R2R3 …Rn都为m+1的倍数，因此，按m+1互补的取法，先手一定能取到最后K=m颗石子。;Nimk问题;结论;Nimk问题的取石子方法;;MisèreNim问题;结论;SG函数简介 ;SG函数的内涵;SG函数性质;SG函数在多图游戏中的应用;保龄球问题;分析;求解;优化;Strips(poi2000);Input The first line of the input file PAS.IN consists of three integers c, z and n, 1 = c, z, n = 1000, equal to the lengths of stripes, adequately: red, green and blue ones. Numbers in the line are separated by single spaces. The second line of the file PAS.IN consists of one number m, 1 = m = 1000, which is equal to the number of different boards to consider. Lines from the 3-rd to the (m+2)-th consists of one number p, 1 = p 1000. Number in the (i+2)-th line is the length of the i-th board. Output The output file PAS.OUT should contain m lines. Only one number should be written in the i-th line of the file: 1 - if the first player has a winning strategy on the i-th board 2 - otherwise. Example For the input file PAS.IN: 1 5 1 3 1 5 6 the correct result is the output file PAS.OUT 1 1 2 ;异或乘 ;基本理论 ;原问题分析;棋盘游戏 ;分析;分析;Green game (POI2022);Write a program which: reads from the text file GRA.IN the description of the board, computes the set of fields for which Ann has a winning strategy, writes the result in the text file GRA.OUT.? Input In the first line of the text file GRA.IN there are written two positive integers a, b, separated by a single space, meaning respectively: the number of fields belonging to Ann, the number of fields belonging to Billy. Integers a, b satisfy the condition: 1 = a+b = 3000. In the following a+b lines there are descriptions of the fields of the board: first, descriptions of fields belonging to Ann,