{"id":754,"date":"2023-02-08T09:43:06","date_gmt":"2023-02-08T01:43:06","guid":{"rendered":"http:\/\/www.algmain.com\/?page_id=754"},"modified":"2023-02-15T09:26:18","modified_gmt":"2023-02-15T01:26:18","slug":"hashtree","status":"publish","type":"page","link":"http:\/\/www.algmain.com\/index.php\/algorithm-article\/hashtree\/","title":{"rendered":"\u54c8\u5e0c\u6811\u67e5\u627e"},"content":{"rendered":"\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p><strong>\u77e5\u4e4e\uff1a<\/strong><a rel=\"noreferrer noopener\" href=\"https:\/\/zhuanlan.zhihu.com\/p\/290832847\" target=\"_blank\">\u54c8\u5e0c\u6811\uff08HashTree\uff09\u67e5\u627e\u7b97\u6cd5<\/a><br><strong>CSDN :\u00a0<\/strong><a rel=\"noreferrer noopener\" href=\"https:\/\/blog.csdn.net\/weixin_42574918\/article\/details\/109718660\" target=\"_blank\">\u54c8\u5e0c\u6811\uff08HashTree\uff09\u67e5\u627e\u7b97\u6cd5<\/a><br><strong>\u767e\u5ea6\u6587\u5e93\uff1a<\/strong><a rel=\"noreferrer noopener\" href=\"https:\/\/wenku.baidu.com\/view\/16b2c7abd1f34693daef3e58.html\" target=\"_blank\">\u54c8\u5e0c\u6811\uff08HashTree\uff09\u67e5\u627e\u7b97\u6cd5<\/a><\/p>\n<\/blockquote>\n\n\n\n<h2 class=\"wp-block-heading\">\u54c8\u5e0c\u6811(HashTree)<\/h2>\n\n\n\n<p>\u4f9d\u636e\u54c8\u5e0c\u51fd\u6570\u67e5\u627e\u7b97\u6cd5\u8981\u6c42\uff0c\u5c06\u6570\u636e\u96c6\u5408\u4e2d\u7684\u6570\u636e\u8bb0\u5f55\u6309\u7167\u4e00\u5b9a\u7684\u89c4\u5f8b\u7ec4\u7ec7\u8d77\u6765\uff0c\u5f62\u6210\u591a\u53c9\u6811\u7ed3\u6784\u3002\u8be5\u6570\u636e\u7ed3\u6784\u53ef\u4ee5\u88ab\u79f0\u4e3a\u54c8\u5e0c\u6811\uff08HashTree\uff09\u3002<\/p>\n\n\n\n<p>\u5728\u8fd9\u91cc\u5047\u5b9a\u6240\u6709\u7684\u6570\u636e\u8bb0\u5f55\u5747\u4ee5\\((key, value)\\)\u7684\u5f62\u5f0f\u8fdb\u884c\u5b58\u50a8\u3002\u5176\u4e2d\\(key\\)\u4ee3\u8868\u6570\u636e\u8bb0\u5f55\u7684\u5173\u952e\u5b57\uff0c\\(value\\)\u4ee3\u8868\u5177\u4f53\u7684\u6570\u636e\u3002\u5bf9\u4e8e\u7ed9\u5b9a\u7684\u6570\u503c\\(k\\)\uff0c\u67e5\u627e\u7684\u76ee\u7684\u5c31\u662f\u5728\u6570\u636e\u96c6\u5408\u4e2d\u627e\u5230\\(key = k\\)\u7684\u6570\u636e\u8bb0\u5f55\uff0c\u6216\u8005\u8fd4\u56de\u6570\u636e\u96c6\u5408\u4e2d\u4e0d\u5b58\u5728\u8fd9\u6837\u7684\\(key\\)&nbsp;\u3002\u4e3a\u4e86\u7ed8\u56fe\u548c\u8ba8\u8bba\u7684\u7b80\u4fbf\u6027\uff0c\u540e\u9762\u4ec5\u8ba8\u8bba\u548c\u6570\u503c\u5173\u952e\u5b57\\(key\\)\u90e8\u5206\u3002<\/p>\n\n\n\n<p>\u4e3a\u4e86\u540e\u7eed\u7b97\u6cd5\u8bf4\u660e\u7684\u7b80\u4fbf\u6027\uff0c\u8