{"id":1587,"date":"2023-12-01T15:22:04","date_gmt":"2023-12-01T07:22:04","guid":{"rendered":"https:\/\/blog.cruciferslab.net\/?p=1587"},"modified":"2025-11-26T17:27:49","modified_gmt":"2025-11-26T09:27:49","slug":"advent-of-code-2023","status":"publish","type":"post","link":"https:\/\/blog.cruciferslab.net\/?p=1587","title":{"rendered":"Advent of Code 2023"},"content":{"rendered":"\n<p>\u53c8\u5230\u4e86\u5e74\u672b Advent of Code \u7684\u6642\u9593\u4e86\u3002\u95dc\u65bc\u9019\u500b\u6d3b\u52d5\u9084\u8acb\u53c3\u7167<a href=\"https:\/\/blog.cruciferslab.net\/?p=1153\" data-type=\"post\" data-id=\"1153\">\u53bb\u5e74\u7684\u6587\u7ae0<\/a>\uff1b\u4e0d\u904e\u9451\u65bc\u53bb\u5e74\u524d\u5e7e\u5929\u767c\u751f\u7684\u4e8b\u60c5\uff0c\u4eca\u5e74\u65b0\u589e\u4e86\u4e00\u689d\u300c<a href=\"https:\/\/adventofcode.com\/about#faq_ai_leaderboard\">\u7981\u6b62\u4f7f\u7528 AI \u53bb\u767b\u5165\u5168\u7ad9\u6392\u884c\u699c<\/a>\u300d\u7684\u898f\u5247\u2014\u2014\u4e26\u6c92\u6709\u5168\u9762\u7981\u6b62 AI\uff0c\u53ea\u6709\u4e0d\u5141\u8a31\u4f7f\u7528 AI \u8b93\u81ea\u5df1\u767b\u5165\u5168\u7ad9\u524d\u767e\u540d\u7684\u6392\u884c\u699c\u800c\u5df2\u3002\u7b97\u662f\u500b\u6eff\u5408\u7406\u7684\u9650\u5236\u5c31\u662f\u4e86\u3002<\/p>\n\n\n\n<p>\u8a71\u8aaa\u9019\u4e00\u5e74\u4f86\u9084\u771f\u7684\u6c92\u591a\u5c11\u6587\u7ae0\u8cbc\u51fa\u4f86\u904e\u2026\u2026\u5728\u6aaf\u9762\u4e0b\u505a\u7684\u6771\u897f\u4e00\u76f4\u6709\u5728\u8f49\uff0c\u4f46\u7bc4\u570d\u7a0d\u5fae\u5927\u4e86\u4e00\u9ede\uff08\u6709\u4e00\u500b\u8ddf Advent of Code \u76f8\u95dc\u7684\u6771\u897f\u5dee\u4e86\u6700\u5f8c\u90a3 5% \u9084\u6c92\u5b8c\u6210\uff0c\u7d50\u679c\u4eca\u5e74\u7684\u53c8\u4f86\u4e86\uff09\uff0c\u5de5\u4f5c\u53c8\u76f8\u5c0d\u5fd9\u4e86\u4e00\u4e9b\uff08\u5fd9\u5230\u9023 GMTK Game Jam 2023 \u90fd\u6c92\u80fd\u53c3\u52a0\u2026\u2026\u90a3\u500b\u9031\u672b\u6574\u500b\u7d2f\u58de\u4e86\uff09\uff0c\u6240\u4ee5\u4e00\u76f4\u6c92\u80fd\u8cbc\u4e9b\u6771\u897f\u3002<\/p>\n\n\n\n<p>\u90a3\u9ebc\u7167\u4f8b\u7e7c\u7e8c\u95b1\u8b80\u4e4b\u5f8c\u5c31\u662f\u5404\u984c\u7684\u7c21\u8981\u5fc3\u5f97 (\u65bc\u662f\u81ea\u7136\u6709\u5404\u984c\u7684\u96f7)\uff0c\u7136\u5f8c\u4e5f\u662f\u7167\u4f8b\u6587\u7ae0\u62bc 12\/1 \u767c\u51fa\uff0c\u4f46\u4e4b\u5f8c\u6bcf\u5929\u984c\u76ee\u505a\u5b8c\u90fd\u6703\u4f86\u66f4\u65b0\u3002\u539f\u59cb\u78bc\u6574\u7406\u5728<a href=\"https:\/\/github.com\/progheal\/adventofcode\">\u540c\u4e00\u500b github repo<\/a> \u4e0a\u4e86\u3002<\/p>\n\n\n\n<!--more-->\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">1. Trebushet?!<\/h2>\n\n\n\n<p>\u7167\u4f8b\u7b2c\u4e00\u984c\u662f\u6696\u8eab\u984c\uff0c\u4e0d\u904e\u53ef\u80fd\u56e0\u70ba\u4eca\u5e74\u4e00\u865f\u5728\u9031\u4e94\u5427\uff0c\u4eca\u5e74\u7684\u7b2c\u4e00\u984c\u6709\u597d\u4e9b\u500b\u9677\u9631\u5728\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Part 1 \u4e00\u884c\u4e2d\u53ea\u6709\u4e00\u500b\u963f\u62c9\u4f2f\u6578\u5b57\uff1a<br>\u9019\u4e0d\u592a\u7b97\u662f\u9677\u9631\uff0c\u4f46\u81f3\u5c11\u7b97\u662f\u500b\u8981\u5c0f\u8de8\u4e00\u4e0b\u7684\u5d01\u6c92\u932f\u3002<\/li>\n\n\n\n<li>Part 2 \u6240\u7d66\u7684\u6587\u5b57\u4e2d\u6c92\u6709 zero\uff0c\u7531 one \u958b\u59cb\uff1a<br>\u6240\u4ee5\u5982\u679c\u53ea\u662f\u55ae\u7d14\u5efa\u8868\u7136\u5f8c\u8ff4\u5708\u8dd1\u5c31\u53ef\u80fd\u6703\u6709\u5dee\u4e00\u554f\u984c (<code>\"one\"<\/code> \u5728 <code>[0]<\/code> \u4e4b\u985e\u7684)\u3002<\/li>\n\n\n\n<li>Part 2 \u6578\u5b57\u4e4b\u9593\u53ef\u80fd\u91cd\u758a\uff0c\u4f8b\u5982\u7bc4\u4f8b\u7684 eightwo\uff1a<br>\u6240\u4ee5\u5982\u679c\u662f\u5c07\u6587\u5b57\u53d6\u4ee3\u6210\u6578\u5b57\u518d\u5957 part 1 \u7684\u5c31\u53ef\u80fd\u6703\u6b7b\uff1b\u6211\u5728\u7684 DC \u7fa4\u88e1<sup data-fn=\"ff82ba11-be10-4a9e-a3ff-f7f7d9c4a0e5\" class=\"fn\"><a href=\"#ff82ba11-be10-4a9e-a3ff-f7f7d9c4a0e5\" id=\"ff82ba11-be10-4a9e-a3ff-f7f7d9c4a0e5-link\">1<\/a><\/sup>\u6709\u4e00\u500b\u4eba\u5c31\u4e2d\u4e86\u9019\u62db\u3002<\/li>\n<\/ul>\n\n\n\n<p>\u6211\u5247\u662f\u56e0\u70ba\u4e00\u5e74\u6c92\u6709\u7528 AOC \u51fd\u5f0f\u5eab\u4e86\uff0c\u5dee\u9ede\u5fd8\u8a18\u8981\u600e\u9ebc\u8b80\u5b57\u4e32\u9032\u4f86 XD\u3002\u9019\u984c\u9084\u4e0d\u80fd\u7528\u5148\u524d\u7528\u904e\u7684\u53ea\u8b80\u6578\u5b57\u7684\u62db\uff0c\u56e0\u70ba\u5373\u4f7f\u53ea\u8b80\u963f\u62c9\u4f2f\u6578\u5b57\u7684 part 1 \u4e5f\u662f\u8981\u628a\u6578\u5b57\u7576\u6210\u6587\u5b57\u53bb\u53d6\u9996\u4f4d\uff0c\u5168\u90e8\u8b80\u6210\u4e00\u500b\u5927\u6578\u5b57\u518d\u53d6\u5c31\u6703\u5f88\u96e3\u641e\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">2. Cube Conundrum<\/h2>\n\n\n\n<p>\u6a19\u6e96\u7684\u8f38\u5165\u5206\u6790\u984c\u3002\u65bc\u662f\u53c8\u662f\u8907\u7fd2\u6211\u7684\u8f38\u5165\u51fd\u5f0f\u5eab\u7684\u6642\u5019\u4e86\u3002DC \u7fa4\u88e1\u7684\u67d0\u4eba\u628a\u9019\u7a2e\u5beb\u6cd5\u53eb\u505a slice spam\uff0c\u4e3b\u8981\u662f\u56e0\u70ba JavaScript \u7684\u5b57\u4e32\u6709\u4e00\u500b\u53eb <code>.slice()<\/code> \u7684\u51fd\u6578\u53ef\u4ee5\u5c07\u8f38\u5165\u5b57\u4e32\u4ee5\u7d66\u5b9a\u5b57\u4e32\u505a\u5206\u754c\u9ede\u5207\u958b\uff0c\u6240\u4ee5\u9019\u984c\u7684\u5206\u6790\u5c31\u6703\u8b8a\u6210\uff1a\u7528\u5192\u865f\u5207\u958b\uff0c\u524d\u9762\u662f\u7b2c\u5e7e\u5c40\uff1b\u5f8c\u9762\u7528\u5206\u865f\u5207\u958b\uff0c\u6bcf\u4e00\u6bb5\u662f\u4e00\u6b21\u62bd\u7684\u7d50\u679c\uff1b\u9019\u4e00\u6bb5\u7528\u9017\u865f\u5207\u958b\uff0c\u6bcf\u4e00\u6bb5\u662f\u4e00\u7a2e\u984f\u8272\uff1b\u6700\u5f8c\u518d\u7528\u7a7a\u683c\u5207\u958b\uff0c[0] \u662f\u500b\u6578\uff0c[1] \u662f\u984f\u8272\u3002\u6211\u7684\u7a0b\u5f0f\u5dee\u4e0d\u591a\u4e5f\u662f\u4e00\u6a23\u7684\u908f\u8f2f\uff0c\u53ea\u662f\u6211\u662f\u7528\u6211\u81ea\u5df1\u7684\u5207\u5272\u51fd\u6578\u5c31\u662f\u4e86\u3002<\/p>\n\n\n\n<p>\u6211\u5176\u5be6\u4e00\u76f4\u89ba\u5f97\uff0c\u5b57\u4e32\u8655\u7406\u7df4\u7fd2\u984c\u662f\u6e2c\u8a66\u4e00\u500b\u7a0b\u5f0f\u521d\u5b78\u8005\u5c0d\u4ed6\u6240\u5b78\u7fd2\u7684\u7a0b\u5f0f\u8a9e\u8a00\u7684\u719f\u6089\u5ea6\u5f88\u68d2\u7684\u984c\u6750\u3002\u9019\u5169\u5929\u7684\u984c\u76ee\u53ef\u4ee5\u770b\u51fa\u9019\u4e00\u9ede\uff1aDay 1 part 2 \u662f\u5c0b\u627e\u5b50\u5b57\u4e32\uff0cDay 2 \u7684\u8f38\u5165\u672c\u8eab\u5247\u662f\u6a19\u6e96\u7684\u5b57\u4e32\u62c6\u5206\uff0c\u800c\u9019\u5169\u5929\u90fd\u5f88\u5e38\u770b\u5230 reddit \u4e0a\u6709\u5404\u7a2e\u6c42\u6551\u7121\u5f9e\u4e0b\u624b\u7684\u63d0\u554f\uff1bAoC \u8f38\u5165\u6a94\u6848\u7684\u591a\u6a23\u6027\u53ef\u4ee5\u8b93\u4eba\u7df4\u7fd2\u7c21\u55ae\u7a0b\u5ea6\u7684\u8f38\u5165\u5206\u6790\uff0c\u6211\u89ba\u5f97\u662f\u4ef6\u4e0d\u932f\u7684\u4e8b\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">3. Gear Ratios<\/h2>\n\n\n\n<p>\u7d50\u679c\u4eca\u5e74\u7684\u958b\u5834\u90fd\u662f\u5b57\u4e32\u5206\u6790\u984c\u55ce XDDDDD \u5beb\u6587\u7576\u4e0b\u9084\u6c92\u722c\u6587\uff0c\u4e0d\u904e\u6211\u53ef\u4ee5\u60f3\u898b\u6703\u6709\u4e0d\u5c11\u4eba\u6293\u7834\u982d\u60f3\u4e0d\u5230\u8981\u600e\u9ebc\u505a\u3002<\/p>\n\n\n\n<p>\u6211\u7684\u505a\u6cd5\u6bd4\u8f03\u76f4\u63a5\u4e00\u9ede\uff1aPart 1 \u4ee5\u6578\u5b57\u70ba\u6e96\uff0c\u627e\u5230\u6578\u5b57\u4e4b\u5f8c\u53bb\u56db\u5468\u770b\u4e00\u770b\u6709\u6c92\u6709\u7b26\u865f\uff1bPart 2 \u60f3\u4e86\u4e00\u4e0b\uff0c\u767c\u89ba\u5982\u679c\u4ee5\u7b26\u865f\u70ba\u4e3b\u689d\u4ef6\u6703\u4e0d\u592a\u597d\u5beb\uff0c\u6240\u4ee5\u4ecd\u7136\u4f7f\u7528\u539f\u672c\u4ee5\u6578\u5b57\u70ba\u6e96\u7684\u627e\u6cd5\uff0c\u53ea\u662f\u5c0d\u5468\u570d\u6240\u6709\u7b26\u865f\uff0c\u5982\u679c\u662f\u661f\u865f\u5c31\u8a18\u4e0b\u9019\u500b\u4f4d\u7f6e\u6709\u9019\u500b\u6578\u5b57\uff0c\u7136\u5f8c\u6700\u5f8c\u518d\u8dd1\u4e00\u6b21\u6240\u6709\u661f\u865f\u7d00\u9304\u5c31\u884c\u4e86\u3002<\/p>\n\n\n\n<p>\u4e4b\u6240\u4ee5\u4ee5\u7b26\u865f\u70ba\u4e3b\u689d\u4ef6\u4e0d\u597d\u5beb\u7684\u539f\u56e0\u662f\uff1a\u4f8b\u5982\u770b\u5230\u4e86\u4e00\u500b\u661f\u865f\u3002\u8981\u600e\u9ebc\u5224\u65b7\u4e0a\u9762\u6216\u4e0b\u9762\u7684\u6578\u5b57\u54ea\u4e9b\u662f\u4e00\u8d77\u7684\uff0c\u54ea\u4e9b\u662f\u5206\u958b\u7684\uff1f\u8981\u600e\u9ebc\u5f9e\u7b26\u865f\u56db\u5468\u7684\u6578\u5b57\u53bb\u627e\u51fa\u5b83\u7684\u5de6\u53f3\u7aef\u9ede\uff1f\u9019\u7a2e\u554f\u984c\u7684\u5224\u65b7\u689d\u4ef6\u5f88\u7d30\u7bc0\uff0c\u5f88\u5bb9\u6613\u5beb\u932f\uff0c\u7136\u5f8c\u5c31\u6709\u4e00\u5806\u908a\u754c\u689d\u4ef6\u8981\u6e2c\u8a66\uff1b\u4f46\u7576\u6709 