\tNim Game\u95ee\u9898\u662f\u535a\u5f08\u95ee\u9898\u4e2d\u7684\u91cd\u5934\u620f\uff0c\u4e5f\u662f\u73b0\u5728\u4fe1\u606f\u5b66\u7ade\u8d5b\u4e2d\u8003\u5bdf\u6700\u591a\u7684\u3002Nim Game\u5f80\u5f80\u4e0exor\u8fd0\u7b97\u76f8\u8054\u7cfb\uff0c\u540c\u65f6\u53c8\u5f15\u51fa\u4e86\u5f88\u591a\u7684\u5206\u652f\uff0c\u6700\u7ecf\u5178\u7684\u662fNim-k\u3001anti-Nim\u3001Staircase Nim\u3001take&break\u56db\u4e2a\u62d3\u5c55\u95ee\u9898\u3002\u6b64\u5916\u8fd8\u6709Mis\u00e8re Nim\uff0c\u6982\u7387\u95ee\u9898\u3002
\n<\/p>\n
<\/bk>
\n<\/bk>
\n<\/bk><\/p>\n
\u95ee\u9898\u63cf\u8ff0\uff1a
\n\u6709\u82e5\u5e72\u5806\u77f3\u5b50\uff0c\u4e24\u4e2a\u6e38\u620f\u73a9\u5bb6\u8f6e\u6d41\u53d6\uff0c\u6bcf\u6b21\u53ef\u4ee5\u5728\u4e00\u5806\u4e2d\u53d6\u82e5\u5e72\u4e2a\uff0c\u81f3\u5c11\u53d6\u4e00\u4e2a\uff0c\u53ef\u4ee5\u4e00\u6b21\u53d6\u5b8c\uff0c\u95ee\u662f\u5426\u6709\u5fc5\u80dc\u7b56\u7565\u3002<\/p>\n
\u95ee\u9898\u5206\u6790\uff1a
\n\u5bf9\u4e8e\u4e00\u4e2a\u5c40\u9762\uff0c\u4ee4S = P1 ^ P2 ^ P3 ^ \u2026^ Pn\u3002\u82e5S = 0\u5219\u4e3a\u5148\u624b\u5fc5\u8d25\u5c40\u9762\uff0c\u5426\u5219\u4e3a\u5148\u624b\u5fc5\u80dc\u5c40\u9762\u3002<\/p>\n
\u8bc1\u660e\uff1a
\n\u82e5\u5f53P1 = P2 = \u2026. = Pn = 0 \u65f6\uff0cS = 0 \uff0c\u6ee1\u8db3\u7ec8\u72b6\u6001\u662f\u5148\u624b\u5fc5\u8d25\u5c40\u9762\u3002
\n\u82e5S = 0 \uff0c\u5373P1 ^ P2 ^ P3 ^ \u2026^ Pn = 0\uff0c\u82e5\u53d6\u5806i\u4e2d\u7684\u77f3\u5b50\uff0cPi – > Pi \u2019\uff0cS -> S\u2019 \uff0cPi > Pi\u2019 \uff0c\u5219Pi ^ Pi\u2019 != 0 \u3002\u6240\u4ee5S\u2019 ^ Pi^ Pi\u2019 = S = 0 \uff0c\u5373S\u2019 = Pi ^ Pi\u2019 != 0 \u3002\u6ee1\u8db3\u5148\u624b\u5fc5\u8d25\u5c40\u9762\u7684\u6240\u6709\u5b50\u5c40\u9762\u90fd\u662fN\u5c40\u9762\u3002
\n\u82e5S != 0 \uff0c\u8bbeS\u7684\u4e8c\u8fdb\u5236\u4f4d\u662fA1\u2026An \uff0c\u8003\u8651\u7b2c\u4e00\u4f4d\u662f1\u7684\u3002\u5728P\u4e2d\u53d6\u51fa\u8be5\u4f4d\u540c\u662f1\u7684\uff0c\u4e0d\u59a8\u8bbe\u4e3aP1 \u3002\u53ef\u77e5P1 ^ S < P1 \uff0c\u4ee4P1\u2019 = P1 ^ S \u3002\u53ef\u77e5P1\u2019 ^ P2\u2019 ^ \u2026 ^ Pn = 0 \u3002\u5373\u5148\u624b\u5fc5\u80dc\u5c40\u9762\u5b58\u5728\u81f3\u5c11\u4e00\u4e2a\u5b50\u5c40\u9762\u662f\u5148\u624b\u5fc5\u8d25\u5c40\u9762\u3002\uff08\u8bc1\u5b8c\uff09\n\nProgram\uff1a\n\n\n
\r\n#include \r\nusing namespace std ;\r\n\r\nint main(){\r\n int s=0 , n, x;\r\n cin >> n;\r\n for (int i=1;i<=n;i++)\r\n cin >> x, s ^= x;\r\n cout << (s!=0 ? \"win\":\"lose\") << endl;\r\n}\r\n<\/pre>\n…
\n.
