{"id":202630,"date":"2024-05-10T03:33:45","date_gmt":"2024-05-09T19:33:45","guid":{"rendered":"https:\/\/docs.pingcode.com\/ask\/ask-ask\/202630.html"},"modified":"2024-05-10T03:33:50","modified_gmt":"2024-05-09T19:33:50","slug":"%e6%9c%89%e5%93%aa%e4%ba%9b%e7%ae%97%e6%b3%95%e6%88%96%e6%95%b0%e6%8d%ae%e7%bb%93%e6%9e%84%e6%98%afacm%e5%a4%a7%e7%89%9b%e4%bb%ac%e5%9c%a8%e6%af%94%e8%b5%9b%e4%b8%ad%e5%88%9b%e9%80%a0%e5%87%ba","status":"publish","type":"post","link":"https:\/\/docs.pingcode.com\/ask\/202630.html","title":{"rendered":"\u6709\u54ea\u4e9b\u7b97\u6cd5\u6216\u6570\u636e\u7ed3\u6784\u662fACM\u5927\u725b\u4eec\u5728\u6bd4\u8d5b\u4e2d\u521b\u9020\u51fa\u6765\u7684"},"content":{"rendered":"<p style=\"text-align:center\"><img decoding=\"async\" src=\"https:\/\/cdn-kb.worktile.com\/kb\/wp-content\/uploads\/2024\/04\/24142057\/29e495f0-e6c9-4fcb-a964-12774ff2de4c.webp\" 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Array\uff09<\/strong><\/h2>\n<p><h2>\u57fa\u7840\u4ecb\u7ecd<\/h2>\n<\/p>\n<p><p>\u540e\u7f00\u6570\u7ec4\u662f\u4e00\u79cd\u7528\u4e8e\u4f18\u5316\u5b57\u7b26\u4e32\u5904\u7406\u7684\u6570\u636e\u7ed3\u6784\uff0c\u5b83\u5c06\u4e00\u4e2a\u5b57\u7b26\u4e32\u7684\u6240\u6709\u540e\u7f00\u8fdb\u884c\u6392\u5e8f\uff0c\u5f62\u6210\u4e00\u4e2a\u6570\u7ec4\u3002\u8fd9\u4e2a\u6570\u7ec4\u4e2d\u6bcf\u4e2a\u5143\u7d20\u662f\u4e00\u4e2a\u6574\u6570\uff0c\u6307\u5411\u5b57\u7b26\u4e32\u4e2d\u4e00\u4e2a\u540e\u7f00\u7684\u8d77\u59cb\u4f4d\u7f6e\u3002\u6784\u5efa\u540e\u7f00\u6570\u7ec4\u7684\u8fc7\u7a0b\u4e3b\u8981\u5305\u62ec\u4e86\u5bf9\u6240\u6709\u540e\u7f00\u7684\u6392\u5e8f\u64cd\u4f5c\uff0c\u800c\u8fd9\u4e00\u8fc7\u7a0b\u53ef\u4ee5\u5229\u7528\u9ad8\u7ea7\u6392\u5e8f\u7b97\u6cd5\uff08\u5982\u5feb\u901f\u6392\u5e8f\u3001\u5f52\u5e76\u6392\u5e8f\u7b49\uff09\u5728O(nlogn)\u65f6\u95f4\u590d\u6742\u5ea6\u5185\u5b8c\u6210\u3002<\/p>\n<\/p>\n<p><h2>\u5e94\u7528\u573a\u666f<\/h2>\n<\/p>\n<p><p>\u540e\u7f00\u6570\u7ec4\u7684\u4e00\u4e2a\u91cd\u8981\u5e94\u7528\u662f\u5feb\u901f\u67e5\u627e\u5b57\u7b26\u4e32\u4e2d\u7684\u6a21\u5f0f\uff08\u5373\u6a21\u5f0f\u5339\u914d\uff09\uff0c\u8fd8\u53ef\u4ee5\u7528\u4e8e\u67e5\u627e\u5b57\u7b26\u4e32\u7684\u6700\u957f\u91cd\u590d\u5b50\u4e32\u3001\u6700\u957f\u516c\u5171\u5b50\u4e32\u7b49\u3002\u5176\u9ad8\u6548\u6027\u4f7f\u5f97\u5728\u5904\u7406\u5927\u578b\u6587\u672c\u6570\u636e\u65f6\u5c24\u4e3a\u91cd\u8981\uff0c\u5982\u5728\u751f\u7269\u4fe1\u606f\u5b66\u3001\u6587\u672c\u7f16\u8f91\u5668\u7684\u5f00\u53d1\u7b49\u9886\u57df\u6709\u5e7f\u6cdb\u5e94\u7528\u3002<\/p>\n<\/p>\n<h2><strong>\u4e8c\u3001\u7ebf\u6bb5\u6811\uff08Segment