part 1 \u7684\u57fa\u790e\u7a0b\u5f0f\u78bc\u4e4b\u5f8c\uff0c\u53ea\u8981\u6ce8\u610f\u5230 part 1 \u6240\u5224\u65b7\u7684\u689d\u4ef6\u5176\u5be6\u5c31\u662f\u5efa\u7acb\u4e86\u6211\u5011 part 2 \u6240\u9700\u8981\u7684\u9023\u7d50\u2014\u2014\u9019\u500b\u6578\u5c6c\u65bc\u9019\u88e1\u7684\u7b26\u865f\uff0c\u90a3\u9ebc part 2 \u5c31\u53ea\u662f\u5c0d\u9019\u500b\u9023\u7d50\u9032\u884c\u53cd\u5411\u67e5\u8a62\u800c\u5df2\uff0c\u4e0d\u5fc5\u8981\u91cd\u65b0\u5f9e\u53e6\u4e00\u7aef\u518d\u6b21\u5efa\u7acb\u9023\u7d50\u3002<\/p>\n\n\n\n<p>\u88dc\u8a3b\uff1a\u7d50\u679c\u7a0d\u5fae\u722c\u904e reddit \u5f8c\u767c\u73fe\u6700\u5927\u7684\u5751\u5176\u5be6\u662f <code>indexOf<\/code> \u985e\u578b\u7684\u51fd\u6578\u2026\u2026\u81f3\u5c11\u770b\u5230\u6709\u4e09\u500b\u4eba\u6389\u5230\u9019\u500b\u5751\u88e1\u3002\u4e3b\u8981\u554f\u984c\u5728\u4ed6\u5011\u662f\u5148\u7be9\u51fa\u6578\u5b57\u518d\u7528 <code>indexOf<\/code> \u985e\u578b\u51fd\u6578\u56de\u982d\u627e\u4f4d\u7f6e\uff0c\u7136\u5f8c\u5c31\u88ab\u540c\u4e00\u884c\u4e2d\u524d\u9762\u51fa\u73fe\u7684\u76f8\u540c\u6578\u5b57\u7d66\u5751\u4e86\u3002<\/p>\n\n\n\n<p>\u88dc\u8a3b\u7684\u88dc\u8a3b\uff1a\u5beb\u4e0a\u9762\u9019\u6bb5\u8a71\u6642\u6211\u53ea\u770b\u5230\u4e09\u500b\uff0c\u4f46\u770b\u4e86\u4e00\u665a\u4e0a\u6211\u767c\u73fe\u6389\u9032\u9019\u5751\u7684\u4eba\u4e0d\u662f\u666e\u901a\u7684\u591a\u2026\u2026\u6703\u6389\u9032\u53bb\u7684\u5e7e\u4e4e\u90fd\u662f\u652f\u63f4 regex \u641c\u5c0b\u7684\u8a9e\u8a00\uff0c\u5982 python\u3001javascript \u7b49\uff0c\u5927\u6982\u56e0\u70ba\u6709\u7684\u662f\u9019\u7a2e\u627e\u51fa\u300c\u5b57\u300d\u800c\u4e0d\u662f\u627e\u51fa\u300c\u4f4d\u7f6e\u300d\u7684\u51fd\u6578\u624d\u6703\u6389\u9032\u56de\u982d\u641c\u5c0b\u641c\u932f\u5730\u65b9\u7684\u5751\u88e1\uff1b\u561b\uff0c\u8a8d\u771f\u8aaa\u8d77\u4f86\u5176\u5be6\u9019\u985e\u578b\u7684\u51fd\u6578\u7684\u56de\u50b3\u7d50\u679c\u4e00\u5b9a\u4e0d\u53ea\u662f\u627e\u5230\u4ec0\u9ebc\u5b57\uff0c\u4f46\u6211\u60f3\u5f9e\u7bc4\u4f8b\u5b78\u7a0b\u5f0f\u7684\u4eba\u61c9\u8a72\u5f88\u96e3\u6703\u4e3b\u52d5\u53bb\u627e\u51fd\u5f0f\u5eab\u8cc7\u6599\u770b\u6709\u6c92\u6709\u5176\u4ed6\u6771\u897f\u53ef\u4ee5\u7528\u5c31\u662f\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">4. Scratchcards<\/h2>\n\n\n\n<p>\u7d42\u65bc\u56de\u5230\u4e86\u6a19\u6e96\u5316\u8f38\u5165\u7684\u984c\u76ee\u4e86\u3002\u9019\u984c\u662f\u7c21\u55ae\u7684\u6a02\u900f\u5c0d\u734e\u984c\uff0c\u61c9\u8a72\u4e0d\u662f\u4ec0\u9ebc\u56f0\u96e3\u7684\u6771\u897f\uff1b\u5927\u6982\u56e0\u6b64 part 2 \u52a0\u4e86\u4e00\u500b\u6efe\u96ea\u7403\u5f0f\u514c\u734e\u6cd5\uff0c\u662f\u500b\u8981\u60f3\u4e00\u4e0b\u600e\u9ebc\u5beb\u6703\u6bd4\u8f03\u5bb9\u6613\u7684\u984c\u76ee\u3002<\/p>\n\n\n\n<p>\u2026\u2026\u53ea\u662f\u6211\u679c\u7136\u9084\u662f\u5c0f\u770b\u4e86\u601d\u8003\u4e00\u76f4\u7dda\u7684\u4eba\u662f\u600e\u9ebc\u60f3\u7684\u3002Reddit \u4e0a\u770b\u5230\u7684\u554f\u984c\u4e3b\u8981\u662f\uff1a\u7528\u6700\u76f4\u89ba\u7684\u65b9\u6cd5\u6efe\u96ea\u7403\uff0c\u6240\u4ee5\u4e00\u5f35\u4e2d\u4e86\u4e09\u500b\u5c31\u53bb\u547c\u53eb\u5f8c\u4e09\u500b\u4f86\u7b97\u3002\u9019\u6a23\u7576\u7136\u6703\u905e\u8ff4\u7206\u70b8\u554a\u2026\u2026<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">5. If You Give A Seed A Fertilizer<\/h2>\n\n\n\n<p>\u4eca\u5e74\u7684\u96e3\u5ea6\u770b\u8d77\u4f86\u6703\u5f88\u98c4\uff1a\u524d\u4e94\u984c\u662f 1\u30013\u30015 \u504f\u96e3\uff0c2\u30014 \u504f\u7c21\u55ae\u3002<\/p>\n\n\n\n<p>\u9019\u984c\u7684\u984c\u76ee\u6558\u8ff0\u770b\u8d77\u4f86\u5f88\u7121\u8f9c\uff1a\u7d66\u5b9a\u4e00\u9023\u4e32\u7684\u5c0d\u61c9\u51fd\u6578 (\u4e00\u500b\u51fd\u6578\u7531\u591a\u5217 <code>dest src len<\/code> \u8868\u793a\uff0c\u6bcf\u4e00\u500b\u9019\u6a23\u7684\u5217\u8868\u793a\u7531 src \u5230 src+len-1 \u7684\u503c\u7d93\u904e\u51fd\u6578\u5f8c\u4f9d\u5e8f\u8b8a\u6210 dest \u5230 dest+len-1)\uff0c\u6c42\u7d66\u5b9a\u503c\u5e8f\u5217\u7d93\u904e\u9019\u4e00\u4e32\u51fd\u6578\u5f8c\u7684\u6700\u5f8c\u7d50\u679c\u4e2d\u6700\u5c0f\u7684\u90a3\u500b\u3002\u770b\u8d77\u4f86\u5f88 OK \u5c0d\u5427\uff1f\u7136\u5f8c\u7576\u4f60\u6253\u958b\u8f38\u5165\u6a94\u767c\u73fe\u6240\u6709\u6578\u5b57\u90fd\u662f 9 \u4f4d 10 \u4f4d\u7684\u6574\u6578\u3002\u597d\uff0c\u90a3\u5c31\u7528\u7bc4\u570d\u6bd4\u5c0d\u4e00\u8def\u67e5\u904e\u53bb\u884c\u4e86\u5427\uff1f\u7136\u5f8c part 2 \u544a\u8a34\u4f60\u300c\u5662\uff0c\u7d66\u4f60\u7684\u9019\u5e8f\u5217\u5176\u5be6\u6bcf\u4e00\u5c0d\u6578\u5b57\u662f\u4e00\u500b\u7bc4\u570d\uff0c\u6240\u4ee5\u5176\u5be6\u8f38\u5165\u503c\u4e5f\u6709 (\u67d0 10 \u4f4d\u6578) \u500b\u300d\u3002<\/p>\n\n\n\n<p>\u70ba\u6b64\u6211\u5728 part 1 \u5230 part 2 \u4e2d\u9593\u628a part 1 \u88e1\u5beb\u5728\u5c0d\u7167\u8868\u88e1\u7684\u6574\u6578\u5340\u9593\u7d66\u5b8c\u5168\u91cd\u69cb\u51fa\u4f86\uff0c\u7368\u7acb\u6210\u4e00\u500b\u5340\u9593 class\u3002\u597d\u5728\u5404\u7a2e\u7d30\u7bc0\u4e0a\u7684\u5be6\u4f5c\u6c92\u6709\u4ec0\u9ebc\u554f\u984c\uff0c\u5340\u9593 class \u641e\u5b9a\u4e4b\u5f8c\u4e3b\u908f\u8f2f\u4e00\u6b21\u901a\u95dc\uff1b\u7136\u5f8c\u53c8\u8b93\u6211\u597d\u597d (\u6feb) \u7528\u4e86 <code>&lt;=&gt;<\/code> \u9019\u6771\u897f\u4e86\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">6. Wait For It<\/h2>\n\n\n\n<p>\u96d6\u7136\u6709\u5176\u4ed6\u505a\u6cd5\uff0c\u4f46\u9019\u984c\u5c0d\u6211\u4f86\u8aaa\u662f\u767e\u5206\u4e4b\u767e\u7684\u6578\u5b78\u984c\u3002<\/p>\n\n\n\n<details class=\"wp-block-inline-spoilers-block\"><summary>\u9ede\u9078\u6b64\u8655\u5c55\u958b\u672c\u984c\u6578\u5b78\u89e3\u3002<\/summary>\u4ee4\u7e3d\u8cfd\u4e8b\u7684\u6642\u9593\u662f \\(T\\)\uff0c\u7d00\u9304\u8ddd\u96e2\u70ba \\(D\\)\uff0c\u6309\u4f4f\u6309\u9215\u7684\u6642\u9593\u70ba \\(t\\)\uff1b\u90a3\u9ebc\u884c\u8d70\u7684\u8ddd\u96e2\u5c31\u662f \\(t(T-t)\\)\u3002\u9019\u662f\u500b\u51f9\u5411\u4e0b\u7684\u4e8c\u6b21\u51fd\u6578\uff0c\u56e0\u6b64\u5728 \\(t(T-t)=D\\) \u7684\u5169\u89e3\u4e4b\u9593\u7684 \\(t\\) \u5373\u662f\u6703\u8d85\u904e\u7d00\u9304\u7684\u503c\u3002\u8981\u6c42\u9019\u4e9b\u503c\u7684\u500b\u6578\u53ef\u4ee5\u4f86\u6c42\u6b64\u65b9\u7a0b\u5169\u89e3\u7684\u5dee\uff0c\u7531\u6839\u8207\u4fc2\u6578\u95dc\u4fc2\u53ef\u5f97\u9019\u500b\u5dee\u662f \\(d=\\sqrt{T^2-4D}\\)\uff1b\u4f46\u56e0\u70ba\u6211\u5011\u53ea\u8981\u6574\u6578\u89e3\uff0c\u800c\u6574\u6578\u89e3\u7684\u5dee\u6703\u662f\u548c \\(T\\) \u4e00\u6a23\u5947\u5076\u6027\u7684\u6574\u6578\uff0c\u56e0\u6b64\u6211\u5011\u8981\u6c42\u7684\u662f\u6bd4 \\(d\\) \u5c0f\u53c8\u548c \\(T\\) \u4e00\u6a23\u5947\u5076\u6027\u7684\u6574\u6578\u3002\u6c42\u5f97\u5dee\u4e4b\u5f8c\u6839\u64da\u690d\u6a39\u554f\u984c\u518d\u52a0 1 \u5373\u662f\u8981\u6c42\u7684\u500b\u6578\u4e86\u3002\n\n\n\n<p>\u4ee5\u7b2c\u4e00\u500b\u7bc4\u4f8b\u4f86\u8aaa\uff0c\\(T=7, D=9\\)\uff0c\u6c42\u5f97 \\(d=\\sqrt{7^2-4\\times9}=\\sqrt{13}\\)\uff0c\u6bd4\u5b83\u5c0f\u53c8\u662f\u5947\u6578\u7684\u6574\u6578\u662f 3\uff0c\u56e0\u6b64\u6b64\u4f8b\u6709 3+1=4 \u89e3\u80fd\u8d85\u904e\u7d00\u9304\u3002\u53e6\u5916\u5169\u500b\u7bc4\u4f8b\u662f \\(\\sqrt{15^2-4\\times40}=\\sqrt{65}&gt;8\\)\uff0c\u5411\u4e0b\u53d6\u5947\u6578\u5f97 7\uff0c\u89e3\u6578\u70ba 8\uff1b\\(\\sqrt{30^2-4\\times200}=10\\)\uff0c\u5411\u4e0b\u53d6\u5076\u6578\u70ba 8\uff0c\u89e3\u6578\u70ba 9\u3002\u6240\u4ee5\u6240\u6c42\u5373\u70ba\\(4\\times8\\times9\\)\u3002\u6ce8\u610f\u5230\u7b2c\u4e09\u500b\u7bc4\u4f8b\u6b63\u597d\u662f 10\uff1b\u4e8b\u5be6\u4e0a 200 \u662f\u6b63\u597d\u6309\u4f4f 10 \u79d2\u7684\u8ddd\u96e2\uff0c\u56e0\u6b64\u9019\u4e00\u7d44\u89e3\u4e0d\u80fd\u7b97\uff0c\u89e3\u6578\u624d\u6703\u662f 8+1=9 \u800c\u975e 10+1=11\u3002<\/p><\/details>\n\n\n\n<p>\u7136\u5f8c part 2\u2026\u2026Eric \u4f60\u4eca\u5e74\u662f\u4e0d\u662f\u6709\u4e00\u500b\u88cf\u4e3b\u984c\u53eb\u505a\u9632\u6b62\u66b4\u641c\u554a (\u7b11\u6b7b)\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">7. Camel Cards<\/h2>\n\n\n\n<p>\u6163\u4f8b<sup data-fn=\"25a46db4-e11a-411c-998a-dc5b8a3db574\" class=\"fn\"><a href=\"#25a46db4-e11a-411c-998a-dc5b8a3db574\" id=\"25a46db4-e11a-411c-998a-dc5b8a3db574-link\">2<\/a><\/sup>\u7684\u64b2\u514b\u984c\u3002\u597d\u5728\u9019\u984c\u4e00\u4f86\u6c92\u6709\u9806\u5b50\uff0c\u6240\u4ee5\u724c\u578b\u5224\u65b7\u76f4\u63a5\u7d2f\u8a08\u4e4b\u5f8c\u770b\u7d2f\u8a08\u6578\u5c31\u597d\u4e86\uff1b\u4e8c\u4f86\u4e0d\u6392\u724c\uff0c\u724c\u7684\u5927\u5c0f\u53ea\u548c\u724c\u7684\u9806\u5e8f\u6709\u95dc (\u800c\u4e0d\u662f\u50cf\u4e00\u822c\u64b2\u514b\u4e00\u6a23\u8981\u5148\u770b\u591a\u5f35\u724c\u7684\u724c\u503c\u5927\u5c0f)\uff0c\u6240\u4ee5\u76f4\u63a5\u628a\u724c\u63a5\u6210\u4e00\u500b\u6574\u6578\u5c31\u80fd\u6bd4\u5927\u5c0f\u4e86\u3002<\/p>\n\n\n\n<p>\u5012\u662f part 2 \u7684\u9b3c\u724c\u78ba\u5be6\u662f\u795e\u4f86\u4e00\u7b46\uff0c\u597d\u5728\u6211\u5beb\u64b2\u514b\u7df4\u7fd2\u984c\u6642\u90fd\u7fd2\u6163\u628a A \u7576\u505a 14 \u9ede\u4f86\u7528\uff0c\u6240\u4ee5\u7576 J \u8b8a\u6210\u9b3c\u724c\u6642\u53ea\u8981\u7576 J \u662f 1 \u9ede\u5c31\u884c\u4e86\uff1b\u724c\u578b\u5224\u65b7\u5247\u5bb9\u6613\u77e5\u9053\u56e0\u70ba\u6c92\u6709\u9806\uff0c\u6240\u4ee5\u6240\u6709\u9b3c\u724c\u90fd\u7576\u6700\u591a\u5f35\u7684\u90a3\u500b\u9ede\u6578\u6703\u6700\u5927\uff0c\u6240\u4ee5\u5728\u724c\u578b\u5224\u65b7\u7684\u6392\u5e8f\u524d\u5148\u628a\u9b3c\u724c\u62ff\u51fa\u4f86\uff0c\u6392\u4e0b\u53bb\u5f8c\u518d\u628a\u9b3c\u724c\u585e\u9032\u6700\u591a\u5f35\u6578\u7684\u90a3\u683c\u53bb\u3002<\/p>\n\n\n\n<p>\u7136\u5f8c\u6211\u61c9\u8a72\u53ef\u4ee5\u671f\u5f85 reddit \u4e0a\u5404\u7a2e\u82b1\u5f0f\u5224\u65b7\u724c\u578b\u7684\u689d\u4ef6\u5f0f\u548c\u9b3c\u724c\u7684\u8655\u7406 XD<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">8. Haunted Wasteland<\/h2>\n\n\n\n<p>\u9019\u984c\u6211\u89ba\u5f97 Eric \u51fa\u58de\u4e86\u3002\u96d6\u7136\u5f80\u5e74\u4e0d\u662f\u6c92\u6709\u904e\u984c\u76ee\u8f38\u5165\u53ea\u6709\u6240\u63cf\u8ff0\u7bc4\u570d\u7684\u4e00\u5c0f\u90e8\u4efd\uff0c\u4f46\u662f\u9019\u984c\u4e5f\u9650\u7e2e\u7684\u592a\u5c0f\u4e86\uff1b\u5176\u4e2d\u4e00\u500b\u7c21\u55ae\u89e3\u9700\u8981\u7684\u6027\u8cea\u4e0d\u662f\u90a3\u9ebc\u5bb9\u6613\u9a57\u8b49\u7684\u3002\u561b\uff0c\u4e0d\u904e\u8003\u616e\u5230\u524d\u9762\u984c\u6578\u6709\u4e00\u5927\u5806\u6240\u8b02\u300c\u60c5\u7406\u4e4b\u4e2d\u610f\u6599\u4e4b\u5916\u300d\u7684\u8f38\u5165\uff0c\u5012\u4e5f\u4e0d\u592a\u80fd\u8aaa Eric \u600e\u6a23\u5c31\u662f\u4e86\u3002<\/p>\n\n\n\n<p>Part 1 \u6c92\u4ec0\u9ebc\u597d\u722d\u8b70\u7684\u5c31\u662f\u8dd1\u904e\u53bb\u5c31\u5c0d\u4e86\uff0c\u4f46 Part 2 \u5c31\u4e0d\u662f\u9019\u6a23\u4e86\u3002\u7406\u8ad6\u4e0a\uff0c\u8981\u6c42\u9019\u7a2e\u5171\u540c\u76ee\u7684\u61c9\u8a72\u8981\u5148\u6c42\u51fa\u6bcf\u500b\u8ff4\u5708\u7684\u958b\u982d\uff0c\u56e0\u70ba\u8ff4\u5708\u4e0d\u4e00\u5b9a\u6703\u8dd1\u56de\u539f\u7bc0\u9ede (\u7bc4\u4f8b\u5c31\u5df2\u7d93\u4e0d\u662f\u4e86\uff0c\u53ea\u662f\u500b\u5225 Z \u7684\u4e0b\u4e00\u6b65\u7b49\u540c\u65bc A \u7684\u7b2c\u4e00\u6b65)\uff1b\u4f46\u770b\u8d77\u4f86\u7d66\u5b9a\u7684\u8f38\u5165\u5c31\u662f\u5229\u7528\u4e86\u985e\u4f3c\u65bc\u8dd1\u56de\u539f\u7bc0\u9ede\u7684\u65b9\u5f0f\u8b93\u6c42\u89e3\u8005\u4e0d\u7528\u53bb\u7b97\u8ff4\u5708\u524d\u7684\u9577\u5ea6\uff0c\u76f4\u63a5\u628a\u8ff4\u5708\u9577\u5ea6\u505a LCM \u5c31\u662f\u7b54\u6848\u3002\u4e0d\u7136\u7684\u8a71\u5c31\u6703\u9700\u8981\u4e2d\u570b\u5269\u9918\u5b9a\u7406\u4e86\uff0c\u800c\u6839\u64da\u5f80\u5e74\u7684\u7d93\u9a57\u9019\u4e26\u4e0d\u662f\u4eba\u4eba\u90fd\u80fd\u61c9\u7528\u7684\u6280\u5de7\u3002(\u8981\u7528\u4e0a\u4e2d\u570b\u5269\u9918\u5b9a\u7406\u7684\u8a71\u9019\u984c\u53ef\u80fd\u8981\u5f80\u5f8c\u63a8\u81f3\u5c11\u4e00\u661f\u671f\uff0c\u50cf\u53bb\u5e74\u7684 Day 17 \u90a3\u6a23)<\/p>\n\n\n\n<p>\u6211\u6703\u8aaa\u51fa\u984c\u51fa\u58de\u4e86\u7684\u539f\u56e0\u662f\uff0c\u9019\u500b\u6027\u8cea\u5176\u5be6\u61c9\u8a72\u8981\u5728\u984c\u76ee\u4e2d\u63d0\u51fa\u4f86\u7684\uff0c\u53ea\u662f\u53ef\u80fd\u9019\u6545\u4e8b\u7684\u5beb\u6cd5\u8b93 Eric \u4e0d\u592a\u597d\u6574\u5408\u5427\uff0c\u6240\u4ee5\u53ea\u6709\u7559\u4e0b\u4e00\u500b\u300cA \u5c3e\u548c Z \u5c3e\u7684\u500b\u6578\u4e00\u6a23\u300d\u7684 (\u9023\u4e00\u534a\u90fd\u7a31\u4e0d\u592a\u4e0a\u7684) \u63d0\u793a\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">9. Mirage Maintenance<\/h2>\n\n\n\n<p>\u9019\u771f\u7684\u662f\u521d\u7d1a\u9031\u672b\u984c\u55ce\uff1f\uff01\u662f\u5566\uff0c\u5c0d\u521d\u5b78\u8005\u4f86\u8aaa\u9663\u5217\u7ba1\u7406\u662f\u500b\u4e2d\u578b\u7684\u984c\u6750\uff0c\u4f46\u9019\u611f\u89ba\u4e0d\u50cf\u662f\u500b\u9031\u672b\u984c\u2026\u2026\u5c31\u7b97\u8981\u628a\u5b83\u653e\u5728\u9031\u672b\u9019\u984c\u4e5f\u61c9\u8a72\u662f Day 3 \u9019\u7a2e\u6696\u8eab\u9031\u672b\u984c\u624d\u662f\u3002<\/p>\n\n\n\n<p>\u984c\u76ee\u6c92\u4ec0\u9ebc\u7279\u5225\u7684\uff0c\u5c31\u7167\u505a\u5c31\u884c\u4e86\uff1b\u6ce8\u610f\u5230\u984c\u76ee\u88e1\u7684\u905e\u8ff4\u7d50\u69cb\u9019\u751a\u81f3\u6709\u4e00\u500b\u5f88\u81ea\u7136\u7684\u905e\u8ff4\u89e3\u3002Part 2 \u4e5f\u6c92\u4ec0\u9ebc\u7279\u5225\u7684\uff0c\u5c31\u53ea\u662f\u5f80\u524d\u7b97\u800c\u5df2\u3002\u6709\u4eba\u751a\u81f3\u767c\u73fe\u4e86\u53ef\u4ee5\u4e0d\u7528\u5012\u7b97\u56de\u4f86\u7684\u65b9\u6cd5\uff0c\u9084\u6eff\u5de7\u7684\u3002<\/p>\n\n\n\n<p>\u2026\u2026\u7136\u5f8c\u6211\u4eca\u5e74\u5c31\u5728\u9019\u88e1\u5403\u4e86\u7b2c\u4e00\u6b21 WA\u3002\u53bb\u5e74\u5beb\u4e86\u500b\u53ea\u8b80\u6578\u5b57\u7684\u8b80\u53d6\u51fd\u6578\uff0c\u7136\u5f8c\u56e0\u70ba\u770b\u8d77\u4f86\u5c31\u662f\u4e00\u5806\u6578\u5b57\u6240\u4ee5\u5c31\u62ff\u4f86\u7528\u4e86\uff0c\u7136\u5f8c\u5c31\u88ab\u8f38\u5165\u6a94\u88e1\u7684\u8ca0\u865f\u7d66\u5a4a\u4e86\u3002\u61c9\u8a72\u8981\u76f4\u63a5\u7528\u5207\u958b\u5f8c\u8f49\u63db\u7684\u51fd\u6578\u7684\u3002(\u5606\u6c23) \u7136\u5f8c\u5728 reddit \u767c\u73fe\u9084\u4e0d\u53ea\u6211\u4e00\u500b\u4eba\u4e2d\u62db\u3002(\u518d\u6b21\u5606\u6c23)<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">10. Pipe Maze<\/h2>\n\n\n\n<p>Part 1 \u662f\u500b\u5f88\u7c21\u55ae\u7684 BFS \u641c\u5c0b\u984c\uff0c\u6240\u4ee5\u5c31\u628a\u641c\u5c0b\u51fd\u5f0f\u5eab\u62ff\u4f86\u7528\u4e86\uff1b\u7528 BFS \u641c\u7684\u8a71\u6700\u5f8c\u4e00\u500b\u9ede\u5c31\u662f\u6700\u9060\u7684\u9ede\uff0c\u90a3\u500b\u9ede\u7684\u8ddd\u96e2\u5c31\u662f\u6240\u6c42\u4e86\u3002<\/p>\n\n\n\n<p>Part 2 \u5247\u610f\u5916\u5730\u662f\u500b\u8a08\u7b97\u5e7e\u4f55\u984c\u3002\u6211\u8cbc\u5230 reddit \u4e0a\u53bb\u7684\u89e3\u6cd5\u6211\u5728\u90a3\u88e1\u628a\u5b83\u53eb\u505a\u300c\u76ae\u514b\u7684\u978b\u5e36\u300d\uff0c\u76f4\u63a5\u61c9\u7528\u4e86\u5169\u500b\u8a08\u7b97\u7c21\u55ae\u591a\u908a\u5f62\u7684\u516c\u5f0f\uff1a<a href=\"https:\/\/zh.wikipedia.org\/wiki\/%E7%9A%AE%E5%85%8B%E5%AE%9A%E7%90%86\">\u76ae\u514b\u5b9a\u7406<\/a>\u548c<a href=\"https:\/\/en.wikipedia.org\/wiki\/Shoelace_formula\">\u978b\u5e36\u516c\u5f0f<\/a>\u3002<\/p>\n\n\n\n<details class=\"wp-block-inline-spoilers-block\"><summary>\u9ede\u9078\u6b64\u8655\u770b\u61c9\u7528\u7d30\u7bc0\u3002<\/summary>\u8aaa\u7a7f\u4e86\u5176\u5be6\u5f88\u7c21\u55ae\uff0c\u7576\u628a\u76e4\u9762\u653e\u5230\u5ea7\u6a19\u5e73\u9762\u4e0a\u4e4b\u5f8c\uff0c\u6cbf\u8457\u5708\u8d70\u53ef\u4ee5\u9010\u500b\u8a08\u7b97\u978b\u5e36\u516c\u5f0f\u7684\u6bcf\u4e00\u9805\uff0c\u7136\u5f8c\u8d70\u904e\u7684\u9ede\u6578\u5c31\u662f\u76ae\u514b\u5b9a\u7406\u7684\u908a\u754c\u9ede\u6578\uff0c\u76ae\u514b\u5b9a\u7406\u7684\u53e6\u4e00\u9805\u5167\u90e8\u9ede\u6578\u5c31\u662f\u6211\u5011\u8981\u6c42\u7684\u6771\u897f\uff1b\u65bc\u662f\u7e5e\u5b8c\u4e4b\u5f8c\u6211\u5011\u5f97\u5230\u9762\u7a4d\u7684\u5169\u500d\u53ca\u908a\u754c\u9ede\u6578\uff0c\u4ee3\u76ae\u514b\u5b9a\u7406\u5c31\u80fd\u6c42\u5f97\u6211\u5011\u8981\u7684\u5167\u90e8\u9ede\u6578\u4e86\u3002<\/details>\n\n\n\n<p>\u65e2\u7136\u662f\u8a08\u7b97\u5e7e\u4f55\u984c\uff0c\u56e0\u6b64\u5224\u65b7\u9ede\u5728\u5708\u5167\u6216\u5708\u5916\u7576\u7136\u4e5f\u6709\u5176\u4ed6\u65b9\u5f0f\uff0c\u4f46\u662f\u56e0\u70ba\u6211\u5011\u7684\u5708\u908a\u754c\u548c\u5ea7\u6a19\u8ef8\u5e73\u884c\uff0c\u4f8b\u5982\u50cf\u5c04\u7dda\u6cd5\u53ef\u80fd\u6703\u6709\u5c04\u7dda\u548c\u908a\u754c\u91cd\u5408\u7684\u72c0\u6cc1\uff0c\u689d\u4ef6\u5224\u65b7\u6703\u8b8a\u5f97\u6bd4\u8f03\u9ebb\u7169\uff1b\u6211\u662f\u5728\u5403\u4e2d\u9910\u6642\u624d\u60f3\u5230\u6709\u76ae\u514b\u5b9a\u7406\u53ef\u4ee5\u62ff\u4f86\u7528\u3002\u5176\u4ed6\u6211\u4e5f\u770b\u904e\u6709\u628a\u5716\u5f62\u653e\u5927\uff0c\u628a\u539f\u4f86\u7684\u6bcf\u500b\u5b57\u653e\u5927\u6210 3&#215;3\uff0c\u7136\u5f8c\u5c31\u53ef\u4ee5\u7528\u6df9\u6c34\u6f14\u7b97\u6cd5\u4f86\u947d\u904e\u539f\u984c\u88e1\u7ba1\u7dda\u4e4b\u9593\u7684\u6d1e\u7684\u505a\u6cd5\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">11. Cosmic Expansion<\/h2>\n\n\n\n<p>\u53c8\u662f\u4e00\u500b\u300cPart 