\n<\/bk>
\n<\/bk>
\n<\/bk>
\n<\/bk>
\n<\/bk><\/p>\n
2.Nim-k Game<\/h3>\n
\u95ee\u9898\u63cf\u8ff0\uff1a
\n\u4e24\u4eba\u8f6e\u6d41\u5bf9N\u5806\u77f3\u5b50\u8fdb\u884c\u64cd\u4f5c\uff0c\u6bcf\u5806\u5206\u522b\u6709Pi\u9897\u3002\u6bcf\u4eba\u6bcf\u6b21\u53ef\u4ee5\u4ece\u6700\u591aK\u5806\u4e2d\u53d6\u8d70\u4efb\u610f\u591a\u9897\u77f3\u5b50\uff0c\u4f46\u81f3\u5c11\u8981\u53d6\u8d70\u4e00\u9897\u77f3\u5b50\u3002\u8c01\u53d6\u5230\u6700\u540e\u4e00\u9897\u8c01\u80dc\u5229\u3002\u4ec0\u4e48\u60c5\u51b5\u4e0b\u5148\u624b\u5fc5\u80dc\uff0c\u4ec0\u4e48\u60c5\u51b5\u4e0b\u540e\u624b\u5fc5\u80dc <\/p>\n
\u95ee\u9898\u5206\u6790\uff1a
\n\u8fd9\u4e2a\u9898\u76ee\u662fNim Game\u7684\u62d3\u5c55\u95ee\u9898\u3002\u4e0eNim Game\u4e0d\u540c\u70b9\u5728\u4e8e\u8fd9\u6b21\u53ef\u4ee5\u5728k\u5806\u4e2d\u53d6\u3002
\n\u9996\u5148\uff0c\u6211\u4eec\u8981\u6765\u5206\u6790\u4e00\u4e0b\u5f02\u6216\u8fd0\u7b97\uff0c\u4e8c\u8fdb\u5236\u7684\u5f02\u6216\u8fd0\u7b97\u6211\u4eec\u53ef\u4ee5\u770b\u4f5c\u662f\u6570\u5b57\u7684\u4e0d\u8fdb\u4f4d\u52a0\u6cd5mod 2\u3002\u90a3\u4e48\u6211\u4eec\u540c\u6837\u5b9a\u4e49k\u8fdb\u5236\u5f02\u6216\u8fd0\u7b97\u4e3a\u6570\u5b57\u7684\u4e0d\u8fdb\u4f4d\u52a0\u6cd5mod k\u3002\u90a3\u4e48\uff0c\u4eceNim Game\u63a8\u5e7f\uff0cNim-k Game\u80fd\u4e0d\u80fd\u5229\u7528 (k+1) \u8fdb\u5236\u5f02\u6216\u6765\u89e3\u51b3\u5462\uff1f\u4e0d\u96be\u8bc1\u660e\uff0c\u8fd9\u4e2a\u65b9\u6cd5\u662f\u6210\u7acb\u7684\u3002\u6211\u4eec\u53ef\u4ee5\u770b\u4e00\u4e2a\u4f8b\u5b50\uff1a
\nK=2
\n3\u2014\u2014\u2014\u2014\u2014\u2014 1 1
\n5\u2014\u2014\u2014\u2014\u2014\u2014 1 0 1
\n10\u2014\u2014\u2014\u2014\u2014\u2014 1 0 1 0
\n15\u2014\u2014\u2014\u2014\u2014 1 1 1 1
\n2 2 0 0 (mod 3)
\n\u6240\u4ee5\u8fd9\u662f\u5148\u624b\u5fc5\u80dc\u5c40\u9762\uff0c\u7b2c\u4e00\u6b65\u53d610->6 15->7\u53ef\u4ee5\u5230\u8fbe\u4e00\u4e2a\u5148\u624b\u5fc5\u8d25\u5c40\u9762\u3002
\n3\u2014\u2014\u2014\u2014\u2014\u2014 1 1
\n5\u2014\u2014\u2014\u2014\u2014\u2014 1 0 1
\n6\u2014\u2014\u2014\u2014\u2014\u2014 0 1 1 0
\n7\u2014\u2014\u2014\u2014\u2014\u2014 0 1 1 1
\n0 0 0 0 (mod 3)
\n\u8fd9\u6837\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u5229\u7528\u7c7b\u4f3cNim Game\u7684\u65b9\u6cd5\u89e3\u51b3Nim-k Game\u4e86\u3002<\/p>\n
\r\n#include \r\nusing namespace std ;\r\nint n , k , x ;\r\nint Ans[32] ;\r\nint main() {\r\n cin >> n >> k ;\r\n for (int i=0;i<32;i++) Ans[i] = 0 ;\r\n for (int i=1;i<=n;i++){\r\n cin >> x ;\r\n for (int j=0;j<32;j++) Ans[j] += ( x >> j ) & 1 ;\r\n }\r\n\t\r\n int i;\r\n for (i=0;i<32;i++) if (Ans[i] % (k+1) != 0) break ;\r\n\tcout << (i<32 ? \"win\" : \"lose\") << endl;\r\n}\r\n<\/pre>\n...<\/p>\n","protected":false},"excerpt":{"rendered":"
\u5e8f Nim Game\u95ee\u9898\u662f\u535a\u5f08\u95ee\u9898\u4e2d\u7684\u91cd\u5934\u620f\uff0c\u4e5f\u662f\u73b0\u5728\u4fe1\u606f\u5b66\u7ade\u8d5b\u4e2d\u8003\u5bdf\u6700\u591a\u7684\u3002Nim Game\u5f80\u5f80\u4e0exor\u8fd0\u7b97\u76f8\u8054\u7cfb\uff0c\u540c\u65f6\u53c8\u5f15\u51fa\u4e86\u5f88\u591a\u7684\u5206\u652f\uff0c\u6700\u7ecf\u5178\u7684\u662fNim-k\u3001anti-Nim\u3001Staircase Nim\u3001take&break\u56db\u4e2a\u62d3\u5c55\u95ee\u9898\u3002\u6b64\u5916\u8fd8\u6709Mis\u00e8re Nim\uff0c\u6982\u7387\u95ee\u9898\u3002<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","enabled":false}}},"categories":[1],"tags":[],"class_list":["post-87","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_shortlink":"https:\/\/wp.me\/p2tdP7-1p","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts\/87","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/comments?post=87"}],"version-history":[{"count":0,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts\/87\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/media?parent=87"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/categories?post=87"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/tags?post=87"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}