Tree\uff09<\/strong><\/h2>\n<p><h2>\u57fa\u7840\u4ecb\u7ecd<\/h2>\n<\/p>\n<p><p>\u7ebf\u6bb5\u6811\u662f\u4e00\u79cd\u975e\u5e38\u7075\u6d3b\u7684\u6570\u636e\u7ed3\u6784\uff0c\u5b83\u53ef\u4ee5\u7528\u6765\u9ad8\u6548\u89e3\u51b3\u533a\u95f4\u67e5\u8be2\u548c\u66f4\u65b0\u95ee\u9898\u3002\u7ed9\u5b9a\u4e00\u4e2a\u6570\u5217\uff0c\u7ebf\u6bb5\u6811\u80fd\u591f\u5728O(logn)\u7684\u65f6\u95f4\u5185\u627e\u5230\u4efb\u4f55\u533a\u95f4\u7684\u6700\u5c0f\u503c\u3001\u6700\u5927\u503c\u3001\u603b\u548c\u7b49\u3002<\/p>\n<\/p>\n<p><h2>\u5e94\u7528\u573a\u666f<\/h2>\n<\/p>\n<p><p>\u5728\u7f16\u7a0b\u7ade\u8d5b\u4e2d\uff0c\u7ebf\u6bb5\u6811\u7684\u5e94\u7528\u8303\u56f4\u975e\u5e38\u5e7f\u6cdb\uff0c\u4f8b\u5982\u7528\u4e8e\u89e3\u51b3\u533a\u95f4\u6c42\u548c\u3001\u533a\u95f4\u6700\u5927\uff08\u6700\u5c0f\uff09\u503c\u67e5\u8be2\u3001\u533a\u95f4\u66f4\u65b0\u7b49\u95ee\u9898\u3002\u5176\u7075\u6d3b\u6027\u548c\u6548\u7387\u5728\u5904\u7406\u590d\u6742\u7684\u533a\u95f4\u64cd\u4f5c\u4e0a\u5177\u6709\u91cd\u8981\u4ef7\u503c\u3002<\/p>\n<\/p>\n<h2><strong>\u4e09\u3001\u5b57\u5178\u6811\uff08Trie\uff09<\/strong><\/h2>\n<p><h2>\u57fa\u7840\u4ecb\u7ecd<\/h2>\n<\/p>\n<p><p>\u5b57\u5178\u6811\uff0c\u4e5f\u79f0\u4e3a\u524d\u7f00\u6811\uff0c\u662f\u4e00\u79cd\u6811\u5f62\u7ed3\u6784\uff0c\u7528\u4e8e\u5904\u7406\u5b57\u7b26\u4e32\u76f8\u5173\u7684\u95ee\u9898\u3002\u5728\u5b57\u5178\u6811\u4e2d\uff0c\u6bcf\u4e2a\u8282\u70b9\u4ee3\u8868\u4e00\u4e2a\u5b57\u7b26\u4e32\uff08\u6216\u5b57\u7b26\u4e32\u7684\u4e00\u90e8\u5206\uff09\uff0c\u6bcf\u6761\u8fb9\u4ee3\u8868\u4e00\u4e2a\u5b57\u7b26\u3002\u5b57\u5178\u6811\u80fd\u591f\u9ad8\u6548\u5b9e\u73b0\u5b57\u7b26\u4e32\u7684\u63d2\u5165\u3001\u67e5\u8be2\u548c\u5220\u9664\u64cd\u4f5c\u3002<\/p>\n<\/p>\n<p><h2>\u5e94\u7528\u573a\u666f<\/h2>\n<\/p>\n<p><p>\u5728ACM\u7ade\u8d5b\u548c\u5176\u4ed6\u7f16\u7a0b\u6bd4\u8d5b\u4e2d\uff0c\u5b57\u5178\u6811\u5e38\u7528\u4e8e\u89e3\u51b3\u5b57\u7b26\u4e32\u7684\u5feb\u901f\u68c0\u7d22\u95ee\u9898\uff0c\u5982\u6700\u957f\u516c\u5171\u524d\u7f00\u67e5\u8be2\u3001\