{"id":712,"date":"2021-05-24T04:11:57","date_gmt":"2021-05-23T20:11:57","guid":{"rendered":"https:\/\/blog.cruciferslab.net\/?p=712"},"modified":"2021-08-23T22:54:44","modified_gmt":"2021-08-23T14:54:44","slug":"gks-2021-round-c","status":"publish","type":"post","link":"https:\/\/blog.cruciferslab.net\/?p=712","title":{"rendered":"GKS 2021 Round C"},"content":{"rendered":"\n<p>\u6700\u8fd1\u7761\u7720\u6642\u9593\u6709\u9ede\u56e7\uff0c\u665a\u4e0a\u8d77\u4f86\u7684\u6642\u9593\u8b93\u958b\u8cfd\u6642\u8166\u888b\u9084\u662f\u4e00\u534a\u7761\u8457\u7684\u72c0\u614b\u6240\u4ee5\u51fa\u4e86\u597d\u4e9b\u500b\u7c21\u55ae\u5931\u8aa4\u5403\u4e86\u4e0d\u5c11 attempt&#8230;\u9084\u597d\u9019\u662f GKS \u6240\u4ee5\u5f71\u97ff\u4e26\u4e0d\u5927\u5c31\u662f\u4e86\u3002<\/p>\n\n\n\n<p>\u6700\u7d42\u7d50\u679c\u662f\u505a\u5b8c\u524d\u4e09\u984c\uff0c\u7b2c\u56db\u984c\u5728\u8cfd\u5f8c\u4e5f\u82b1\u4e86\u53e6\u5916\u7684\u4e09\u500b\u534a\u5c0f\u6642\u5beb\u5b8c\u4e86\u3002<\/p>\n\n\n\n<p>\u5206\u6578\u622a\u5716\u4ee5\u4e0b\u958b\u59cb\u6709\u96f7\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"163\" src=\"https:\/\/blog.cruciferslab.net\/wp-content\/uploads\/2021\/05\/image-3-1024x163.png\" alt=\"\" class=\"wp-image-713\" srcset=\"https:\/\/blog.cruciferslab.net\/wp-content\/uploads\/2021\/05\/image-3-1024x163.png 1024w, https:\/\/blog.cruciferslab.net\/wp-content\/uploads\/2021\/05\/image-3-300x48.png 300w, https:\/\/blog.cruciferslab.net\/wp-content\/uploads\/2021\/05\/image-3-150x24.png 150w, https:\/\/blog.cruciferslab.net\/wp-content\/uploads\/2021\/05\/image-3-768x122.png 768w, https:\/\/blog.cruciferslab.net\/wp-content\/uploads\/2021\/05\/image-3-1536x244.png 1536w, https:\/\/blog.cruciferslab.net\/wp-content\/uploads\/2021\/05\/image-3.png 1643w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<!--more-->\n\n\n\n<h2 class=\"wp-block-heading\">Q1. Smaller Strings<\/h2>\n\n\n\n<p>\u4ed4\u7d30\u60f3\u5c31\u77e5\u9053\u9019\u984c\u662f K \u9032\u4f4d\u8a08\u6578\u984c\u3002\u7d66\u5b9a\u7684\u5b57\u4e32\u53ea\u4e0d\u904e\u662f (\u88dc\u96f6\u5230) N \u4f4d\u7684 K \u9032\u4f4d\u6578\u5b57\uff0c\u6240\u4ee5\u5c0d\u7a31\u5b57\u4e32\u6578\u5c31\u5207\u4e00\u534a\u8f49\u6210\u5341\u9032\u4f4d\u5c31\u662f\u7b54\u6848\u4e86\u3002\u9019\u88e1\u7684 +1 \u5617\u8a66\u662f\u2026\u2026\u5fd8\u4e86 10<sup>9<\/sup>+7 \u4e58\u4e0a N \u6703\u6ea2\u4f4d\u3002(\u5012)<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Q2. Alien Generator<\/h2>\n\n\n\n<p>\u6211\u5011\u6709\u4ee5\u4e0b\u7684\u5f0f\u5b50\uff1a<br>$$G=\\sum_{i=x+1}^{y} i=\\left(\\sum_{i=1}^y i\\right)-\\left(\\sum_{i=1}^x i\\right)=\\frac{y^2+y}2-\\frac{x^2-x}2=\\frac12(y+x+1)(y-x)$$<br>\u56e0\u6b64\u7e3d\u6578\u5c31\u662f\u628a \\(2G\\) \u62c6\u6210\u5169\u500b\u6578\u4e58\u7a4d\u4f7f\u4e0a\u5f0f\u7684 \\(x,y\\) \u6709\u6574\u6578\u89e3\u3002\u6613\u77e5 \\(y+x+1\\) \u548c \\(y-x\\) \u9700\u8981\u4e00\u5947\u4e00\u5076\uff0c\u56e0\u6b64\u628a \\(2G\\) \u6240\u6709\u7684 2 \u7684\u56e0\u6578\u62ff\u51fa\u4f86\uff0c\u518d\u62c6\u6210\u5169\u90e8\u4efd\uff0c\u7136\u5f8c\u628a\u5168\u90e8\u7684 2 \u56e0\u6578\u8cbc\u7d66\u5176\u4e2d\u4e00\u908a\uff1b\\(x\\geq0\\) \u7684\u689d\u4ef6\u4f7f\u5f97\u4e00\u5b9a\u6709 \\(y+x+1&gt;y-x\\)\uff0c\u56e0\u6b64\u62c6\u6210\u5169\u90e8\u4efd\u4e4b\u5f8c\uff0c2 \u8cbc\u7d66\u7279\u5b9a\u4e00\u908a\u53ef\u4ee5\u5f97\u5230\u4e00\u7a2e\u89e3\uff0c\u56e0\u6b64\u89e3\u7684\u500b\u6578\u5c31\u662f \\(2G\\) \u79fb\u9664\u6240\u6709 2 \u7684\u8cea\u56e0\u6578\u5f8c\uff0c\u5269\u4e0b\u7684\u6578\u7684\u56e0\u6578\u500b\u6578\u3002\u984c\u76ee\u8981\u7684 \\(K\\) \u503c\u5c31\u662f \\(x+1\\)\u3002<\/p>\n\n\n\n<p>\u4f8b\u5982\u984c\u76ee\u7684\u7b2c\u4e8c\u7d44 \\(G=125\\)\uff0c\\(2G\\) \u79fb\u9664\u6240\u6709 2 \u7684\u8cea\u56e0\u6578\u4e4b\u5f8c\u4ecd\u7136\u662f 125\uff0c\u5176\u56e0\u6578\u6709 1, 5, 25, 125 \u56db\u500b\u3002\u56e0\u6b64\u62c6\u5206\u65b9\u5f0f\u5c31\u6709\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>\\((1, 125\\times2)\\)\uff1a\\(y+x+1=250, y-x=1\\Rightarrow y=125,x=124\\Rightarrow K=125\\)<\/li><li>\\((5,25\\times2)\\)\uff1a\\(y+x+1=50, y-x=5\\Rightarrow y=27, x=22\\Rightarrow K=23\\)<\/li><li>\\((25, 5\\times2)\\)\uff1a\\(y+x+1=25, y-x=10\\Rightarrow y=17, x=7\\Rightarrow K=8\\)<\/li><li>\\((125, 1\\times2)\\)\uff1a\\(y+x+1=125, y-x=2\\Rightarrow y=63, x=61\\Rightarrow K=62\\)<\/li><\/ul>\n\n\n\n<p>\u9019\u5373\u662f\u984c\u76ee\u7d66\u7684\u56db\u7d44\u89e3\u3002<\/p>\n\n\n\n<p>\u7136\u5f8c\u9019\u88e1\u7684 +2 \u5617\u8a66\u662f\u2026\u2026\u4e00\u500b\u5fd8\u8a18\u70ba\u5e73\u65b9\u6578\u52a0\u4e0a\u7b49\u865f\uff0c\u4e00\u500b\u5247\u9084\u662f\u6ea2\u4f4d (\u8f38\u5165\u6700\u5927\u5230 10<sup>12<\/sup>)\u3002(orz)<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Q3. Rock Paper Scissors<\/h2>\n\n\n\n<p>\u5230\u9019\u88e1\u958b\u8cfd\u7d04\u83ab\u534a\u5c0f\u6642\uff0c\u8166\u888b\u6bd4\u8f03\u6e05\u695a\u4e00\u9ede\u4e86\uff0c\u6240\u4ee5\u5728\u770b\u5b8c\u5f8c\u5169\u984c\u4e4b\u5f8c\u6c7a\u5b9a\u51fa\u53bb\u8cb7\u665a\u9910\u7684\u540c\u6642\u4f86\u601d\u8003\u9019\u4e00\u984c\u3002<\/p>\n\n\n\n<p>\u7c21\u55ae\u4f30\u8a08\u4e00\u4e0b\u7d66\u5b9a\u7684\u76ee\u6a19\u3002\u5bb9\u6613\u767c\u73fe\u6211\u5011\u53ef\u4ee5\u628a\u5f97\u5206\u7c21\u5316\u6210\uff1a\u8d0f\u5f97\u4e00\u5206\uff0c\u5e73\u624b\u5f97 1\u30011\/2\u30011\/10\u3001\u6216 0 \u5206\uff0c\u7136\u5f8c\u518d\u4e58\u4e0a\u5be6\u969b\u8d0f\u7684\u5f97\u5206\u4f86\u5f97\u5230\u6700\u5f8c\u5f97\u5206\u3002\u7531\u65bc\u6240\u6709\u6e2c\u8cc7\u5e73\u5747\u4e0b\u4f86\u6bcf\u6b21\u8d0f\u7684\u5e73\u5747\u5f97\u5206\u662f 500\uff0c\u56e0\u6b64\u7d66\u5b9a\u7684\u76ee\u6a19 X \u9664\u4ee5 500 \u5373\u53ef\u8f49\u5316\u70ba\u7c21\u5316\u7248\u7684\u5f97\u5206\u3002\u4e09\u7d44\u6e2c\u8cc7\u5206\u5225\u5c0d\u61c9 29.2\u300131\u300132.8 \u5206\u3002<\/p>\n\n\n\n<p>\u4e0d\u904e\u4e5f\u8a31\u4e5f\u662f\u56e0\u70ba\u55ae\u7d14\u53ea\u6709\u60f3\u7684\u95dc\u4fc2\uff0c\u4e00\u958b\u59cb\u6389\u9032\u4e86\u4e00\u500b\u5f88\u5927\u7684\u8aa4\u5340\uff1a\u6216\u8a31\u53ef\u4ee5\u7d93\u7531\u9650\u5236\u81ea\u5df1\u7684\u51fa\u7684\u62f3\u7a2e\u4f86\u5f37\u8feb\u5c0d\u65b9\u51fa\u4e0d\u5229\u62f3\u7a2e\u3002\u9019\u53ef\u80fd\u662f\u88ab\u7bc4\u4f8b\u6e2c\u8cc7\u7684\u958b\u982d\u7d66\u8aa4\u5c0e\u4e86\u5427\uff1a\u7bc4\u4f8b\u7b2c\u4e00\u62f3\u51fa\u77f3\u982d\uff0c\u56e0\u6b64\u5c0d\u65b9\u7684\u7b2c\u4e8c\u62f3\u5fc5\u5b9a\u662f\u5e03\uff0c\u56e0\u6b64\u81ea\u5df1\u7b2c\u4e8c\u62f3\u51fa\u526a\u5200\u5373\u53ef\u78ba\u5be6\u7372\u52dd\u3002\u7136\u5f8c\u6211\u5c31\u5728\u601d\u8003\u5230\u5e95\u8981\u600e\u9ebc\u8abf\u6574\u5169\u62f3\u7684\u6bd4\u4f8b\u7d66\u81ea\u5df1\u512a\u52e2\u3002<\/p>\n\n\n\n<p>\u5728\u8003\u616e\u4e86\u534a\u5929\u6c92\u6709\u4e00\u500b\u597d\u7d50\u8ad6\u7684\u6642\u5019\u6c7a\u5b9a\u5c31\u5b9a\u4e00\u500b\u7c21\u55ae\u4e00\u9ede\u7684\u7b56\u7565\u4e0b\u53bb\u5beb\u7a0b\u5f0f\u4f86\u8a66\u2026\u2026\u7d50\u679c\u5e73\u5747\u6700\u597d\u7684\u5206\u6578\u662f 23.7 \u5206\u3002\u8a73\u7d30\u7b56\u7565\u5c31\u4e0d\u63d0\u4e86\uff0c\u4e0d\u904e\u9019\u7a2e\u721b\u5206\u6578\u9023\u7b2c\u4e00\u7d44\u6e2c\u8cc7\u90fd\u904e\u4e0d\u4e86\u2026\u2026<\/p>\n\n\n\n<p>\u4e0d\u904e\uff0c\u4e5f\u662f\u56e0\u70ba\u9019\u6b21\u5be6\u969b\u4e0b\u53bb\u5beb\u7a0b\u5f0f\u624d\u8b93\u6211\u6ce8\u610f\u5230\uff1a\u9019\u984c\u4e26\u4e0d\u9700\u8981\u63d0\u524d\u6c7a\u5b9a\u4ec0\u9ebc\u7b56\u7565\u4e5f\u53ef\u4ee5\u76f4\u63a5\u505a\u3002\u5f88\u5bb9\u6613\u770b\u5230\u4e0d\u7ba1\u662f\u4ec0\u9ebc\u7b56\u7565\uff0c\u5728\u8a08\u7b97\u6700\u4f73\u6b65\u9a5f\u6642\u4e00\u5b9a\u7b26\u5408 DP \u7d50\u69cb (\u56fa\u5b9a\u5df2\u51fa\u62f3\u7684\u6578\u91cf\uff0c\u51fa\u4ec0\u9ebc\u62f3\u53ef\u4ee5\u7531\u5c11\u6389\u8a72\u62f3\u7684\u6700\u4f73\u7d50\u679c\u9032\u884c\u6bd4\u8f03\u800c\u5f97)\uff0c\u56e0\u6b64\u4e0d\u9700\u8981\u63d0\u524d\u8a2d\u5b9a\u4ec0\u9ebc\u7b56\u7565\uff0c\u76f4\u63a5\u5229\u7528\u9019\u500b DP \u7d50\u69cb\u4e0b\u53bb\u8dd1\u5c31\u884c\u4e86\u3002<\/p>\n\n\n\n<p>\u4e5f\u5c31\u662f\u8aaa\uff0c\u9019\u984c\u662f\u500b\u5305\u88dd\u7684\u5f88\u7cbe\u7f8e\u7684\u7c21\u55ae DP \u984c\u3002\u6642\u9593\u8907\u96dc\u5ea6\u53ef\u4ee5\u9019\u9ebc\u4f30\u8a08\uff1a\u7e3d\u5171\u81f3\u591a N \u62f3\u7684\u5df2\u51fa\u62f3\u6578\u91cf\u7684\u7a2e\u985e\u6578\u662f \\(C^{N+3}_3=O(N^3)\\)\uff0c\u6bcf\u4e00\u683c\u6bd4\u8f03\u4e09\u7a2e\u62f3\u54ea\u4e00\u500b\u80fd\u5f97\u5230\u6700\u597d\u7684\u7d50\u679c\uff0c\u6240\u4ee5\u6642\u9593\u662f \\(O(N^3)\\)\uff1b\u984c\u76ee\u53ea\u6709\u56db\u7a2e\u4e0d\u540c\u7684 E\/W \u6bd4\u4f8b\uff0c\u6240\u4ee5\u751a\u81f3\u53ef\u4ee5\u5148\u628a\u56db\u7a2e\u6bd4\u4f8b\u7684\u6700\u4f73\u89e3\u90fd\u7b97\u51fa\u4f86 (\u5bb9\u6613\u770b\u5230\u6bd4\u4f8b\u76f8\u540c\u7684\u8f38\u5165\u6700\u4f73\u89e3\u4e5f\u6703\u76f8\u540c)\uff0c\u984c\u76ee\u7d66\u4ec0\u9ebc\u5c31\u4e1f\u4ec0\u9ebc\u51fa\u53bb\u5c31\u597d\u4e86\u3002<\/p>\n\n\n\n<p>\u6211 DP \u51fa\u4f86\u7684\u7d50\u679c\uff0c\u56db\u7a2e\u6bd4\u4f8b\u7684\u7c21\u5316\u5206\u6578\u5206\u5225\u662f\uff1aE\/W=1 \u5f97 41.64 \u5206\u3001E\/W=1\/2 \u5f97 33.34 \u5206\u3001E\/W=1\/10 \u5f97 29.15 \u5206\u3001E\/W=0 \u5f97 28.47 \u5206\uff0c\u56e0\u6b64\u5168\u90e8\u56db\u7a2e\u72c0\u614b\u7b49\u6bd4\u4f8b\u7684\u5e73\u5747\u503c\u662f 33.15 \u5206\uff0c\u8f15\u9b06\u8d85\u904e\u4e86\u984c\u76ee\u8981\u6c42\u7684 32.8 \u5206\u7684\u76ee\u6a19\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Q4. Binary Operator<\/h2>\n\n\n\n<p>\u9019\u984c\u4e4b\u6240\u4ee5\u6211\u9023\u5728\u8cfd\u5f8c\u90fd\u6c7a\u5b9a\u60f3\u8981\u628a\u5b83\u5beb\u51fa\u4f86\u7684\u539f\u56e0\u662f\uff1a\u9019\u984c\u660e\u64fa\u8457\u7d66\u4f60\u770b\u5c31\u662f\u500b\u8a9e\u6cd5\u6a39\u64cd\u4f5c\u984c\uff0c\u7b97\u662f\u6211\u70ba\u6578\u4e0d\u591a\u7684\u5f37\u9805\u4e4b\u4e00\u3002\u66fe\u7d93\u5728\u6211\u5927\u5b78\u51fa\u570b\u6bd4 ACM-ICPC \u7684\u6642\u5019\uff0c2009 \u5e74\u7684\u9996\u723e\u7ad9 pG \u6b63\u662f\u4e00\u500b\u8a9e\u6cd5\u6a39\u984c (\u90a3\u984c\u7c21\u55ae\u7684\u8aaa\u662f\uff1a\u7d66\u4f60\u4e00\u500b\u7c21\u5316\u7248\u7684 C struct \u5ba3\u544a\u53ca\u5c0d\u9f4a\u503c\uff0c\u6c42\u51fa\u8a72 struct \u4f54\u7684\u7a7a\u9593)\uff0c\u90a3\u4e00\u6b21\u6211\u5728\u8cfd\u4e2d\u96fb\u8166\u9592\u8457\u7684\u6642\u5019\u5c31\u4f54\u4f86\u5beb\u9019\u4e00\u984c\uff0c\u6700\u7d42\u62ff\u5230\u4e86\u9019\u984c\u7684\u9996\u6bba XD \u5370\u8c61\u6c92\u932f\u7684\u8a71\u4e8b\u5f8c\u770b\u6210\u7e3e\u8868\u597d\u50cf\u5168\u5834\u9023\u6211\u5011\u968a\u53ea\u6709\u5169\u968a\u9084\u4e09\u968a\u6709\u89e3\u51fa\u9019\u4e00\u984c\u7684\u6a23\u5b50\u3002<\/p>\n\n\n\n<p>\u9019\u4e00\u984c\u6c92\u6709\u50cf\u90a3\u984c ACM \u4e00\u6a23\u53ef\u6015\uff0c\u56e0\u70ba\u7d66\u4f60\u7684\u8f38\u5165\u5b57\u4e32\u751a\u81f3\u5e6b\u4f60\u5b8c\u5168\u62ec\u865f\uff0c\u4e5f\u5c31\u662f\u6211\u5011\u53ef\u4ee5\u7c21\u55ae\u5224\u65b7\u9019\u662f\u4e0d\u662f\u5f0f\u5b50\uff0c\u662f\u5f0f\u5b50\u7684\u8a71\u904b\u7b97\u5b50\u5728\u54ea\u88e1\uff1b\u4f46\u9019\u984c\u7684\u91cd\u9ede\u5176\u5be6\u662f\u8a9e\u6cd5\u6a39\u7684\u64cd\u4f5c\uff0c\u56e0\u70ba\u5c31\u9023\u5c0f\u6e2c\u8cc7\u90fd\u6703\u9700\u8981\u5c0d\u5f0f\u5b50\u9032\u884c\u4ea4\u63db\u5f8b\u3001\u7d50\u5408\u5f8b\u3001\u5206\u914d\u5f8b\u7684\u64cd\u4f5c\uff0c\u5927\u6e2c\u8cc7\u751a\u81f3\u9084\u9700\u8981\u5408\u4f75\u540c\u985e\u9805\uff1b\u9019\u5982\u679c\u6c92\u6709\u4e00\u500b\u597d\u7684\u8cc7\u6599\u7d50\u69cb\u7684\u8a71\u6703\u767c\u89ba\u975e\u5e38\u96e3\u4e0b\u624b\u64cd\u4f5c\u3002\u984c\u89e3\u88e1\u5c0d\u65bc\u5c0f\u6e2c\u8cc7\u7684\u5316\u7c21\u662f\u5229\u7528\u4e00\u500b\u56db\u5143\u7d44 <code>(A,B,C,D)<\/code> \u8868\u793a <code>(A#B)*C+D<\/code>\uff0c\u5229\u7528\u9019\u500b\u8868\u793a\u6cd5\u7684\u8a71\u4ea4\u63db\u5f8b\u548c\u7d50\u5408\u5f8b\u81ea\u52d5\u9069\u7528\uff0c\u5206\u914d\u5f8b\u5247\u53ea\u8981\u7c21\u55ae\u5730\u5c0d <code>C<\/code> \u548c <code>D<\/code> \u505a\u904b\u7b97\u5373\u53ef\u3002<\/p>\n\n\n\n<p>\u6211\u9019\u4e00\u984c\u672c\u4f86\u5c31\u662f\u6253\u7b97\u8981\u4e00\u53e3\u6c23\u5beb\u5168\u90e8\u7684\uff0c\u6240\u4ee5\u67b6\u69cb\u4e00\u958b\u59cb\u5c31\u4e0d\u662f\u9019\u7a2e\u7c21\u55ae\u7684\u5b9a\u5f0f\uff0c\u800c\u662f\u6bd4\u8f03\u901a\u7528\u7684\u591a\u9805\u5f0f\u7d50\u69cb\uff0c\u4e0d\u904e\u7d30\u7bc0\u5012\u4e5f\u662f\u7d93\u904e\u4e86\u5169\u4e09\u6b21\u7684\u6539\u52d5\u5c31\u662f\u3002\u6700\u7d42\u901a\u904e\u7684\u67b6\u69cb\u662f\u9019\u6a23\u7684\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>\u8f38\u4eba\u7684\u5b57\u4e32\u5c07\u5b83\u8f49\u6210\u985e\u4f3c\u984c\u89e3\u88e1\u63d0\u7684\u90a3\u7a2e\u8a9e\u6cd5\u6a39\uff0c\u7136\u5f8c\u5c31\u76f4\u63a5\u628a\u5f0f\u5b50\u5c55\u958b\u3002<ul><li>\u57fa\u672c\u55ae\u4f4d\u662f <code>vector&lt;\u4e58\u9805&gt;<\/code>\uff0c\u8868\u793a\u9019\u4e9b\u4e58\u9805\u7684\u548c\uff1b\u9019\u5c31\u662f\u6211\u4e0a\u9762\u63d0\u5230\u7684\u300c\u591a\u9805\u5f0f\u300d\u3002<\/li><li>\u5169\u500b\u9019\u6771\u897f\u7684 # \u904b\u7b97\u5c31\u7c21\u55ae\u5730\u628a\u5169\u8005\u5404\u81ea\u8f49\u6210\u5b57\u4e32\uff0c\u9023\u8d77\u4f86\u7576\u505a\u8ddf x y \u9019\u7a2e\u6771\u897f\u4e00\u6a23\u7684\u300c\u8b8a\u6578\u300d\u3002\u9019\u500b\u6703\u8b8a\u6210\u4e58\u9805\u7684\u8b8a\u6578\u55ae\u4f4d\uff1b\u6bcf\u500b\u4e58\u9805\u5176\u5be6\u5c31\u662f\u4e00\u500b <code>multiset<\/code> \u6536\u96c6\u9019\u4e00\u9805\u7684\u6240\u6709\u8b8a\u6578\u540d\uff0c\u52a0\u4e0a\u4e00\u500b\u5e38\u6578\u8868\u793a\u4fc2\u6578\u3002<\/li><li>\u5169\u500b\u9019\u6771\u897f\u76f8\u52a0\u5c31\u9032\u884c\u540c\u985e\u9805\u5224\u5b9a\u52a0\u8d77\u4f86\u3002\u6709\u4e86\u4e0a\u9762\u7684 <code>multiset<\/code>\uff0c\u540c\u985e\u9805\u5c31\u76f4\u63a5\u6bd4\u8f03\u5169\u500b <code>multiset<\/code> \u662f\u5426\u76f8\u7b49\u5373\u53ef\u3002<\/li><\/ul><ul><li>\u5169\u500b\u9019\u6771\u897f\u7684\u4e58\u6cd5\u5c31\u7c21\u55ae\u5730\u9032\u884c\u5206\u914d\u5f8b\u5168\u90e8\u4e58\u958b\uff0c\u5f97\u5230\u4e00\u5806\u4e58\u9805\u518d\u52a0\u8d77\u4f86\uff0c\u540c\u6a23\u9032\u884c\u540c\u985e\u9805\u5224\u5b9a\u3002<\/li><li>\u4e0a\u9762\u9019\u4e9b\u8655\u7406\u6703\u5c0d 0 \u9805\u7279\u5225\u64cd\u4f5c\uff1a0 \u52a0\u4efb\u4f55\u6771\u897f\u90fd\u4e0d\u8b8a\uff0c\u4e58\u4efb\u4f55\u6771\u897f\u90fd\u6703\u8b8a\u6210 0\u3002<\/li><\/ul><\/li><li>\u8655\u7406\u5b8c\u4e4b\u5f8c\u76f4\u63a5\u8f49\u6210\u5b57\u4e32\u3002\u70ba\u4e86\u4fdd\u8b49\u8f49\u6210\u7684\u5b57\u4e32\u552f\u4e00\uff0c\u984d\u5916\u505a\u4e86\u9019\u4e9b\u8655\u7406\uff1a<ul><li>\u591a\u9805\u5f0f\u628a\u6bcf\u500b\u4e58\u9805\u5404\u81ea\u5b57\u4e32\u5316\uff0c\u7528\u5b57\u4e32\u6392\u5e8f\u5f8c\u518d\u7528 <code>'+'<\/code> \u9023\u8d77\u4f86\uff1b<\/li><li>\u800c\u4e58\u9805\u7684\u5b57\u4e32\u5316\u5247\u76f4\u63a5\u4f7f\u7528 <code>multiset<\/code> \u5e6b\u5fd9\u6392\u7684\u9806\u5e8f\uff0c\u628a\u8b8a\u6578\u540d\u7528 <code>'*'<\/code> \u9023\u8d77\u4f86\uff1b<\/li><li># \u904b\u7b97\u7684\u5b57\u4e32\u5316\u5df2\u7d93\u5728\u4e0a\u9762\u63cf\u8ff0\u4e86\uff0c\u5404\u81ea\u905e\u8ff4\u5730\u61c9\u7528\u9019\u88e1\u63cf\u8ff0\u7684\u4e58\u9805\u548c\u5b57\u4e32\u5316\u3002<\/li><li>\u9019\u6a23\u505a\u96d6\u7136\u985e\u4f3c\u7684\u5f0f\u5b50\u6703\u6709\u4e0d\u540c\u7684\u540c\u985e\u9805\u6392\u5e8f\u9806\u5e8f\uff0c\u4f46\u81f3\u5c11\u5b83\u5011\u4e0d\u540c\uff1b\u56e0\u6b64\u6211\u5011\u53ea\u8981\u7c21\u55ae\u7684\u6bd4\u5c0d\u5b57\u4e32\u662f\u5426\u76f8\u540c\u5373\u53ef\u5224\u65b7\u662f\u5426\u662f\u4e00\u6a23\u7684\u5f0f\u5b50\u4e86\u3002<\/li><\/ul><\/li><li>\u53e6\u5916\uff0c\u5982\u540c\u7bc4\u4f8b\u6e2c\u8cc7\u7684\u7b2c\u4e09\u7d44\u6240\u6697\u793a\u7684\uff0c\u9019\u984c\u7684\u5e38\u6578\u6703\u9700\u8981\u5927\u6578\uff0c\u597d\u5728\u53ea\u6709\u52a0\u548c\u4e58\u6240\u4ee5\u5beb\u8d77\u4f86\u9084\u7b97\u7c21\u55ae\u3002<\/li><\/ul>\n\n\n\n<p>\u7531\u65bc\u6bcf\u500b\u5f0f\u5b50\u6700\u591a\u53ea\u6709 100 \u500b\u5b57\u5143\u9577\uff0c\u7d50\u69cb\u7684\u7e3d\u9577\u5ea6\u4e26\u4e0d\u6703\u592a\u9577\uff1b\u984c\u89e3\u88e1\u63d0\u5230\u7684\u5206\u914d\u5f8b\u5730\u7344\u8f38\u5165\uff1a<\/p>\n\n\n\n<p class=\"has-text-align-center\"><code>((0#1)+1)*((0#2)+1)*((0#3)+1)*\u2026<\/code><\/p>\n\n\n\n<p>\u4ed4\u7d30\u7b97\u4e00\u7b97\u5c31\u6703\u767c\u73fe\u8a08\u5165\u5b8c\u5168\u62ec\u865f\u5f8c\u6700\u591a\u53ea\u6703\u6709\u516b\u500b\u52a0\u9805\u76f8\u4e58\uff0c\u4e5f\u5c31\u662f\u540c\u985e\u9805\u81f3\u591a\u53ea\u6709 