1 \u7684\u300e\u76f4\u89ba\u300f\u505a\u6cd5\u5728 Part 2 \u88ab\u5a4a\u6158\u300d\u7684\u984c\u578b\u4e86\u3002\u984c\u76ee\u4e0d\u96e3\uff0c\u4f46\u8981\u505a\u5c0d\u78ba\u5be6\u9700\u8981\u4e00\u9ede\u7d44\u7e54\uff1b\u4e0d\u904e\u5982\u679c\u6709\u671f\u5f85\u5230\u67d0\u500b\u500d\u6578\u6703\u8b8a\u5927\u7684\u8a71\u662f\u53ef\u4ee5\u505a\u6210 Part 1 \u53ea\u6539\u4e00\u884c\u5c31\u8b8a\u6210 Part 2 \u7684\u89e3\u7684\u3002<\/p>\n\n\n\n<p>\u7136\u5f8c\u6211\u61c9\u8a72\u662f\u627e\u5230\u4e00\u500b\u5728\u6383\u5b8c # \u5b57\u4e4b\u5f8c\u53ea\u8981\u6392\u5e8f+\u7dda\u6027\u6642\u9593\u7684\u505a\u6cd5\u4e86\u3002<details class=\"wp-block-inline-spoilers-block\"><summary>\u9ede\u6b64\u770b\u89e3\u6cd5<\/summary>\u9996\u5148\u66fc\u54c8\u9813\u8ddd\u96e2\u548c\u8868\u793a\u6211\u5011\u53ef\u4ee5\u628a\u5169\u8ef8\u62c6\u958b\u7b97\u3002\u5c0d\u6bcf\u4e00\u500b\u8ef8\uff0c\u5c07\u5ea7\u6a19\u6392\u5e8f\uff0c\u9019\u6a23\u5b83\u5011\u9593\u7684\u66fc\u54c8\u9813\u8ddd\u96e2\u548c\u53ef\u4ee5\u8dd1\u4e00\u6b21\u9663\u5217\uff0c\u4f9d\u5e8f\u4e58\u4e0a (n-1) (n-3) (n-5) \u5230 -(n-1) \u6c42\u548c\uff1b\u81f3\u65bc\u4f38\u5c55\u7684\u7a7a\u9593\uff0c\u6ce8\u610f\u5230\u6bcf\u500b\u5ea7\u6a19\u9ede\u8207\u9ede\u4e4b\u9593\u7684\u7a7a\u9593\u88ab\u8e29\u7684\u6b21\u6578\u662f\u5df2\u77e5\u7684 (\u5de6\u908a\u9ede\u500b\u6578\u4e58\u4ee5\u53f3\u908a\u9ede\u500b\u6578)\uff0c\u56e0\u6b64\u540c\u6a23\u4e58\u8d77\u4f86\u6c42\u548c\uff0c\u6700\u5f8c\u4e58\u4e0a (\u4f38\u5c55\u500d\u6578-1) \u518d\u548c\u524d\u9805\u76f8\u52a0\u5373\u662f\u7e3d\u8ddd\u96e2\u4e86\u3002<\/details><\/p>\n\n\n\n<h2 class=\"wp-block-heading\">12. Hot Springs<\/h2>\n\n\n\n<p>\u65bc\u662f\u9019\u984c\u662f\u4e00\u7dad<a href=\"https:\/\/zh.m.wikipedia.org\/zh-tw\/%E6%95%B8%E7%B9%94\">\u6578\u7e54 (nonogram)<\/a> \u7684\u984c\u76ee\u3002\u8aaa\u8d77\u4f86\u9019\u8b93\u6211\u60f3\u5230\u6211\u597d\u4e45\u4ee5\u524d\u6709\u5beb\u904e\u4e00\u500b\u4e0d\u600e\u9ebc\u6a23\u7684\u6578\u7e54\u89e3\u984c\u7a0b\u5f0f\uff0c\u5b83\u7684\u89e3\u984c\u908f\u8f2f\u5168\u90e8\u9760\u5728\u8f38\u5165\u984c\u76ee\u6642\u751f\u6210\u7684\u6bcf\u5217\u6240\u6709\u7a2e\u985e\uff0c\u7136\u5f8c\u518d\u53bb\u505a\u7be9\u9078\uff1b\u60f3\u7576\u7136\u9019\u652f\u7a0b\u5f0f\u53ea\u80fd\u505a\u50cf 15&#215;15 \u9019\u7a2e\u5c0f\u5152\u79d1\u7684\u6771\u897f\uff0c\u50cf 50&#215;50 \u90a3\u7a2e\u4e00\u5b9a\u6c92\u6551\u3002<\/p>\n\n\n\n<p>\u4e0d\u904e\u4e5f\u662f\u6709\u5beb\u904e\u90a3\u73a9\u610f\u7684\u7d93\u9a57\u624d\u99ac\u4e0a\u60f3\u5230\u9019\u984c\u53ef\u4ee5\u5c0d (\u5217\u683c, \u7dda\u7d22\u7d22\u5f15) \u7684\u6578\u5c0d\u505a DP\uff0c\u5b58\u7684\u662f\u6b64\u5217\u81ea\u6b64\u683c\u4e4b\u5f8c\u7684\u5df2\u77e5\u5716\u6848\u914d\u4e0a\u7dda\u7d22\u5217\u81ea\u6b64\u7d22\u5f15\u8d77\u7684\u7dda\u7d22\u7684\u7a2e\u985e\u6578\uff1b\u6c42\u7684\u6642\u5019\u5c31\u5617\u8a66\u770b\u770b\u4e0b\u4e00\u500b\u7dda\u7d22\u80fd\u5920\u653e\u5728\u958b\u59cb\u7684\u4ec0\u9ebc\u5730\u65b9\uff0c\u53d6\u8d70\u4e4b\u5f8c\u67e5 DP \u8868\u5373\u53ef\u3002\u6211\u662f\u628a\u5b83\u5beb\u6210\u8a18\u61b6\u905e\u8ff4\u51fd\u6578\u5566\uff0c\u4e0d\u904e\u6982\u5ff5\u662f\u4e00\u6a23\u7684\u3002<\/p>\n\n\n\n<p>\u7136\u5f8c part 2 \u679c\u7136\u6c92\u8b93\u6211\u5011\u5931\u671b\uff0c\u76f4\u63a5\u628a\u8f38\u5165\u8b8a\u6210\u4e94\u500d\uff01<sup data-fn=\"b370ff7b-6b1c-4c8c-9ab8-20f2d6dadd88\" class=\"fn\"><a href=\"#b370ff7b-6b1c-4c8c-9ab8-20f2d6dadd88\" id=\"b370ff7b-6b1c-4c8c-9ab8-20f2d6dadd88-link\">3<\/a><\/sup>\u9084\u597d\u9019\u500b DP \u505a\u6cd5\u7684\u5728\u5169\u500b\u90fd\u8b8a\u4e94\u500d\u6642\u7528\u7684\u6642\u9593\u53ea\u6709 25 \u500d\uff0c\u9084\u662f\u53ef\u4ee5\u8f15\u9b06\u641e\u5b9a\u3002<\/p>\n\n\n\n<p><a href=\"https:\/\/redd.it\/18gepxd\">\u88dc\u8a3b<\/a>\uff1a\u5c45\u7136 <a href=\"https:\/\/dmoj.ca\/problem\/ioi16p4\">IOI 2016 \u6709\u4e00\u984c<\/a>\u5c31\u662f\u9019\u984c\u7684\u518d\u9032\u968e\u7248\u2026\u2026<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">13. Point of Incidence<\/h2>\n\n\n\n<p>\u61c9\u8a72\u662f\u500b\u6c92\u4ec0\u9ebc\u597d\u8aaa\u7684\u4e00\u984c\u3002\u5c31\u9023 part 2 \u7684\u6975\u66b4\u529b\u89e3\u61c9\u8a72\u90fd\u6709\u6a5f\u6703\u8dd1\u5b8c\uff0c\u554f\u984c\u61c9\u8a72\u53ea\u6703\u5728\u8f38\u5165\u5206\u6790<s>\u8ddf\u773c\u6b98<\/s>\u5427\u3002<\/p>\n\n\n\n<p>\u4e0d\u904e\u5012\u662f\u7a0d\u5fae\u7814\u7a76\u4e86\u4e00\u4e0b\u6709\u6c92\u6709 <a href=\"https:\/\/en.wikipedia.org\/wiki\/Longest_palindromic_substring#Manacher's_algorithm\">Manacher<\/a> \u4e0a\u5834\u7684\u6a5f\u6703\uff1b\u770b\u8d77\u4f86\u53ea\u6709 part 1 \u80fd\u7528\uff0cpart 2 \u6703\u6bd4\u8f03\u9ebb\u7169\u3002(\u88dc\u8a3b\uff1a<a href=\"https:\/\/redd.it\/18higps\" data-type=\"link\" data-id=\"https:\/\/redd.it\/18higps\">\u6709\u4eba\u5be6\u4f5c\u51fa\u4f86\u4e86<\/a>\uff0c\u53ef\u4ee5\u53c3\u8003\u770b\u770b)<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">14. Parabolic Reflector Dish<\/h2>\n\n\n\n<p>\u7b97\u662f\u984c\u5f88\u76f4\u63a5\u7684\u6a21\u64ec\u984c\u3002\u9019\u984c\u5176\u5be6\u6703\u8b93\u6211\u60f3\u5230 2021 Day 25\uff0c\u540c\u6a23\u90fd\u662f\u8981\u628a\u4e00\u7fa4\u6771\u897f\u540c\u6642\u5f80\u67d0\u500b\u65b9\u5411\u79fb\u7684\u984c\u76ee\uff1b\u4e0d\u904e\u90a3\u984c\u6771\u897f\u5728\u79fb\u6642\u5982\u679c\u524d\u9762\u6709\u6771\u897f\uff0c\u4e0d\u8ad6\u524d\u9762\u662f\u4e0d\u662f\u8981\u79fb\u958b\u4e00\u5f8b\u81ea\u5df1\u4e0d\u79fb\uff1b\u9019\u984c\u5247\u662f\u771f\u7684\u8981\u8003\u616e\u524d\u9762\u662f\u4e0d\u662f\u8981\u79fb\u958b\u4e86\u3002<\/p>\n\n\n\n<p>\u6211\u5728 part 1 \u5beb\u7684\u662f\u56fa\u5b9a\u5f80\u4e0a\u7684\u51fd\u6578\uff0c\u4e0d\u904e part 2 \u9019\u500b\u52d5\u56db\u500b\u65b9\u5411\u7684\u6211\u4e0d\u60f3\u8981\u8907\u88fd\u4e00\u4efd\u6539\u4e09\u6b21\uff0c\u6240\u4ee5\u9084\u662f\u591a\u82b1\u4e86\u4e00\u9ede\u6642\u9593\u5beb\u6210\u628a\u79fb\u52d5\u65b9\u5411\u7576\u6210\u53c3\u6578\u7684\u51fd\u6578\u3002\u9664\u932f\u5beb\u4e86\u4e00\u5806\uff0c\u78ba\u5b9a\u641e\u5b9a\u4e4b\u5f8c\u63db\u6210\u8ff4\u5708\u5075\u6e2c\u641e\u7838\u4e86\uff0c\u9084\u56e0\u6b64\u5403\u4e86\u4e00\u500b WA\u2026\u2026<\/p>\n\n\n\n<p>\u6700\u5f8c\u7684\u8ff4\u5708\u5075\u6e2c\u662f\u6700\u66b4\u529b\u7684\u90a3\u7a2e\uff0c\u628a\u8981\u8f38\u51fa\u7684\u503c\u8ddf\u7576\u6642\u7684\u76e4\u9762\u7d66\u5b58\u8d77\u4f86\uff0c\u4ee5\u8f38\u51fa\u503c\u7576\u505a\u4e00\u500b\u5f88\u7c21\u55ae\u7684 hash \u505a\u8ff4\u5708\u5075\u6e2c\uff0c\u770b\u5230\u8f38\u51fa\u503c\u4e00\u6a23\u624d\u53bb\u6bd4\u5c0d\u76e4\u9762\uff0c\u76e4\u9762\u6bd4\u5c0d\u4e00\u6a23\u624d\u7b97\u8ff4\u5708\u3002<\/p>\n\n\n\n<p>\u9996\u9801\u7684\u5730\u5716\u7d42\u65bc\u5230\u4e86\u6700\u9ad8\u9ede\u4e86\uff0c\u63a5\u4e0b\u4f86\u8981\u4e00\u8def\u5411\u4e0b\u4e86\u5427 XD<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">15. Lens Library<\/h2>\n\n\n\n<p>\u4eca\u5929\u662f\u8cc7\u6599\u7d50\u69cb\u5be6\u4f5c\u984c\uff0c\u5c31\u662f\u8cc7\u6599\u7d50\u69cb\u8ab2\u7a0b\u4e0a\u5230\u96dc\u6e4a\u8868\u6642\u8981\u4f60\u56de\u53bb\u5be6\u4f5c\u4e00\u500b\u7684\u90a3\u500b\u7df4\u7fd2\u984c\u3002\u6240\u4ee5\u6c92\u4ec0\u9ebc\u597d\u8aaa\u7684\u3002<\/p>\n\n\n\n<p>\u4e0d\u904e\u661f\u671f\u4e94\u9019\u9ebc\u7c21\u55ae\uff0c\u662f\u4e0d\u662f\u9019\u500b\u9031\u672b\u8981\u6709\u66b4\u98a8\u96e8 (?) \u4f86\u81e8\u4e86\u5462\u2026\u2026<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">16. The Floor Will Be Lava<\/h2>\n\n\n\n<p>\u662f\u500b\u5f88\u666e\u901a\u7684\u6a21\u64ec\u984c\u3002\u662f\u8aaa\u6211\u5230\u89e3\u5b8c\u4e86\u53bb\u770b reddit \u6587\u7ae0\u6642\u624d\u767c\u73fe\u9019\u5176\u5be6\u5c31\u662f BFS \u641c\u5c0b\u2026\u2026<\/p>\n\n\n\n<p>\u8aaa\u8d77\u4f86\u9019\u984c\u7684\u984c\u76ee\u8ddf\u4eca\u5e74\u6211\u60f3\u5728\u9019\u6bb5\u671f\u9593\u5167\u505a\u7684\u4e8b\u60c5\u6709\u4e00\u9ede\u9ede\u91cd\u758a\u5230\u4e86\uff0c\u6240\u4ee5\u5176\u5be6\u6709\u9ede\u5687\u4e86\u4e00\u8df3\u5c31\u662f\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">17. Clumsy Crucible<\/h2>\n\n\n\n<p>\u8aaa\u597d\u7684\u6700\u77ed\u8def\u5f91\u984c\u7d42\u65bc\u4f86\u4e86\u3002\u4e0d\u904e\u9019\u6b21\u9084\u591a\u4e86\u4e00\u500b\u6897\uff1a\u8def\u7dda\u4e2d\u76f4\u7dda\u9577\u5ea6\u53ea\u80fd\u5728\u67d0\u500b\u7bc4\u570d\u88e1\u2014\u2014part 1 \u662f 1 \u5230 3\uff0cpart 2 \u662f 4 \u5230 