fd9\u91cc\u9009\u62e9\u54c8\u5e0c\u51fd\u6570\u7684\u9664\u6570\u5e8f\u5217\\(M=\\{2,3,5\\}\\)&nbsp;\u3002\uff08\u5176\u4e2d\uff09\\(M(n)\\)\u8868\u793a\u9664\u6570\u5e8f\u5217\u6570\u7ec4\u7684\u6570\u503c\u3002\u4f8b\u5982\uff1a\\(M(1)=2&nbsp;\uff0cM(2)=3&nbsp;\uff0cM(3)=5\\)\u3002\u5177\u4f53\u7a0b\u5e8f\u8bbe\u8ba1\u65f6\uff0c\u53ef\u4ee5\u6309\u7167\u672c\u6587\u4e4b\u524d\u63a8\u8350\u7684\u65b9\u6cd5\u9009\u62e9\u9664\u6570\u5e8f\u5217\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u7ec4\u7ec7\u7ed3\u6784<\/h2>\n\n\n\n<p>\u54c8\u5e0c\u6811\u6570\u636e\u7ed3\u6784\u662f\u4e00\u79cd\u5178\u578b\u7684\u591a\u53c9\u6811\u7ed3\u6784\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"474\" height=\"199\" src=\"http:\/\/www.algmain.com\/wp-content\/uploads\/2023\/02\/v2-819341880f126b8b6c51fc870a55f753_1440w.jpg\" alt=\"\" class=\"wp-image-1013\" srcset=\"http:\/\/www.algmain.com\/wp-content\/uploads\/2023\/02\/v2-819341880f126b8b6c51fc870a55f753_1440w.jpg 474w, http:\/\/www.algmain.com\/wp-content\/uploads\/2023\/02\/v2-819341880f126b8b6c51fc870a55f753_1440w-300x126.jpg 300w\" sizes=\"(max-width: 474px) 100vw, 474px\" \/><figcaption class=\"wp-element-caption\">\u56fe1 \u5178\u578b\u7684\u591a\u53c9\u6811\u7ed3\u6784<\/figcaption><\/figure>\n\n\n\n<p>\u4f46\u662f\u54c8\u5e0c\u6811\u6570\u636e\u7ed3\u6784\u4e0e\u5e38\u89c1\u7684\u591a\u53c9\u6811\u53c8\u6709\u663e\u8457\u7684\u4e0d\u540c\u3002\u4e0b\u56fe\u662f\u4e00\u4e2a\u5178\u578b\u7684\u54c8\u5e0c\u6811\u6570\u636e\u7ed3\u6784\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"353\" height=\"937\" src=\"http:\/\/www.algmain.com\/wp-content\/uploads\/2023\/02\/v2-8b1bd0bd4ae9e32ed8d78d039d2dc305_1440w.webp\" alt=\"\" class=\"wp-image-1015\" srcset=\"http:\/\/www.algmain.com\/wp-content\/uploads\/2023\/02\/v2-8b1bd0bd4ae9e32ed8d78d039d2dc305_1440w.webp 353w, http:\/\/www.algmain.com\/wp-content\/uploads\/2023\/02\/v2-8b1bd0bd4ae9e32ed8d78d039d2dc305_1440w-113x300.webp 113w\" sizes=\"(max-width: 353px) 100vw, 353px\" \/><figcaption class=\"wp-element-caption\">\u56fe2 \u57fa\u4e8e\u9664\u6570\u5e8f\u5217M\u7684\u54c8\u5e0c\u6811\u6570\u636e\u7ed3\u6784<\/figcaption><\/figure>\n\n\n\n<p>\u5982\u56fe2\u6240\u793a\uff0c\u8be5\u54c8\u5e0c\u6811\u6570\u636e\u7ed3\u6784\u662f\u57fa\u4e8e\u9664\u6570\u5e8f\u5217\u6784\u5efa\u7684\u3002<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Root\u4e3a\u54c8\u5e0c\u6811\u7684\u6839\uff08\u6df1\u84dd\u8272\u8282\u70b9\uff09\u3002<\/li>\n\n\n\n