256 \u7a2e\uff0c\u6240\u4ee5\u751a\u81f3\u9023\u540c\u985e\u9805\u5224\u5b9a\u90fd\u4e0d\u9700\u8981\u984d\u5916\u8cc7\u6599\u7d50\u69cb\uff0c\u628a\u6240\u6709\u9805\u7dda\u6027\u5730\u6383\u904e\u4e00\u6b21\u90fd\u662f\u8db3\u5920\u7684\uff1b\u800c\u8f38\u5165\u7684\u5f0f\u5b50\u6700\u591a\u4e5f\u53ea\u6709 100 \u500b\uff0c\u56e0\u6b64\u5224\u5b9a\u5f0f\u5b50\u662f\u5426\u76f8\u7b49\u4e5f\u53ef\u4ee5\u7dda\u6027\u5730\u6383\u904e\u4e00\u6b21 (\u800c\u4e14\u5f88\u5927\u6a5f\u7387\u5169\u500b\u5b57\u4e32\u9577\u5ea6\u4e0d\u540c\uff0c\u6240\u4ee5\u5224\u5b9a\u4e0d\u540c\u7684\u901f\u5ea6\u5e7e\u4e4e\u90fd\u5f88\u5feb)\u3002\u6211\u9001\u901a\u904e\u7684\u7a0b\u5f0f\u88e1\u7684\u5e38\u6578\u8a08\u7b97\u751a\u81f3\u5168\u90e8\u90fd\u662f\u5341\u9032\u4f4d\u5927\u6578\uff0c\u4f46\u5c31\u9023\u9019\u6a23\u7684\u8a08\u7b97\u91cf\u90fd\u662f\u80fd\u5920\u901a\u904e\u6e2c\u8a66\u7684\u3002<\/p>\n\n\n\n<p>\u9019\u88e1\u53ef\u4ee5\u4e5f\u63d0\u4e00\u4e0b\u984c\u89e3\u88e1\u63d0\u5230\u7684\u53e6\u985e\u505a\u6cd5\u3002\u9019\u5176\u5be6\u662f\u4e00\u500b\u66f4\u5ee3\u4e00\u9ede\u7684\u6982\u5ff5\u7684\u61c9\u7528\uff1a\u5169\u500b (\u6709\u9650\u7684) \u591a\u9805\u5f0f\u5982\u679c\u5b83\u5011\u4e0d\u6046\u7b49\uff0c\u5247\u5b83\u5011\u53d6\u503c\u76f8\u540c\u7684\u5730\u65b9\u53ea\u6703\u662f\u76f8\u5c0d\u5f88\u5c0f\u5f88\u5c0f\u7684\u4e00\u90e8\u4efd\u3002\u56e0\u6b64\u5982\u679c\u6211\u5011\u5c07\u8b8a\u6578\u96a8\u6a5f\u53d6\u503c\u7684\u8a71\uff0c\u6709\u5f88\u5927\u6a5f\u7387\u6703\u628a\u4e0d\u540c\u7684\u591a\u9805\u5f0f\u5c0d\u61c9\u5230\u4e0d\u540c\u7684\u503c\uff0c\u5c31\u80fd\u85c9\u6b64\u5224\u65b7\u5169\u8005\u662f\u5426 (\u6709\u5f88\u9ad8\u7684\u6a5f\u6703) \u4e0d\u6046\u7b49\u3002\u540c\u6a23\u6982\u5ff5\u7684\u5176\u4ed6\u61c9\u7528\u9084\u6709\u4f7f\u7528\u5728\u96fb\u8166\u5c0d\u5c40\u7684 <a href=\"https:\/\/en.wikipedia.org\/wiki\/Zobrist_hashing\">Zobrist Hashing<\/a>\uff0c\u5b83\u5c07\u5c40\u9762\u5316\u6210\u4e86\u5404\u9805\u8981\u7d20\u7684\u96c6\u5408\uff0c\u7136\u5f8c\u5c07\u8981\u7d20\u96a8\u6a5f\u53d6\u503c\uff0c\u4ee3\u5165\u7e3d\u96c6\u7684\u7dda\u6027\u904b\u7b97 (\u591a\u534a\u662f XOR) \u7576\u4e2d\u5f97\u5230\u9019\u500b\u5c40\u9762\u7684\u96dc\u6e4a\u503c\uff1b\u6839\u64da\u985e\u4f3c\u7684\u7406\u7531\uff0c\u4e0d\u540c\u7684\u5c40\u9762\u56e0\u70ba\u5177\u6709\u7684\u8981\u7d20\u4e0d\u540c\uff0c\u7dda\u6027\u904b\u7b97\u7684\u7d50\u679c\u6709\u5f88\u5927\u6a5f\u7387\u6703\u662f\u4e0d\u540c\u7684\u96dc\u6e4a\u503c\uff0c\u5c31\u80fd\u7528\u5f88\u5c11\u91cf\u7684\u8a08\u7b97\u53bb\u5feb\u901f\u5224\u65b7\u5169\u500