10\u3002\u53ef\u80fd\u662f\u56e0\u70ba\u683c\u5b50\u4e0a\u7684\u6700\u77ed\u8def\u5f91\u984c\u5f88\u5bb9\u6613\u60f3\u8aaa\u300c\u4e00\u6b65\u5c31\u662f\u4e00\u683c\u300d\u5427\uff0c\u6211\u7b2c\u4e00\u6b21\u7684\u5beb\u6cd5\u88e1\u628a\u76f4\u7dda\u9577\u5ea6\u7576\u6210\u72c0\u614b\u7684\u4e00\u90e8\u4efd\u4f86\u8a18\u4e86\uff0c\u7136\u5f8c\u9084\u56e0\u6b64\u5728 part 2 \u7bc4\u570d\u6709\u8b8a\u6642\u5c07\u72c0\u614b\u8b8a\u6210\u552f\u4e00\u503c\u7684\u51fd\u6578\u767c\u751f\u78b0\u649e\u4e86\u4ee5\u81f4\u65bc\u5403\u4e86\u500b WA\u3002<\/p>\n\n\n\n<p>\u7136\u5f8c\uff0c\u5728 reddit \u4e0a\u770b\u8a0e\u8ad6\u624d\u767c\u73fe\u300c\u5c0d\u8036\uff0c\u6211\u53ef\u4ee5\u4e00\u6b21\u8de8\u5927\u4e00\u9ede\u300d\u2014\u2014\u4e0d\u904e\u5176\u5be6\u6211\u4e00\u958b\u59cb\u7684\u5beb\u6cd5\u5c31\u5df2\u7d93\u6709\u4e00\u90e8\u4efd\u5730\u7528\u4e86\u9019\u500b\u9ede\u5b50\u4e86\uff1a\u5728 part 2 \u8981\u8de8 4 \u5230 10 \u6b65\u6642\uff0c\u6211\u70ba\u4e86\u4e0d\u60f3\u53e6\u5916\u5beb\u8aaa 1 \u5230 3 \u6b65\u4e0d\u5141\u8a31\u8f49\u5f4e\uff0c\u6240\u4ee5\u5728\u8f49\u5f4e\u6642\u5c31\u5df2\u7d93\u662f\u4e00\u53e3\u6c23\u8f49\u5b8c\u5f8c\u8d70 4 \u6b65\u4e86\u3002\u5f9e\u9019\u88e1\u6539\u6210\u4e00\u53e3\u6c23\u8de8 4 \u5230 10 \u6b65\u53ea\u662f\u518d\u591a\u8de8\u4e00\u9ede\u683c\u5b50 (\u548c\u908f\u8f2f) \u800c\u5df2\u3002\u9019\u6a23\u5c31\u53ef\u4ee5\u4e0d\u5fc5\u628a\u76f4\u7dda\u9577\u5ea6\u653e\u5230\u72c0\u614b\u88e1\u4e86\u3002(Repo \u88e1\u7684 17large.cpp \u5373\u662f\u6574\u500b\u6539\u6210\u9019\u500b\u65b9\u5f0f\u7684\u505a\u6cd5\u3002)<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">18. Lavaduct Lagoon<\/h2>\n\n\n\n<p>Part 1 \u672c\u4f86\u9084\u5728\u60f3\u8aaa\u5927\u6982\u4e4b\u5f8c\u8981\u5c0d\u9019\u5f35\u5716\u505a\u4e8b\u6240\u4ee5\u505a\u4e86\u4e00\u4e9b\u5be6\u969b\u586b\u5716\u7684\u7a0b\u5f0f\uff0c\u7d50\u679c part 2 \u4e00\u51fa\u4f86\u76f4\u63a5\u7b11\u6b7b\uff1a\u539f\u4f86\u9019\u5929\u7684\u984c\u76ee\u662f\u978b\u5e36 (\u516c\u5f0f) \u7684\u9006\u8972 XD \u5c31\u662f\u8981\u7a0d\u5fae\u60f3\u4e00\u4e0b\u6211\u5011\u9019\u500b\u7c21\u55ae\u591a\u908a\u5f62\u7684\u5916\u6846\u984d\u5916\u4f54\u591a\u5c11\u3002<\/p>\n\n\n\n<details class=\"wp-block-inline-spoilers-block\"><summary>\u9ede\u6b64\u770b\u6578\u5b78<\/summary>\u5916\u6846\u7684\u90e8\u4efd\uff0c\u6bcf\u500b\u5167\u8f49\u5f4e\u6703\u591a 3\/4 \u683c\uff0c\u5916\u8f49\u5f4e\u6703\u591a 1\/4 \u683c\uff0c\u4e0d\u8f49\u5f4e\u7684\u908a\u5247\u591a 1\/2 \u683c\u3002\u5bb9\u6613\u77e5\u9053\u5167\u8f49\u5f4e\u6c38\u9060\u6bd4\u5916\u8f49\u5f4e\u591a 4 \u500b (\u56e0\u70ba\u6211\u5011\u7e5e\u4e86\u4e00\u5708\u56de\u5230\u539f\u9ede\u4e86)\uff0c\u6240\u4ee5\u7e3d\u8a08\u5916\u6846\u7684\u9762\u7a4d\u5c31\u662f\u5468\u9577\u6578\u503c\u500b 1\/2 \u683c\u52a0 4 \u500b 1\/4 \u683c\uff0c\u5373\u70ba\u5468\u9577\u9664\u4ee5 2 \u52a0 1\u3002\u628a\u9019\u500b\u5916\u6846\u9762\u7a4d\u52a0\u5230\u978b\u5e36\u516c\u5f0f\u6c42\u51fa\u4f86\u7684\u9762\u7a4d\u5373\u662f\u7b54\u6848\u4e86\u3002\n\n\n\n<p>\u2026\u2026\u6211\u662f\u4e0d\u662f\u81ea\u5df1\u8b49\u4e86\u4e00\u6b21\u7c21\u55ae\u7248\u7684\u76ae\u514b\u5b9a\u7406\uff1f\uff01<\/p><\/details>\n\n\n\n<h2 class=\"wp-block-heading\">19. Aplenty<\/h2>\n\n\n\n<p>\u4eca\u5929\u7684 part 1 \u662f\u57fa\u672c\u7684\u72c0\u614b\u6a5f\uff0c\u6bd4\u8f03\u8907\u96dc\u7684\u9664\u4e86\u5206\u6790\u8f38\u5165\u4e4b\u5916\u5c31\u662f\u8cc7\u6599\u7d44\u7e54\u4e86\uff0c\u5982\u679c\u6c92\u6709\u7d44\u7e54\u597d\u7a0b\u5f0f\u6703\u975e\u5e38\u4e82\u3002Part 2 \u2026\u2026 Day 5 \u7684\u5340\u9593\u904b\u7b97\u9006\u8972\u4e86\u3002\u6211\u5dee\u9ede\u60f3\u628a Day 5 \u7684\u5340\u9593\u7d50\u69cb\u5148\u91cd\u69cb\u51fa\u4f86\u518d\u5beb part 2\uff0c\u597d\u5728\u4ed4\u7d30\u60f3\u60f3\u4e4b\u5f8c\u767c\u73fe\u9019\u6b21\u5176\u5be6\u6c92\u90a3\u9ebc\u8907\u96dc\uff0c\u96d6\u7136\u662f 4D \u8d85\u7acb\u65b9\u5340\u9593\uff0c\u4f46\u6bcf\u6b21\u5207\u5272\u9802\u591a\u5207\u6210\u5169\u584a\uff0c\u7136\u5f8c\u4ed6\u5011\u5c31\u5206\u958b\u7d66\u4e0d\u540c\u72c0\u614b\u4e86\uff0c\u6240\u4ee5\u5c31\u76f4\u63a5\u5207\u4e0b\u53bb\u5206\u958b\u4e86\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">20. Pulse Propagation<\/h2>\n\n\n\n<p>\u7d50\u679c\u771f\u7684\u4f86\u9019\u62db\u4e86\u3002Part 1 \u662f\u500b\u8868\u9762\u4e0a\u6709\u9ede\u53ef\u6015\u7684\u81ea\u52d5\u6a5f\u6a21\u64ec\u984c\uff0c\u4e0d\u904e\u81f3\u5c11\u8cc7\u6599\u7d50\u69cb\u597d\u4e00\u9ede\u5c31\u80fd\u8f15\u9b06\u5beb\u5f97\u51fa\u4f86\uff1b\u4e0d\u904e part 2 \u5c31\u51fa\u4e8b\u4e86\u3002\u9019\u53c8\u662f\u4e00\u500b\u76f4\u63a5\u6a21\u64ec\u4e0d\u53ef\u80fd\u5728\u5408\u7406\u6642\u9593\u5167\u6a21\u64ec\u51fa\u7d50\u679c\u7684\u8f38\u5165\uff1a\u9019\u6b21\u9006\u8972\u7684\u662f Day 8 \u7684\u5faa\u74b0\u5075\u6e2c\u8ddf Day 14 \u6642\u5927\u5bb6\u8a0e\u8ad6\u4e2d\u6709\u8a0e\u8ad6\u5230\u7684\u4e92\u8cea\u8ff4\u5708\u8907\u5408\uff0c\u5169\u500b\u6771\u897f\u5408\u5728\u4e00\u8d77\u5c31\u662f\u9019\u6b21\u984c\u76ee\u7684\u8f38\u5165\u8cc7\u6599\u3002<\/p>\n\n\n\n<p>\u5728\u767c\u73fe\u76f4\u63a5\u8dd1\u8dd1\u4e0d\u5b8c\u7684\u6642\u5019\u679c\u65b7\u653e\u68c4\uff0c\u5229\u7528\u4e00\u4e9b\u7a7a\u6a94\u601d\u8003\u4e86\u597d\u4e9b\u8ff4\u5708\u5075\u6e2c\u65b9\u5f0f\u4e4b\u5f8c\uff0c\u6700\u5f8c\u6c7a\u5b9a\uff1a\u53ea\u8b93\u6bcf\u500b\u6a21\u7d44\u5728\u6bcf\u6b21\u50b3\u5b8c\u4e4b\u5f8c\u7d00\u9304\u81ea\u5df1\u7684\u72c0\u614b\uff0c\u7136\u5f8c\u76f4\u63a5\u7528\u9019\u500b\u72c0\u614b\u5c0b\u627e\u662f\u5426\u6709\u8ff4\u5708\uff0c\u7b49\u5230\u6bcf\u500b\u6a21\u7d44\u90fd (\u4ee5\u67d0\u500b\u7c21\u55ae\u689d\u4ef6) \u8a8d\u70ba\u81ea\u5df1\u5728\u8ff4\u5708\u88e1\u4e4b\u5f8c\u628a\u6240\u6709\u4eba\u8a8d\u70ba\u7684\u8ff4\u5708\u9577\u5ea6\u7d66\u5370\u51fa\u4f86\u3002\u5728\u8dd1\u4e86\u7d04\u5169\u842c\u591a\u6b21\u5f8c\u8df3\u51fa\u6a21\u64ec\uff0c\u679c\u7136\u7d50\u679c\u7576\u4e2d\u51fa\u73fe\u4e86\u56db\u500b\u4e2d\u7b49\u5927\u7684\u6578\u5b57\uff0c\u65bc\u662f\u7a0d\u5fae\u7528\u4e86\u9ede vim \u628a\u8f38\u5165\u6539\u6210 graphviz \u63cf\u8ff0\u8a9e\u8a00\u4f86\u756b\u5716\uff0c\u679c\u7136\u51fa\u73fe\u4e86\u8a08\u6578\u5668\u7d50\u69cb\uff0c\u4e5f\u5f9e\u9019\u7d50\u69cb\u4e2d\u8b80\u51fa\u4e86\u8f38\u51fa\u4e2d\u7684\u6578\u5b57\uff0c\u9032\u4e00\u6b65\u78ba\u5b9a\u4e86\u9019\u56db\u500b\u6578\u5b57\u5c31\u662f\u56db\u584a\u7684\u8ff4\u5708\u9577\u5ea6\uff0c\u6240\u4ee5\u7b54\u6848\u5c31\u662f\u5b83\u5011\u5168\u90e8\u4e58\u8d77\u4f86\u4e86\u3002<\/p>\n\n\n\n<p>\u6709\u4e00\u9ede\u9ede\u95dc\u9023\u7684\u984c\u5916\u8a71\u662f\uff1a\u4e5f\u8a31\u662f\u56e0\u70ba Minecraft 1.21 \u65b0\u589e\u9285\u71c8\uff0c\u4e00\u5806\u4eba\u7528\u9285\u71c8\u505a\u4e86\u6975\u7c21\u55ae\u7684\u8a08\u6578\u5668\u7684\u95dc\u4fc2\uff0c\u7576\u8b80\u5230\u984c\u76ee\u4e2d\u7684\u5169\u7a2e\u6a21\u7d44\u662f\u6b63\u53cd\u5668\u8ddf\u5408\u4f75\u904b\u7b97\u6642\u99ac\u4e0a\u60f3\u5230\u7684\u662f\u9019\u6b63\u53cd\u5668\u8a72\u4e0d\u6703\u62ff\u4f86\u7576\u8a08\u6578\u5668\u4e86\u5427\uff1b\u6240\u4ee5\u770b\u5230\u756b\u51fa\u4f86\u7684\u5716\u6642\u5b8c\u5168\u4e0d\u610f\u5916\uff0c\u53ea\u6709\u89e3\u8b80\u5beb\u5728\u88e1\u9762\u7684\u6578\u5b57\u8981\u600e\u9ebc\u8b80\u82b1\u4e86\u7d04\u83ab\u5341\u5206\u9418\u5de6\u53f3\u800c\u5df2\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">21. Step Counter<\/h2>\n\n\n\n<p>\u7167\u4f8b\uff0cpart 1 \u662f\u500b\u76f8\u5c0d\u53cb\u5584\u7684\u984c\u76ee\uff0c\u662f\u500b\u5f88\u57fa\u672c\u7684\u683c\u5b50\u5716\u4e0a\u7684\u55ae\u9ede\u6700\u77ed\u8def\u5f91\u554f\u984c\uff0c\u9019\u90e8\u4efd\u61c9\u8a72\u4e0d\u7528\u591a\u8aaa\u3002<\/p>\n\n\n\n<p>\u7136\u5f8c part 2 \u5c31\u8981\u9032\u5165\u5e73\u884c\u5b87\u5b99<sup data-fn=\"15040fe3-7a70-43ef-9607-c801827fe006\" class=\"fn\"><a href=\"#15040fe3-7a70-43ef-9607-c801827fe006\" id=\"15040fe3-7a70-43ef-9607-c801827fe006-link\">4<\/a><\/sup>\u4e86\u3002\u597d\u5728\u8f38\u5165\u6a94\u53c8\u6709\u82b1\u62db\uff1a\u9664\u4e86\u6bd4\u8f03\u660e\u986f\u7684\u947d\u77f3\u5f62\u659c\u5411\u7a7a\u8def\u4e4b\u5916\uff0c\u5176\u5be6\u9084\u6709\u597d\u5e7e\u500b\u884c\u5217\u662f\u5168\u7a7a\u7684\uff0c\u9019\u4ee3\u8868\u5c31\u7b97\u8981\u8d70\u5230\u9060\u8655\uff0c\u6211\u53ef\u4ee5\u6cbf\u8457\u5168\u7a7a\u7684\u8def\u5148\u885d\u5230\u9644\u8fd1\u518d\u8d70\u51fa\u53bb\u3002\u9019\u8868\u793a\uff0c\u7576\u5730\u5716\u5c55\u5230\u5f88\u9060\u7684\u6642\u5019\uff0c\u53ef\u5230\u9054\u9ede\u7684\u6a23\u5f0f\u6703\u662f\u4e00\u500b\u4e2d\u9593\u96a8\u8457\u5730\u5716\u91cd\u8986\u4e5f\u4e00\u8d77\u91cd\u8986\u7684\u6a23\u5f0f\uff0c\u908a\u754c\u6a23\u5f0f\u6578\u91cf\u6703\u7dda\u6027\u6210\u9577\uff0c\u4e2d\u9593\u6eff\u5716\u6a23\u5f0f\u6578\u91cf\u5247\u662f\u4e8c\u6b21\u6210\u9577 (\u4e0d\u8ad6\u5947\u5716\u6216\u5076\u5716\u90fd\u662f)\uff0c\u6240\u4ee5\u6700\u7d42\u7576\u53d6\u56fa\u5b9a\u6b65\u6578\u9593\u9694\u53d6\u6a23\u6642 (\u6211\u662f\u53d6\u5169\u500b\u5e73\u884c\u5b87\u5b99\u9577\uff0c\u4ee5\u4fdd\u6301\u5947\u5076\u6027\u6b63\u78ba)\uff0c\u7e3d\u53ef\u5230\u9054\u9ede\u6578\u91cf\u6703\u662f\u4e00\u500b\u4e8c\u6b21\u51fd\u6578\u3002\u65bc\u662f\u8dd1\u4e45\u4e00\u9ede\u8dd1\u51fa\u524d\u5e7e\u9805\uff0c\u5c31\u80fd\u5916\u63d2\u51fa\u6700\u7d42\u7d50\u679c\u4e86\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">22. Sand Slabs<\/h2>\n\n\n\n<p>\u610f\u5916\u7684\u662f\u500b\u57fa\u790e\u5716\u8ad6\u984c\u3002Part 1 \u7c21\u55ae\u7684\u4f9d\u5e95\u90e8\u6392\u5e8f (\u56e0\u70ba\u5927\u5bb6\u90fd\u662f\u9577\u65b9\u9ad4) \u4e4b\u5f8c\u5c31\u80fd\u5f9e\u5e95\u4e0b\u4e00\u8def\u8a66\u6389\uff0c\u53ea\u8981\u518d\u7d00\u9304\u4e00\u500b\u9ad8\u5ea6\u5716\u5c31\u80fd\u7c21\u55ae\u7684\u6aa2\u67e5\u6bcf\u500b\u65b9\u584a\u6703\u6389\u5230\u4ec0\u9ebc\u5730\u65b9\u53bb\uff0c\u4ee5\u53ca\u5b83\u6703\u88ab\u8ab0\u7d66\u63a5\u8457\uff0c\u628a\u9019\u500b\u63a5\u8457\u7684\u95dc\u9023\u53cd\u904e\u4f86\u5c31\u662f\u81ea\u5df1\u652f\u6490\u8457\u8ab0\uff1b\u90a3\u9ebc\u984c\u76ee\u8981\u7684\u6aa2\u67e5\uff0c\u5c31\u662f\u7576\u53d6\u8d70\u4e00\u584a\u6642\uff0c\u9019\u4e00\u584a\u6240\u652f\u6490\u7684\u65b9\u584a\u9084\u6709\u6c92\u6709\u5225\u7684\u65b9\u584a\u53ef\u4ee5\u652f\u6490\u3002<\/p>\n\n\n\n<p>Part 2 \u5247\u8b93\u6211\u60f3\u5230\u6211\u5728\u505a\u7de8\u8b6f\u5668\u7406\u8ad6\u6642\u63a5\u89f8\u5230\u7684<a href=\"https:\/\/zh.wikipedia.org\/wiki\/%E6%94%AF%E9%85%8D_(%E5%9C%96%E8%AB%96)\">\u7bc0\u9ede\u652f\u914d<\/a>\u7684\u6982\u5ff5\uff0c\u4e0d\u904e\u9451\u65bc\u9019\u984c\u7684\u5716\u662f\u500b DAG\uff0c\u662f\u4e0d\u592a\u9700\u8981\u9019\u9ebc\u8907\u96dc\u7684\u8655\u7406\u7684\u3002\u9019\u984c\u5982\u679c\u7167\u984c\u610f\u53bb\u63a8\u5230\u5e95\u62ff\u6389\u9019\u584a\u6703\u6709\u8ab0\u6389\u4e0b\u4f86\u7684\u8a71\uff0c\u91cd\u8986\u7684\u5de5\u5f88\u591a\uff1b\u4f46\u53cd\u904e\u4f86\u7684\u95dc\u4fc2\u2014\u2014\u7576\u8ab0\u88ab\u62ff\u6389\u6642\u81ea\u5df1\u6703\u6389\u2014\u2014\u5247\u662f\u500b\u5f88\u5bb9\u6613\u5f80\u5f8c\u63a8\u7684\u95dc\u9023\uff1a\u6211\u6703\u6389\u7684\u5145\u8981\u689d\u4ef6\u5c31\u662f\u62ff\u6389\u90a3\u4e00\u584a\u6703\u4f7f\u5f97\u6240\u6709\u652f\u6490\u6211\u7684\u4eba\u90fd\u6703\u6389\u3002\u56e0\u6b64\u5c31\u6aa2\u67e5\u652f\u6490\u8457\u81ea\u5df1\u7684\u65b9\u584a\uff0c\u5982\u679c\u53ea\u6709\u4e00\u584a\u90a3\u5c31\u662f\u4ed6\u7684\u6389\u843d\u689d\u4ef6\u52a0\u4ed6\u672c\u8eab\uff0c\u5982\u679c\u6709\u591a\u584a\u5247\u662f\u9019\u4e9b\u584a\u7684\u6389\u843d\u689d\u4ef6\u7684\u4ea4\u96c6\u3002(\u6240\u4ee5\u96e3\u5f97\u5728\u9019\u88e1\u7528\u4e86\u4e00\u6b21 <code>set_intersection<\/code> \u4e86) \u56e0\u70ba\u9019\u53ea\u662f\u53cd\u904e\u4f86\u7684\u95dc\u4fc2\uff0c\u984c\u76ee\u6240\u6c42\u540c\u6a23\u662f\u9019\u4e9b\u95dc\u4fc2\u6578\u91cf\u7684\u548c\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">23. A Long Walk<\/h2>\n\n\n\n<p>\u4eca\u5929\u7684\u984c\u76ee\u67d0\u7a2e\u7a0b\u5ea6\u4e0a\u9817\u70ba\u300c\u60e1\u8cea\u300d\uff0c\u6240\u4ee5\u64fa\u5728\u6700\u5f8c\u4e00\u500b\u661f\u671f\u516d\u6211\u89ba\u5f97\u662f\u6700\u597d\u7684\u4f4d\u7f6e\u3002(\u4eca\u5e74\u7684\u6700\u5f8c\u4e00\u500b\u661f\u671f\u65e5\u56e0\u70ba\u662f 24 \u865f\u6bd4\u8f03\u4e0d\u80fd\u64fa\u9019\u7a2e\u984c\u76ee\u3002)<\/p>\n\n\n\n<p>\u984c\u76ee\u6558\u8ff0\u4e0a\u662f\u4e00\u500b\u6a19\u6e96\u7684<a href=\"https:\/\/zh.m.wikipedia.org\/zh-tw\/%E6%9C%80%E9%95%BF%E8%B7%AF%E5%BE%84%E9%97%AE%E9%A2%98\">\u6700\u9577\u8def\u5f91\u554f\u984c<\/a>\uff0c\u800c\u6709\u4e9b\u683c\u5b50\u53ea\u80fd\u8d70\u55ae\u5411\u3002\u5982\u540c\u7dad\u57fa\u767e\u79d1\u6240\u8aaa\uff0c\u4e00\u822c\u7684\u6700\u9577\u8def\u5f91\u554f\u984c\u662f NP-Complete\uff0c\u56e0\u6b64\u9019\u984c\u7684\u8f38\u5165\u4e0a\u4e00\u5b9a\u6709\u4e9b\u6897\u5728\u88e1\u9762\u3002Part 1 \u7684\u6897\u662f\u9019\u4e9b\u55ae\u5411\u683c\u9023\u6210\u4e00\u500b <a href=\"https:\/\/zh.m.wikipedia.org\/wiki\/%E6%9C%89%E5%90%91%E6%97%A0%E7%8E%AF%E5%9B%BE\">DAG (\u6709\u5411\u7121\u5708\u5716)<\/a>\uff0c\u6240\u4ee5\u76f4\u63a5\u4ee5\u666e\u901a\u7684 BFS \u641c\u5c0b\u5373\u53ef\u6c42\u5f97\u6700\u9577\u8ddd\u96e2\u3002Part 2 \u4e0d\u7ba1\u55ae\u5411\u683c\u4e86\uff0c\u6bcf\u4e00\u683c\u90fd\u80fd\u5230\u8655\u8d70\uff1b\u9019\u88e1\u7684\u6897\u5247\u662f\u884c\u8d70\u5340\u57df\u5f62\u6210\u7684\u5716\u548c\u4e00\u500b\u53ea\u8003\u616e\u4ea4\u53c9\u9ede\u548c\u5176\u4e4b\u9593\u9023\u63a5\u9577\u5ea6\u7684\u5716\u540c\u80da\uff0c\u6240\u4ee5\u6211\u5011\u53ef\u4ee5\u5728\u9019\u500b\u540c\u80da\u4f46\u7bc0\u9ede\u6578\u5c0f\u5f88\u591a\u7684\u5716\u4e0a\u53bb\u505a\uff0c\u7562\u7adf\u6307\u6578\u6642\u9593\u505a\u6cd5\u53ea\u8981\u7bc0\u9ede\u6578\u80fd\u5c11\u4e00\u9ede\u90fd\u662f\u8cfa\u3002<\/p>\n\n\n\n<p>\u5f80\u5e74\u5176\u5be6\u4e5f\u4e0d\u662f\u6c92\u51fa\u904e\u53ea\u80fd\u786c\u505a\u7684\u984c\u76ee (\u6700\u7d93\u5178\u7684\u662f\u9996\u5e74 (2015) \u6709\u4e00\u984c\u8981\u4f60\u771f\u7684\u6316\u4e00\u500b\u7c21\u5316\u7248\u7684\u52a0\u5bc6\u8ca8\u5e63)\uff0c\u4e0d\u904e\u6211\u6703\u8aaa\u9019\u984c\u67d0\u7a2e\u7a0b\u5ea6\u4e0a\u6709\u9ede\u300c\u60e1\u8cea\u300d\u7684\u539f\u56e0\u662f\uff0c\u4ed6\u51fa\u7684\u662f\u4e00\u500b (\u4e5f\u662f\u7d93\u5178\u7684)\u300c\u96e3\u300d\u984c\uff0c\u4f46\u9019\u7a2e\u984c\u76ee\u7684\u300c\u96e3\u300d\u537b\u4e0d\u662f\u96a8\u4fbf\u4e00\u500b\u4f86\u5617\u8a66\u7684\u4eba\u90fd\u80fd\u99ac\u4e0a\u770b\u5f97\u51fa\u4f86\u7684\u3002\u4e00\u500b\u53ea\u6709\u63a5\u89f8\u904e\u5c11\u6578\u9019\u65b9\u9762\u6750\u6599\u7684\u4eba\uff0c\u5728\u524d\u9762\u984c\u76ee\u7576\u4e2d\u5b78\u5230\u4e86\u8981\u6539\u826f\u6f14\u7b97\u6cd5\u4ee5\u300c\u6700\u4f73\u5316\u300d\u7a0b\u5f0f\u6548\u7387\uff0c\u4f46\u537b\u5728\u9019\u88e1\u88ab\u4e00\u500b\u8de8\u4e0d\u904e\u53bb\u7684\u300cNP-Complete\u300d\u9ad8\u7246\u7d66\u64cb\u4f4f\u4e86\u3002<\/p>\n\n\n\n<p>\u561b\uff0c\u6211\u61c9\u8a72\u5c0d\u70ba\u4ec0\u9ebc\u6703\u9019\u6a23\u505a\u6709\u4e9b\u60f3\u6cd5\uff0c\u4e0d\u904e\u90a3\u5c31\u7559\u5230\u6700\u5f8c\u7e3d\u7d50\u6642\u518d\u4f86\u8a0e\u8ad6\u5427\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">24. Never Tell Me The Odds<\/h2>\n\n\n\n<p>\u771f\u662f\u6b98\u9177\u7684\u4e00\u984c\u3002\u9019\u984c\u5f9e\u4e00\u958b\u59cb\u5c31\u662f\u8a08\u7b97\u5e7e\u4f55\u7684\u984c\u76ee\uff1a\u7d66\u4f60\u4e00\u5806\u4e09\u7dad\u7a7a\u9593\u7684\u5c04\u7dda (\u8d77\u9ede\u548c\u55ae\u4f4d\u6642\u9593\u5167\u79fb\u52d5\u7684\u5411\u91cf)\uff0cpart 1 \u8981\u5148\u5ffd\u7565 z \u65b9\u5411\uff0c\u53ea\u770b x y\uff0c\u554f\u9019\u4e9b\u5c04\u7dda\u6709\u591a\u5c11\u4ea4\u9ede\u5728\u7d66\u5b9a\u7684\u5ea7\u6a19\u7bc4\u570d\u5167\uff1bpart 2 \u5247\u662f\u544a\u8a34\u6211\u5011\uff0c\u5b58\u5728\u4e00\u689d\u7279\u5b9a\u7684\u5c04\u7dda\uff0c\u4f7f\u5f97\u4e00\u500b\u5c0f\u77f3\u982d\u81ea\u6b64\u6cbf\u8457\u9019\u689d\u5c04\u7dda\u4ee5\u7d66\u5b9a\u901f\u5ea6\u98db\u7684\u8a71\uff0c\u6703\u548c\u6240\u6709\u6cbf\u8457\u524d\u9762\u7d66\u7684\u5c04\u7dda\u8dd1\u7684\u51b0\u96f9\u5728\u4ea4\u53c9\u7684\u6642\u5019\u6b63\u597d\u649e\u4e0a\u90a3\u4e9b\u51b0\u96f9\uff0c\u6c42\u51fa\u9019\u689d\u7279\u5b9a\u7684\u5c04\u7dda\u3002<\/p>\n\n\n\n<p>\u6211\u81ea\u8a8d\u8a08\u7b97\u5e7e\u4f55\u4e0d\u7b97\u662f\u6211\u7684\u5f31\u9805\uff0cpart 1 \u7d66\u5b9a\u5169\u689d\u5c04\u7dda\u76f4\u63a5\u806f\u7acb\u53c3\u6578\u5f0f\u5c31\u80fd\u89e3\u4ea4\u9ede\uff0c\u518d\u53bb\u5224\u65b7\u4ea4\u9ede\u662f\u4e0d\u662f\u5728\u5c04\u7dda\u79fb\u52d5\u65b9\u5411\u7684\u672a\u4f86\u4ee5\u53ca\u5176\u5ea7\u6a19\u5373\u53ef\uff1b\u4f46 part 2 \u6211\u662f\u5217\u51fa\u5f0f\u5b50\u4e86\uff0c\u4f46\u90a3\u662f\u516d\u689d\u516d\u5143\u4e8c\u6b21\u806f\u7acb\u65b9\u7a0b\u5f0f\uff0c\u6211\u76ef\u8457\u5b83\u597d\u5e7e\u500b\u5c0f\u6642\u5c31\u662f\u627e\u4e0d\u5230\u65b9\u6cd5\u53ef\u4ee5\u5316\u7c21\u5b83\uff0c\u6700\u5f8c\u662f\u56e0\u70ba\u5728 Mathematica \u88e1\u4e82\u8a66\u767c\u73fe\u5b83\u7adf\u7136\u795e\u5947\u7684\u53ef\u4ee5\u89e3\u51fa\u7b54\u6848\u4f86\uff0c\u5be6\u5728\u842c\u7b56\u76e1\u4e86\u53ea\u597d\u5c31\u628a\u7d66\u6211\u7684\u8f38\u5165\u7684\u5f0f\u5b50\u4e1f\u9032\u53bb\u7d66\u5b83\u89e3\u3002<\/p>\n\n\n\n<details