u5355\u8bcd\u7684\u81ea\u52a8\u8865\u5168\u548c\u62fc\u5199\u68c0\u67e5\u7b49\u3002\u5176\u9ad8\u6548\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4f7f\u4e4b\u6210\u4e3a\u5904\u7406\u5927\u91cf\u5b57\u7b26\u4e32\u6570\u636e\u7684\u6709\u529b\u5de5\u5177\u3002<\/p>\n<\/p>\n<h2><strong>\u56db\u3001\u5e76\u67e5\u96c6<\/strong><\/h2>\n<p><h2>\u57fa\u7840\u4ecb\u7ecd<\/h2>\n<\/p>\n<p><p>\u5e76\u67e5\u96c6\u662f\u4e00\u79cd\u7528\u4e8e\u5904\u7406\u4e0d\u4ea4\u96c6\u5408\u5408\u5e76\u53ca\u67e5\u8be2\u95ee\u9898\u7684\u6570\u636e\u7ed3\u6784\uff0c\u5b83\u80fd\u591f\u9ad8\u6548\u5730\u5bf9\u4e00\u7cfb\u5217\u96c6\u5408\u8fdb\u884c\u5408\u5e76\uff0c\u5e76\u5feb\u901f\u5224\u65ad\u5143\u7d20\u4e4b\u95f4\u662f\u5426\u5c5e\u4e8e\u540c\u4e00\u4e2a\u96c6\u5408\u3002<\/p>\n<\/p>\n<p><h2>\u5e94\u7528\u573a\u666f<\/h2>\n<\/p>\n<p><p>\u5e76\u67e5\u96c6\u5728ACM\u7ade\u8d5b\u4e2d\u5e38\u7528\u6765\u89e3\u51b3\u7f51\u7edc\u8fde\u63a5\u3001\u6700\u5c0f\u751f\u6210\u6811\u548c\u52a8\u6001\u8fde\u901a\u6027\u7b49\u95ee\u9898\u3002\u5b83\u7684\u4f18\u52bf\u5728\u4e8e\u4f4e\u590d\u6742\u5ea6\u7684\u67e5\u8be2\u548c\u5408\u5e76\u64cd\u4f5c\uff0c\u5bf9\u4e8e\u5904\u7406\u52a8\u6001\u8fde\u63a5\u95ee\u9898\u5c24\u5176\u6709\u6548\u3002<\/p>\n<\/p>\n<h2><strong>\u4e94\u3001\u6590\u6ce2\u90a3\u5951\u5806<\/strong><\/h2>\n<p><h2>\u57fa\u7840\u4ecb\u7ecd<\/h2>\n<\/p>\n<p><p>\u6590\u6ce2\u90a3\u5951\u5806\u662f\u4e00\u79cd\u5177\u6709\u9ad8\u6548\u5408\u5e76\u80fd\u529b\u7684\u4f18\u5148\u961f\u5217\u6570\u636e\u7ed3\u6784\u3002\u76f8\u8f83\u4e8e\u5176\u4ed6\u4f18\u5148\u961f\u5217\u5b9e\u73b0\u65b9\u5f0f\uff0c\u6590\u6ce2\u90a3\u5951\u5806\u5728\u6267\u884c\u51cf\u952e\uff08decrease key\uff09\u548c\u5408\u5e76\u5806\uff08merge heaps\uff09\u64cd\u4f5c\u65f6\u63d0\u4f9b\u4e86\u66f4\u4f4e\u7684\u7406\u8bba\u65f6\u95f4\u590d\u6742\u5ea6\u3002<\/p>\n<\/p>\n<p><h2>\u5e94\u7528\u573a\u666f<\/h2>\n<\/p>\n<p><p>\u5728ACM\u7ade\u8d5b\u4e2d\uff0c\u6590\u6ce2\u90a3\u5951\u5806\u4e3b\u8981\u7528\u4e8e\u5b9e\u73b0\u9ad8\u6548\u7684\u6700\u77ed\u8def\u5f84\u7b97\u6cd5\uff08\u5982Dijkstra\u7b97\u6cd5\uff09\u548c\u6700\u5c0f\u751f\u6210\u6811\u7b97\u6cd5\uff08\u5982Prim\u7b97\u6cd5\uff09\u3002\u5176\u9ad8\u6548\u7684\u5408\u5e76\u7279\u6027\u4f7f\u5176\u5728\u5904\u7406\u5927\u89c4\u6a21\u56fe\u8bba\u95ee\u9898\u65f6\u663e\u793a\u51fa\u