b\u5c40\u9762\u662f\u76f8\u540c\u6216\u662f\u4e0d\u540c\uff0c\u9032\u800c\u53ef\u4ee5\u70ba\u5176\u5efa\u7acb\u96dc\u6e4a\u8868\u683c\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u7e3d\u7d50<\/h2>\n\n\n\n<p>\u9019\u6b21\u7684\u984c\u76ee\u539f\u672c\u4ee5\u70ba\u53ea\u6709\u5169\u984c\u7c21\u55ae\uff0c\u5728\u6df1\u5165\u601d\u8003\u4ee5\u53ca\u5be6\u969b\u5beb\u7a0b\u5f0f\u4e4b\u5f8c\u624d\u6ce8\u610f\u5230\u539f\u4f86\u7b2c\u4e09\u984c\u7684\u6838\u5fc3\u4e5f\u975e\u5e38\u7c21\u55ae\uff0c\u53ea\u662f\u88ab\u5305\u88dd\u5f97\u5f88\u7cbe\u7f8e\u800c\u5df2\u3002\u7b2c\u56db\u984c\u5247\u5f88\u6709\u8da3\uff1a\u6b63\u898f\u8def\u7dda\u5176\u5be6\u4e0d\u597d\u505a\uff0c\u4f46\u53ef\u4ee5\u53d6\u5de7\u5f97\u5230\u4e00\u500b\u9ad8\u6a5f\u7387\u6b63\u78ba\u7684\u505a\u6cd5\u3002<\/p>\n\n\n\n<p>\u5982\u540c\u4e4b\u524d\u63d0\u5230\u7684\uff0c\u4e0b\u4e00\u56de\u4e03\u6708\u521d\u7684 GKS Round D \u6211\u6709\u4e8b\u7121\u6cd5\u53c3\u52a0\uff0cRound E \u5c31\u8981\u5230\u4e09\u500b\u6708\u4e4b\u5f8c\u7684\u516b\u6708\u5e95\u4e86\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u6700\u8fd1\u7761\u7720\u6642\u9593\u6709\u9ede\u56e7\uff0c\u665a\u4e0a\u8d77\u4f86\u7684\u6642\u9593\u8b93\u958b\u8cfd\u6642\u8166\u888b\u9084\u662f\u4e00\u534a\u7761\u8457\u7684\u72c0\u614b\u6240\u4ee5\u51fa\u4e86\u597d\u4e9b\u500b\u7c21\u55ae\u5931\u8aa4\u5403\u4e86\u4e0d\u5c11 attempt [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[7,4],"tags":[],"class_list":["post-712","post","type-post","status-publish","format-standard","hentry","category-gcj","category-programming"],"_links":{"self":[{"href":"https:\/\/blog.cruciferslab.net\/index.php?rest_route=\/wp\/v2\/posts\/712","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.cruciferslab.net\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.cruciferslab.net\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.cruciferslab.net\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.cruciferslab.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=712"}],"version-history":[{"count":6,"href":"https:\/\/blog.cruciferslab.net\/index.php?rest_route=\/wp\/v2\/posts\/712\/revisions"}],"predecessor-version":[{"id":833,"href":"https:\/\/blog.cruciferslab.net\/index.php?rest_route=\/wp\/v2\/posts\/712\/revisions\/833"}],"wp:attachment":[{"href":"https:\/\/blog.cruciferslab.net\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=712"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.cruciferslab.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=712"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.cruciferslab.net\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=712"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}