class=\"wp-block-inline-spoilers-block\"><summary>\u6211\u7684\u5217\u5f0f\u5728\u88e1\u9762<\/summary>\u4ee4\u7b2c \\(i\\) \u689d\u5c04\u7dda\u662f\u81ea \\((p_{i,x},p_{i,y},p_{i,z})\\) \u8d77\u98db\uff0c\u901f\u5ea6\u70ba \\((v_{i,x},v_{i,y},v_{i,z})\\)\uff0c\u518d\u4ee4\u8981\u6c42\u7684\u5c0f\u77f3\u5b50\u7684\u5c04\u7dda\u7684\u4e0b\u6a19\u662f \\(i=0\\)\uff1b\u53c8\u4ee4\u5c0f\u77f3\u5b50\u548c\u7b2c \\(i\\) \u689d\u5c04\u7dda\u4ea4\u53c9\u6642\u7684\u6642\u9593\u662f \\(t_i\\)\u3002\u5247\u6613\u77e5\uff0c\u81ea\u51b0\u96f9\u8d77\u98db\u9ede\u8d77\uff0c\u6cbf\u8457\u51b0\u96f9\u901f\u5ea6\u98db \\(t_i\\) \u6642\u9593\uff0c\u518d\u6cbf\u8457\u5c0f\u77f3\u5b50\u901f\u5ea6\u53cd\u5411\u98db \\(t_i\\) \u6642\u9593\u6703\u56de\u5230\u5c0f\u77f3\u5b50\u7684\u8d77\u9ede\uff0c\u56e0\u6b64\u5c0d\u524d\u4e09\u689d\u5c04\u7dda\u5beb\u51fa\u6b64\u503c\u4ee4\u5176\u76f8\u7b49\u5373\u5f97\uff1a$$\\left\\{\\begin{aligned}p_{1,x}+t_1(v_{1,x}-v_{0,x})&amp;=p_{2,x}+t_2(v_{2,x}-v_{0,x})=p_{3,x}+t_3(v_{3,x}-v_{0,x})=p_{0,x}\\\\p_{1,y}+t_1(v_{1,y}-v_{0,y})&amp;=p_{2,y}+t_2(v_{2,y}-v_{0,y})=p_{3,y}+t_3(v_{3,y}-v_{0,y})=p_{0,y}\\\\p_{1,z}+t_1(v_{1,z}-v_{0,z})&amp;=p_{2,z}+t_2(v_{2,z}-v_{0,z})=p_{3,z}+t_3(v_{3,z}-v_{0,z})=p_{0,z}\\end{aligned}\\right.$$\u6700\u53f3\u908a\u7684 \\(p_{0,*}\\) \u5148\u4e0d\u770b\uff0c\u5de6\u908a\u7684\u516d\u500b\u7b49\u865f\u662f \\((t_1,t_2,t_3,v_{0,x},v_{0,y},v_{0,z})\\) \u516d\u500b\u672a\u77e5\u6578\u7684\u4e8c\u6b21\u806f\u7acb\u65b9\u7a0b\u3002\u9019\u500b\u65b9\u7a0b\u5be6\u5728\u6c92\u4ec0\u9ebc\u597d\u65b9\u6cd5\u53bb\u5316\u7c21\u5b83\uff0c\u4f46\u4e1f\u9032 Mathematica \u537b\u795e\u5947\u5730\u80fd\u89e3\u51fa\u7b54\u6848\u4f86\u3002<\/details>\n\n\n\n<p>\u7136\u5f8c\u5f8c\u4f86\u624d\u77e5\u9053\u539f\u4f86\u4e00\u822c\u4f86\u8aaa\uff0c<a href=\"https:\/\/math.stackexchange.com\/questions\/607348\/\">\u8981\u80fd\u552f\u4e00\u6c7a\u51fa\u4e00\u689d\u76f4\u7dda\u7a7f\u904e\u5176\u4ed6\u76f4\u7dda\u7684\u6578\u76ee\u662f\u56db\u689d<\/a>\uff0c\u4e0d\u904e\u770b\u8d77\u4f86\u597d\u50cf\u4e5f\u6c92\u4ec0\u9ebc\u597d\u7b97\u6cd5\u53bb\u6c42\u89e3\uff1b\u9019\u500b\u9023\u7d50\u88e1\u9762\u597d\u50cf\u63d0\u5230\u8981\u5728\u5c04\u5f71\u5e73\u9762\u53bb\u89e3\u5b83\uff0c\u7136\u5f8c\u4e2d\u9593\u4ecd\u7136\u9084\u662f\u6703\u51fa\u73fe\u4e8c\u6b21\u66f2\u9762\u7684\u6a23\u5b50\uff1f\u6240\u4ee5\u4e8c\u6b21\u5f0f\u9019\u4ef6\u4e8b\u597d\u50cf\u9084\u662f\u8eb2\u4e0d\u6389\u7684\u6a23\u5b50\u2026\u2026<\/p>\n\n\n\n<p>\u88dc\u8a18\uff1a\u679c\u7136\u60f3\u6cd5\u8f49\u500b\u5f4e\u5c31\u80fd\u89e3\u4e86\u3002<a href=\"https:\/\/www.reddit.com\/r\/adventofcode\/comments\/18pnycy\/2023_day_24_solutions\/kesvc7t\/\">Reddit \u4e0a\u7684\u9019\u500b\u89e3\u6cd5<\/a>\u6211\u8f49\u5beb\u4e00\u4e0b\uff1a<\/p>\n\n\n\n<details class=\"wp-block-inline-spoilers-block\"><summary>\u4e0a\u8ff0\u89e3\u6cd5<\/summary>\u628a\u4e0a\u9762\u7684\u7b49\u5f0f\u6539\u89e3\u51fa \\(t_i\\) \u51fa\u4f86\uff0c\u6211\u5011\u6709\uff1a$$t_i=\\frac{p_{0,x}-p_{i,x}}{v_{i,x}-v_{0,x}}=\\frac{p_{0,y}-p_{i,y}}{v_{i,y}-v_{0,y}}=\\frac{p_{0,z}-p_{i,z}}{v_{i,z}-v_{0,z}}$$\u5148\u4e0d\u7ba1 z \u5ea7\u6a19\uff0c\u5c0d x \u548c y \u5ea7\u6a19\u505a\u4ea4\u53c9\u76f8\u4e58\u5f97$$(p_{0,x}-p_{i,x})(v_{i,y}-v_{0,y})-(p_{0,y}-p_{i,y})(v_{i,x}-v_{0,x})=0\\\\(p_{0,x}v_{i,y}-p_{i,x}v_{i,y}-p_{0,x}v_{0,y}+p_{i,x}v_{0,y})-(p_{0,y}v_{i,x}-p_{i,y}v_{i,x}-p_{0,y}v_{0,x}+p_{i,y}v_{0,x})=0$$\u4e0a\u8ff0\u5f0f\u5b50\u5c0d \\(i=1,2\\) \u5217\u51fa\u76f8\u6e1b\u6d88\u53bb\u672a\u77e5\u6578\u7684\u4e58\u7a4d\u9805\u5f97$$\\begin{align}&amp;p_{0,x}(v_{1,y}-v_{2,y})-(p_{1,x}v_{1,y}-p_{2,x}v_{2,y})+(p_{1,x}-p_{2,x})v_{0,y}\\\\&amp;-p_{0,y}(v_{1,x}-v_{2,x})+(p_{1,y}v_{1,x}-p_{2,y}v_{2,x})-(p_{1,y}-p_{2,y})v_{0,x}=0\\end{align}$$\u9019\u662f\u56db\u500b\u672a\u77e5\u6578 \\((p_{0,x},p_{0,y},v_{0,x},v_{0,y})\\) \u7684\u7dda\u6027\u65b9\u7a0b\uff1b\u5c0d\u4efb\u4f55\u5169\u5c0d\u5c04\u7dda\u90fd\u6709\u9019\u689d\u5f0f\u5b50\uff0c\u6240\u4ee5\u5c31\u9078\u56db\u5c0d\u5217\u51fa\u4f86\u4e4b\u5f8c\u514b\u62c9\u746a\u6216\u9ad8\u65af\u5c31\u80fd\u89e3\u4e86\u3002\u91cd\u9ede\u662f\u5728\u6539\u4ee5 \\(t_i\\) \u5217\u7b49\u5f0f\u4e4b\u5f8c\u6211\u5011\u6709\u8fa6\u6cd5\u53d6\u5169\u689d\u7dda\u628a\u4e8c\u6b21\u9805\u7d66\u6d88\u6389\uff0c\u9019\u5728\u4ee5 \\(p_{0,*}\\) \u5217\u7b49\u5f0f\u6642\u662f\u4e0d\u597d\u627e\u7684\u3002<\/details>\n\n\n\n<h2 class=\"wp-block-heading\">25. Snowverload<\/h2>\n\n\n\n<p>\u4f9d\u7167\u6163\u4f8b\uff0c\u6700\u5f8c\u4e00\u5929\u53ea\u6703\u6709\u4e00\u984c\uff0c\u800c\u4e14\u6703\u76f8\u5c0d\u7c21\u55ae\u4e00\u4e9b\u3002\u9019\u984c\u662f\u500b\u7121\u5411\u5716 min cut\uff0c\u65bc\u662f\u6211\u5728\u7dad\u57fa\u767e\u79d1\u4e0a\u7ffb\u4e86\u7ffb\u767c\u73fe\u9019\u500b <a href=\"https:\/\/en.wikipedia.org\/wiki\/Karger%27s_algorithm\">Karger&#8217;s algorithm<\/a>\uff0c\u96d6\u7136\u662f\u96a8\u6a5f\u6f14\u7b97\u6cd5\u4f46\u8dd1\u8d77\u4f86\u610f\u5916\u7684\u5feb\uff0c\u8f38\u5165\u6a94\u4e00\u5343\u56db\u767e\u591a\u500b\u7bc0\u9ede\u5728\u7b2c 15 \u6b21\u5617\u8a66\u5c31\u627e\u5230\u9019\u500b 3 edge cut \u4e86\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u5e74\u5ea6\u5fc3\u5f97<\/h2>\n\n\n\n<p>\u53ef\u4ee5\u770b\u5f97\u51fa\u4f86\u4eca\u5e74\u7684\u984c\u76ee\u6709\u300c\u8907\u96dc\u5316\u300d\u7684\u50be\u5411\u3002\u8a31\u591a\u8f38\u5165\u6a94\u6848\u7684\u6578\u5b57\u90fd\u662f\u76f4\u63a5\u8d85\u904e 32-bit \u6578\u503c\u76f4\u903c 2<sup>53<\/sup><sup data-fn=\"dba4bd6b-7ccb-48dc-8fdb-af3e94fe4e5e\" class=\"fn\"><a href=\"#dba4bd6b-7ccb-48dc-8fdb-af3e94fe4e5e\" id=\"dba4bd6b-7ccb-48dc-8fdb-af3e94fe4e5e-link\">5<\/a><\/sup>\uff0c\u52a0\u4e0a part 2 \u7684\u984c\u76ee\u8a2d\u8a08\u57fa\u672c\u4e0a\u5c31\u662f\u8981\u89e3\u984c\u8005\u8a8d\u771f\u60f3\u65b9\u6cd5\u89e3\uff0c\u4e0d\u8981\u7e3d\u662f\u7528\u529b\u91cf\u649e\u3002(\u4eca\u5e74 reddit \u4e0a\u7684\u597d\u4e9b\u8ff7\u56e0\u90fd\u662f\u5728\u8aaa\u4e0d\u7ba1\u4ec0\u9ebc\u554f\u984c\uff0c\u649e\u500b\u4e09\u5929\u7e3d\u662f\u6703\u8dd1\u51fa\u7b54\u6848\u4f86 XD) \u96d6\u7136 Eric \u6c92\u6709\u516c\u958b\u627f\u8a8d\u904e (\u4ed6\u5728 reddit \u4e0a\u7e3d\u662f\u8aaa\u4ed6\u4eca\u5e74\u505a\u7684\u9664\u4e86\u52a0\u4e0a\u4e0d\u8981\u7528 AI \u7684\u898f\u5247\u4e4b\u5916\u6c92\u4ec0\u9ebc\u4e0d\u4e00\u6a23\u7684)\uff0c\u4f46\u6211\u60f3\u4ed6\u4eca\u5e74\u7684\u51fa\u984c\u65b9\u5411\u78ba\u5be6\u6709\u5728\u671d\u8457\u4e0d\u8981\u8b93\u751f\u6210\u5f0f AI \u6709\u6a5f\u6703\u731c\u4e2d\u7b54\u6848\u524d\u9032\uff1a\u751f\u6210\u5f0f AI \u5c0d\u9019\u7a2e\u4e00\u4e32\u96a8\u6a5f\u6578\u5b57\u7684\u6771\u897f\u4f86\u8aaa\u662f\u6700\u982d\u75db\u7684\uff0c\u56e0\u70ba\u9664\u4e86\u78ba\u5be6\u53bb\u5f9e\u6578\u5b57\u4e2d\u53bb\u731c\u95dc\u4fc2\u4e4b\u5916\uff0c\u5176\u4ed6\u5c0d\u6587\u5b57\u9810\u6e2c\u7684\u77e5\u8b58\u4e0d\u6703\u5c0d\u6b63\u78ba\u7b54\u51fa\u9019\u4e9b\u6771\u897f\u6709\u6240\u5e6b\u52a9\u3002\u9019\u4e00\u9ede\u53ef\u80fd\u4e5f\u662f\u4eca\u5e74\u524d\u4e09\u984c\u90fd\u6709\u8f38\u5165\u5b57\u4e32\u5206\u6790\u7684\u5143\u7d20\u5728\u88e1\u9762\u7684\u539f\u56e0\uff1a\u5f9e\u4e00\u5718\u4e82\u78bc\u6587\u5b57\u88e1\u627e\u8cc7\u8a0a\u4e5f\u4e0d\u662f\u751f\u6210\u5f0f AI \u7684\u5f37\u9805\uff0c\u4ed6\u5011\u53ef\u80fd\u6703\u6df9\u6c92\u5728\u96dc\u8a0a\u7576\u4e2d\u3002<\/p>\n\n\n\n<p>\u540c\u6a23\u7684\u50be\u5411\u4e5f\u8868\u73fe\u5728\u51fa\u984c\u65b9\u5411\uff1a\u5f80\u5e74\u7684\u984c\u76ee\u76f8\u8f03\u8d77\u4f86\u6bd4\u8f03\u6c92\u6709\u90a3\u9ebc\u591a\u300c\u5c08\u696d\u300d\u984c\u2014\u2014\u6211\u6307\u7684\u662f\u5728\u4e00\u822c\u8cc7\u6599\u7d50\u69cb\u53ca\u6f14\u7b97\u6cd5\u8ab2\u7a0b\u88e1\u6703\u5b78\u5230\u7684\u5404\u985e\u578b\u7684\u6f14\u7b97\u6cd5\uff1b\u4ee5\u524d\u5927\u6982\u6700\u591a\u5c31\u662f\u6700\u77ed\u8def\u5f91\u6216\u52d5\u614b\u898f\u5283\u9019\u7a2e\u7a0b\u5ea6\uff0c\u9019\u4e9b\u5c0d\u65bc\u7a0b\u5f0f\u521d\u5b78\u8005\u4f86\u8aaa\u53ea\u8981\u627e\u5230\u597d\u6559\u6750\u4e0a\u624b\u4e0d\u662f\u554f\u984c\uff0c\u4f46\u4eca\u5e74\u4e0d\u4f46\u6709\u4e09\u984c\u8a08\u7b97\u5e7e\u4f55 (Day 10\u3001Day 18\u3001Day 24)\uff0c\u6700\u5f8c\u9019\u5e7e\u984c\u771f\u7684\u5df2\u7d93\u958b\u59cb\u6709 leetcode \u7684\u611f\u89ba\u4e86\u3002Day 23 \u6703\u51fa\u4e00\u984c NP-Complete \u53ef\u80fd\u4e5f\u662f\u9019\u500b\u539f\u56e0\u5427\u3002<\/p>\n\n\n\n<p>\u4e0d\u904e\u5982\u6b64\u8abf\u6574\u7684\u7d50\u679c\uff0c\u4eca\u5e74\u7684\u984c\u76ee\u76f8\u5c0d\u5f80\u5e74\u771f\u7684\u6709\u8b8a\u96e3\uff0c\u4e5f\u6709\u770b\u5230\u4e0d\u5c11\u4eca\u5e74\u624d\u8df3\u9032\u4f86\u7684\u4eba\u6c92\u4e09\u56db\u984c\u5c31\u8df3\u8eca\u4e86\u7684\u6587\u7ae0\uff1b\u800c\u6709\u4e9b\u984c\u76ee\u70ba\u4e86\u8abf\u6574\u96e3\u5ea6\u8b93\u984c\u76ee\u51fa\u7684\u6709\u9ede\u554f\u984c (\u50cf\u662f Day 8 \u7684\u72c0\u6cc1\uff1b\u540c\u6a23\u72c0\u6cc1\u51fa\u5728 Day 20 \u597d\u50cf\u5c31\u76f8\u5c0d\u597d\u4e00\u4e9b\uff0c\u4f46\u51fa\u5728 Day 8 \u8b93\u984c\u76ee\u8b8a\u5f97\u6709\u9ede\u7cdf)\uff0c\u9019\u53ef\u80fd\u4e5f\u662f\u672a\u4f86\u9700\u8981\u6539\u9032\u7684\u5730\u65b9\u3002<\/p>\n\n\n\n<p>\u90a3\u9ebc\u9019\u5c31\u662f\u4eca\u5e74\u7684 Advent of Code \u4e86\u3002\u4e4b\u524d\u63d0\u904e\u6211\u5f8c\u9762\u5728\u505a\u7684\u6771\u897f\u53ef\u80fd\u904e\u5e74\u671f\u9593\u770b\u80fd\u4e0d\u80fd\u6bd4\u8f03\u6709\u7a7a\u628a\u5b83\u6536\u5c3e\u6389\u653e\u51fa\u4f86 XD Merry Christmas!