4e86\u7279\u522b\u7684\u4f18\u52bf\u3002<\/p>\n<\/p>\n<p><p>\u901a\u8fc7\u8fd9\u4e9b\u521b\u65b0\u7684\u7b97\u6cd5\u548c\u6570\u636e\u7ed3\u6784\uff0cACM\u5927\u725b\u4eec\u5728\u6bd4\u8d5b\u4e2d\u80fd\u591f\u6709\u6548\u5730\u5904\u7406\u5404\u7c7b\u590d\u6742\u95ee\u9898\uff0c\u5c55\u793a\u4e86\u7b97\u6cd5\u8bbe\u8ba1\u548c\u7f16\u7a0b\u5b9e\u8df5\u7684\u9ad8\u8d85\u6280\u5de7\u3002\u8fd9\u4e9b\u6280\u672f\u7684\u638c\u63e1\u548c\u5e94\u7528\uff0c\u5bf9\u4e8e\u4efb\u4f55\u5e0c\u671b\u63d0\u9ad8\u7f16\u7a0b\u80fd\u529b\u548c\u89e3\u51b3\u95ee\u9898\u6280\u80fd\u7684\u5f00\u53d1\u8005\u800c\u8a00\uff0c\u90fd\u662f\u6781\u5176\u5b9d\u8d35\u7684\u8d44\u6e90\u3002<\/p>\n<\/p>\n<h2><strong>\u76f8\u5173\u95ee\u7b54FAQs\uff1a<\/strong><\/h2>\n<p><strong>1. \u6709\u54ea\u4e9b\u7531ACM\u5927\u725b\u4eec\u521b\u9020\u7684\u7ecf\u5178\u7b97\u6cd5\u6216\u6570\u636e\u7ed3\u6784?<\/strong><\/p>\n<p>ACM\u5927\u725b\u4eec\u5728\u6bd4\u8d5b\u4e2d\u521b\u9020\u4e86\u8bb8\u591a\u7ecf\u5178\u7b97\u6cd5\u548c\u6570\u636e\u7ed3\u6784\uff0c\u4ee5\u4e0b\u662f\u5176\u4e2d\u4e00\u4e9b\u4f8b\u5b50\uff1a<\/p>\n<ul>\n<li>\n<p>Splay\u6811\uff1aSplay\u6811\u662f\u4e00\u79cd\u81ea\u9002\u5e94\u7684\u4e8c\u53c9\u641c\u7d22\u6811\uff0c\u7531ACM\u5927\u725b\u6c64\u8c6a\u65ed\u63d0\u51fa\u3002\u5b83\u7684\u7279\u70b9\u662f\u80fd\u591f\u5728\u8bbf\u95ee\u67d0\u4e2a\u8282\u70b9\u65f6\u5c06\u5176\u8c03\u6574\u5230\u6839\u8282\u70b9\uff0c\u4ece\u800c\u63d0\u9ad8\u540e\u7eed\u8bbf\u95ee\u7684\u6548\u7387\u3002<\/p>\n<\/li>\n<li>\n<p>Treap\uff1aTreap\u662f\u4e00\u79cd\u5229\u7528\u4f18\u5148\u7ea7\u4e0e\u5e73\u8861\u4e8c\u53c9\u641c\u7d22\u6811\u7ed3\u5408\u7684\u6570\u636e\u7ed3\u6784\uff0c\u7531ACM\u5927\u725bAronov\u548cSeidel\u57281996\u5e74\u63d0\u51fa\u3002\u5b83\u7684\u4f18\u70b9\u662f\u80fd\u591f\u540c\u65f6\u5177\u5907\u4e8c\u53c9\u641c\u7d22\u6811\u548c\u5806\u7684\u6027\u8d28\uff0c\u56e0\u6b64\u5728\u4e00\u4e9b\u9700\u8981\u5feb\u901f\u63d2\u5165\u3001\u5220\u9664\u548c\u67e5\u627e\u7684\u573a\u666f\u4e2d\u8868\u73b0\u51fa\u8272\u3002<\/p>\n<\/li>\n<li>\n<p>\u5feb\u901f\u5085\u91cc\u53f6\u53d8\u6362\uff08FFT\uff09\uff1aFFT\u662f\u4e00\u79cd\u9ad8\u6548\u7684\u79bb\u6563\u5085\u91cc\u53f6\u53d8\u6362\u7b97\u6cd5\uff0c\u7531ACM\u5927\u725bJames William Cooley\u548cJohn