<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">\u8a3b\u8173<\/h2>\n\n\n<ol class=\"wp-block-footnotes\"><li id=\"ff82ba11-be10-4a9e-a3ff-f7f7d9c4a0e5\">\u6211\u53bb\u5e74\u7684\u6587\u7ae0\u88e1\u6709\u63d0\u5230\u904e\u90a3\u500b DC \u7fa4\uff1b\u524d\u5e74 (2021) \u6211\u6703\u8dd1\u56de\u4f86\u505a\u4e5f\u662f\u56e0\u70ba\u5728\u90a3\u7fa4\u88e1\u770b\u5230\u7684\u539f\u56e0\u3002 <a href=\"#ff82ba11-be10-4a9e-a3ff-f7f7d9c4a0e5-link\" aria-label=\"\u8fd4\u56de\u8a3b\u8173\u53c3\u7167 1\">\u21a9\ufe0e<\/a><\/li><li id=\"25a46db4-e11a-411c-998a-dc5b8a3db574\">\u6709\u4eba\u5728 megathread \u88e1\u63d0\u5230 <a href=\"https:\/\/projecteuler.net\/problem=54\">PE054<\/a>\uff0c\u6240\u4ee5\u679c\u7136\u64b2\u514b\u984c\u578b\u662f\u7a0b\u5f0f\u8a2d\u8a08\u7df4\u7fd2\u6311\u6230\u984c\u7684\u6163\u4f8b XD <a href=\"#25a46db4-e11a-411c-998a-dc5b8a3db574-link\" aria-label=\"\u8fd4\u56de\u8a3b\u8173\u53c3\u7167 2\">\u21a9\ufe0e<\/a><\/li><li id=\"b370ff7b-6b1c-4c8c-9ab8-20f2d6dadd88\">\u73fe\u5728\u9084\u6709\u591a\u5c11\u4eba\u8a18\u5f97\u300c\u4eca\u5e74\u662f\u4e94\u500d\u300d\u7684\u54fd\u554a\uff1f\uff01 <a href=\"#b370ff7b-6b1c-4c8c-9ab8-20f2d6dadd88-link\" aria-label=\"\u8fd4\u56de\u8a3b\u8173\u53c3\u7167 3\">\u21a9\ufe0e<\/a><\/li><li id=\"15040fe3-7a70-43ef-9607-c801827fe006\">\u6709\u5728\u770b\u8ff7\u56e0\u7684\u61c9\u8a72\u77e5\u9053\u300c\u6211\u9818\u5148\u4f60\u56db\u500b\u5e73\u884c\u5b87\u5b99\u300d\u7684\u99ac\u5229\u6b50\u7684\u8ff7\u56e0\u5427\uff1f\u9019\u500b\u8ff7\u56e0\u88e1\u7684\u300c\u5e73\u884c\u5b87\u5b99\u300d\u5728\u5176\u539f\u59cb\u4f86\u6e90\u88e1\u5c31\u662f\u5728\u8b1b\u5730\u5716\u91cd\u8986\uff0c\u4e0d\u904e\u9019\u8981\u7d30\u8b1b\u4e0b\u53bb\u5c31\u662f\u4e00\u7bc7\u77ed\u6587\u7684\u7a0b\u5ea6\u4e86\u6240\u4ee5\u5728\u6b64\u7565\u904e\uff1b\u6709\u8208\u8da3\u4e86\u89e3\u7684\u53ef\u4ee5\u770b <a href=\"https:\/\/knowyourmeme.com\/memes\/05x-a-presses-but-first-we-need-to-talk-about-parallel-universes\">knowyourmeme \u7684\u89e3\u8aaa<\/a>\u3002<a href=\"https:\/\/redd.it\/18ngud1\">reddit<\/a> \u4e0a\u4e5f\u6709\u4eba\u63d0\u5230\u9019\u500b\u54fd\u3002 <a href=\"#15040fe3-7a70-43ef-9607-c801827fe006-link\" aria-label=\"\u8fd4\u56de\u8a3b\u8173\u53c3\u7167 4\">\u21a9\ufe0e<\/a><\/li><li id=\"dba4bd6b-7ccb-48dc-8fdb-af3e94fe4e5e\">\u5c0d\u9084\u4e0d\u77e5\u9053\u9019\u500b\u6578\u7684\u7279\u6b8a\u6027\u7684\u4eba\uff1a2<sup>53<\/sup>-1\u9019\u500b\u6578\u5728 JavaScript \u88e1\u7a31\u505a <a href=\"https:\/\/developer.mozilla.org\/en-US\/docs\/Web\/JavaScript\/Reference\/Global_Objects\/Number\/MAX_SAFE_INTEGER\">Number.MAX_SAFE_INTEGER<\/a>\uff0c\u662f\u500d\u7cbe\u78ba\u5ea6\u6d6e\u9ede\u6578\u80fd\u5920\u6b63\u78ba\u8868\u793a (+1 \u6216 -1 \u4e0d\u6703\u56e0\u70ba\u7cbe\u5ea6\u4e0d\u5920\u800c\u8b8a\u56de\u81ea\u5df1) \u7684\u6574\u6578\u6700\u5927\u503c\u3002\u5be6\u969b\u6578\u503c\u7d04\u662f 9\u00d710<sup>15<\/sup>\uff0c\u4ea6\u5373\u5e7e\u4e4e\u6db5\u84cb 16 \u4f4d\u6574\u6578\u7684\u7bc4\u570d\u3002\u9019\u5c0d\u4e00\u4e9b\u6578\u5b57\u578b\u614b\u53ea\u6709\u6d6e\u9ede\u6578\u7684\u7a0b\u5f0f\u8a9e\u8a00 (\u5982 JavaScript \u6216 Lua) \u4f86\u8aaa\u662f\u4ee3\u8868\u4e86\u300c\u6574\u6578\u300d\u7684\u4e0a\u9650\u503c\u3002 <a href=\"#dba4bd6b-7ccb-48dc-8fdb-af3e94fe4e5e-link\" aria-label=\"\u8fd4\u56de\u8a3b\u8173\u53c3\u7167 5\">\u21a9\ufe0e<\/a><\/li><\/ol>","protected":false},"excerpt":{"rendered":"<p>\u53c8\u5230\u4e86\u5e74\u672b Advent of Code \u7684\u6642\u9593\u4e86\u3002\u95dc\u65bc\u9019\u500b\u6d3b\u52d5\u9084\u8acb\u53c3\u7167\u53bb\u5e74\u7684\u6587\u7ae0\uff1b\u4e0d\u904e\u9451\u65bc\u53bb\u5e74\u524d\u5e7e\u5929\u767c\u751f\u7684\u4e8b [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":"[{\"content\":\"\u6211\u53bb\u5e74\u7684\u6587\u7ae0\u88e1\u6709\u63d0\u5230\u904e\u90a3\u500b DC \u7fa4\uff1b\u524d\u5e74 (2021) \u6211\u6703\u8dd1\u56de\u4f86\u505a\u4e5f\u662f\u56e0\u70ba\u5728\u90a3\u7fa4\u88e1\u770b\u5230\u7684\u539f\u56e0\u3002\",\"id\":\"ff82ba11-be10-4a9e-a3ff-f7f7d9c4a0e5\"},{\"content\":\"\u6709\u4eba\u5728 megathread \u88e1\u63d0\u5230 <a href=\\\"https:\/\/projecteuler.net\/problem=54\\\">PE054<\/a>\uff0c\u6240\u4ee5\u679c\u7136\u64b2\u514b\u984c\u578b\u662f\u7a0b\u5f0f\u8a2d\u8a08\u7df4\u7fd2\u6311\u6230\u984c\u7684\u6163\u4f8b XD\",\"id\":\"25a46db4-e11a-411c-998a-dc5b8a3db574\"},{\"content\":\"\u73fe\u5728\u9084\u6709\u591a\u5c11\u4eba\u8a18\u5f97\u300c\u4eca\u5e74\u662f\u4e94\u500d\u300d\u7684\u54fd\u554a\uff1f\uff01\",\"id\":\"b370ff7b-6b1c-4c8c-9ab8-20f2d6dadd88\"},{\"content\":\"\u6709\u5728\u770b\u8ff7\u56e0\u7684\u61c9\u8a72\u77e5\u9053\u300c\u6211\u9818\u5148\u4f60\u56db\u500b\u5e73\u884c\u5b87\u5b99\u300d\u7684\u99ac\u5229\u6b50\u7684\u8ff7\u56e0\u5427\uff1f\u9019\u500b\u8ff7\u56e0\u88e1\u7684\u300c\u5e73\u884c\u5b87\u5b99\u300d\u5728\u5176\u539f\u59cb\u4f86\u6e90\u88e1\u5c31\u662f\u5728\u8b1b\u5730\u5716\u91cd\u8986\uff0c\u4e0d\u904e\u9019\u8981\u7d30\u8b1b\u4e0b\u53bb\u5c31\u662f\u4e00\u7bc7\u77ed\u6587\u7684\u7a0b\u5ea6\u4e86\u6240\u4ee5\u5728\u6b64\u7565\u904e\uff1b\u6709\u8208\u8da3\u4e86\u89e3\u7684\u53ef\u4ee5\u770b <a href=\\\"https:\/\/knowyourmeme.com\/memes\/05x-a-presses-but-first-we-need-to-talk-about-parallel-universes\\\">knowyourmeme \u7684\u89e3\u8aaa<\/a>\u3002<a href=\\\"https:\/\/redd.it\/18ngud1\\\">reddit<\/a> \u4e0a\u4e5f\u6709\u4eba\u63d0\u5230\u9019\u500b\u54fd\u3002\",\"id\":\"15040fe3-7a70-43ef-9607-c801827fe006\"},{\"content\":\"\u5c0d\u9084\u4e0d\u77e5\u9053\u9019\u500b\u6578\u7684\u7279\u6b8a\u6027\u7684\u4eba\uff1a2<sup>53<\/sup>-1\u9019\u500b\u6578\u5728 JavaScript \u88e1\u7a31\u505a <a href=\\\"https:\/\/developer.mozilla.org\/en-US\/docs\/Web\/JavaScript\/Reference\/Global_Objects\/Number\/MAX_SAFE_INTEGER\\\">Number.MAX_SAFE_INTEGER<\/a>\uff0c\u662f\u500d\u7cbe\u78ba\u5ea6\u6d6e\u9ede\u6578\u80fd\u5920\u6b63\u78ba\u8868\u793a (+1 \u6216 -1 \u4e0d\u6703\u56e0\u70ba\u7cbe\u5ea6\u4e0d\u5920\u800c\u8b8a\u56de\u81ea\u5df1) \u7684\u6574\u6578\u6700\u5927\u503c\u3002\u5be6\u969b\u6578\u503c\u7d04\u662f 9\u00d710<sup>15<\/sup>\uff0c\u4ea6\u5373\u5e7e\u4e4e\u6db5\u84cb 16 \u4f4d\u6574\u6578\u7684\u7bc4\u570d\u3002\u9019\u5c0d\u4e00\u4e9b\u6578\u5b57\u578b\u614b\u53ea\u6709\u6d6e\u9ede\u6578\u7684\u7a0b\u5f0f\u8a9e\u8a00 (\u5982 JavaScript \u6216 Lua) \u4f86\u8aaa\u662f\u4ee3\u8868\u4e86\u300c\u6574\u6578\u300d\u7684\u4e0a\u9650\u503c\u3002\",\"id\":\"dba4bd6b-7ccb-48dc-8fdb-af3e94fe4e5e\"}]"},"categories":[51,4],"tags":[31],"class_list":["post-1587","post","type-post","status-publish","format-standard","hentry","category-aoclike","category-programming","tag-advent-of-code"],"_links":{"self":[{"href":"https:\/\/blog.cruciferslab.net\/index.php?rest_route=\/wp\/v2\/posts\/1587","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=1587"}],"version-history":[{"count":72,"href":"https:\/\/blog.cruciferslab.net\/index.php?rest_route=\/wp\/v2\/posts\/1587\/revisions"}],"predecessor-version":[{"id":1728,"href":"https:\/\/blog.cruciferslab.net\/index.php?rest_route=\/wp\/v2\/posts\/1587\/revisions\/1728"}],"wp:attachment":[{"href":"https:\/\/blog.cruciferslab.net\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1587"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.cruciferslab.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1587"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.cruciferslab.net\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1587"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}