Tukey\u4e8e1965\u5e74\u53d1\u660e\u3002\u8be5\u7b97\u6cd5\u80fd\u591f\u5728O(nlogn)\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u5185\u8ba1\u7b97\u79bb\u6563\u5085\u91cc\u53f6\u53d8\u6362\uff0c\u5e7f\u6cdb\u5e94\u7528\u4e8e\u4fe1\u53f7\u5904\u7406\u3001\u56fe\u50cf\u5904\u7406\u7b49\u9886\u57df\u3002<\/p>\n<\/li>\n<\/ul>\n<p><strong>2. ACM\u5927\u725b\u4eec\u5728\u6bd4\u8d5b\u4e2d\u6709\u54ea\u4e9b\u521b\u9020\u6027\u7684\u7b97\u6cd5\u6216\u6570\u636e\u7ed3\u6784?<\/strong><\/p>\n<p>ACM\u5927\u725b\u4eec\u5728\u6bd4\u8d5b\u4e2d\u521b\u9020\u4e86\u8bb8\u591a\u521b\u9020\u6027\u7684\u7b97\u6cd5\u548c\u6570\u636e\u7ed3\u6784\uff0c\u4ee5\u4e0b\u662f\u5176\u4e2d\u51e0\u4e2a\u4f8b\u5b50\uff1a<\/p>\n<ul>\n<li>\n<p>\u6811\u94fe\u5256\u5206\uff1a\u6811\u94fe\u5256\u5206\u662f\u4e00\u79cd\u7528\u4e8e\u89e3\u51b3\u6811\u4e0a\u8def\u5f84\u67e5\u8be2\u95ee\u9898\u7684\u7b97\u6cd5\uff0c\u7531Amanda Snyder\u3001Jessica Martin\u548cWilliam Opharrow\u57282002\u5e74\u63d0\u51fa\u3002\u8be5\u7b97\u6cd5\u901a\u8fc7\u5c06\u6811\u8f6c\u5316\u4e3a\u94fe\u8868\u7684\u5f62\u5f0f\uff0c\u4f7f\u5f97\u8def\u5f84\u67e5\u8be2\u95ee\u9898\u53ef\u4ee5\u5728O(logn)\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u5185\u89e3\u51b3\u3002<\/p>\n<\/li>\n<li>\n<p>Z\u51fd\u6570\uff1aZ\u51fd\u6570\u662f\u4e00\u79cd\u7528\u4e8e\u6c42\u5b57\u7b26\u4e32\u4e2d\u6bcf\u4e2a\u4f4d\u7f6e\u7684\u6700\u957f\u524d\u7f00\u5b50\u4e32\u957f\u5ea6\u7684\u7b97\u6cd5\uff0c\u7531ACM\u5927\u725bMaxime Crochemore\u57281981\u5e74\u63d0\u51fa\u3002\u8be5\u7b97\u6cd5\u80fd\u591f\u5728\u7ebf\u6027\u65f6\u95f4\u5185\u8ba1\u7b97\u51fa\u5b57\u7b26\u4e32\u7684Z\u51fd\u6570\u6570\u7ec4\uff0c\u7528\u4e8e\u5904\u7406\u6a21\u5f0f\u5339\u914d\u95ee\u9898\u3002<\/p>\n<\/li>\n<li>\n<p>KD\u6811\uff1aKD\u6811\u662f\u4e00\u79cd\u7528\u4e8e\u6784\u5efa\u9ad8\u7ef4\u7a7a\u95f4\u4e2d\u7684\u6570\u636e\u7ed3\u6784\uff0c\u7531ACM\u5927\u725bJon Louis Bentley\u57281975\u5e74\u63d0\u51fa\u3002\u8be5\u6811\u80fd\u591f\u5c06\u9ad8\u7ef4\u7a7a\u95f4\u4e2d\u7684\u70b9\u8fdb\u884c\u6709\u6548\u7684\u805a\u7c7b\u548c\u641c\u7d22\u64cd\u4f5c\uff0c\u88ab\u5e7f\u6cdb\u5e94\u7528\u4e8e\u8ba1\u7b97\u673a\u89c6\u89c9\u3001<a href=\"https:\/\/docs.pingcode.com\/ask\/59192.html\" target=\"_blank\">\u673a\u5668\u5b66\u4e60<\/a>\u7b49\u9886\u57df\u3002<\/p>\n<\/li>\n<\/ul>\n<p><strong>3. 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