<li>R0\u548cR1\u4e3a\u7b2c\u4e00\u5c42\u8282\u70b9\uff08\u7070\u8272\u8282\u70b9\uff09\u5171\u67092\u4e2a\uff0c\u5bf9\u5e94\u9664\u6570\u5e8f\u5217\u4e2d\u7684\u7b2c\u4e00\u4e2a\u6570&nbsp;\\(M(1)=2\\)\u3002<\/li>\n\n\n\n<li>R00\u3001R01\u3001R02\u3001R10\u3001R11\u3001R12\u4e3a\u7b2c\u4e8c\u5c42\u8282\u70b9\uff08\u9ec4\u8272\u8282\u70b9\uff09\u51716\u4e2a\u3002\u5176\u4e2dR00\u3001R01\u548cR02\u662f\u5c5e\u4e8eR0\u7684\u5b50\u8282\u70b9\uff0cR10\u3001R11\u548cR12\u662f\u5c5e\u4e8eR1\u7684\u5b50\u8282\u70b9\u3002R0\u548cR1\u4e0b\u5206\u522b\u67093\u4e2a\u5b50\u8282\u70b9\uff0c\u5bf9\u5e94\u9664\u6570\u5e8f\u5217\u4e2d\u7684\u7b2c\u4e8c\u4e2a\u6570\\(M(2)=3\\)\u3002<\/li>\n\n\n\n<li>\u540e\u7eed\u7684R00\u3001R01\u3001R02\u3001R10\u3001R11\u548cR12\u8282\u70b9\u4e0b\u53c8\u5206\u522b\u67095\u4e2a\u5b50\u8282\u70b9\uff08\u767d\u8272\u8282\u70b9\uff09\uff0c\u5bf9\u5e94\u9664\u6570\u5e8f\u5217\u4e2d\u7684\u7b2c\u4e09\u4e2a\u6570\\(M(3)=5\\)\u3002<\/li>\n<\/ol>\n\n\n\n<p>\u8bfb\u8005\u7531\u672c\u4f8b\u53ef\u4ee5\u63a8\u77e5\uff0c\u6bcf\u4e00\u5c42\u8282\u70b9\u4e0b\u7684\u5b50\u8282\u70b9\u4e2a\u6570\u4e0e\u9664\u6570\u5e8f\u5217\u7684\u5173\u7cfb\u3002\u54c8\u5e0c\u6811\u6570\u636e\u7ed3\u6784\u7684\u5b9e\u9645\u60c5\u51b5\uff0c\u4e0e\u6307\u5b9a\u7684\u9664\u6570\u5e8f\u5217\u6709\u7740\u7d27\u5bc6\u7684\u8054\u7cfb\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u63d2\u5165\u6570\u636e<\/h2>\n\n\n\n<p>\uff08\u6b65\u9aa41\uff09\u5047\u8bbe\u5f53\u524d\u54c8\u5e0c\u6811\u6570\u636e\u7ed3\u6784\u4e2d\u6ca1\u6709\u4efb\u4f55\u6570\u636e\u8bb0\u5f55\uff0c\u73b0\u5728\u65b0\u63d2\u5165\u4e00\u6761\u6570\u636e\u8bb0\u5f55&nbsp;(\\(key=25\\))&nbsp;\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"294\" height=\"94\" src=\"http:\/\/www.algmain.com\/wp-content\/uploads\/2023\/02\/v2-8f29373f7ed01e879e7b1fc5c9ef9659_1440w.jpg\" alt=\"\" class=\"wp-image-1233\"\/><figcaption class=\"wp-element-caption\">\u56fe3 \u5728\u54c8\u5e0c\u6811\u4e2d\u63d2\u5165\u4e00\u6761\u6570\u636e\u8bb0\u5f55<\/figcaption><\/figure>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u67e5\u8be2\u9664\u6570\u5e8f\u5217\u53ef\u77e5\uff0c\u6839\u8282\u70b9\u4e0b\u5e94\u8be5\u6709\\(M(1)=2\\)\u4e2a\u8282\u70b9\u3002\u6839\u636e\u524d\u9762\u6240\u63cf\u8ff0\u5f97\u7b97\u6cd5\uff0c\u5c06\u5173\u952e\u5b57\u6570\u503c\u53d6\u4f59\u53ef\u5f97&nbsp;\\(1\\,(25\\, mod \\,2)\\)\u3002\u7531\u4e8e\u6839\u8282\u70b9\u4e0b\u76ee\u524d\u6ca1\u6709\u4efb\u4f55\u5b50\u8282\u70b9\uff0c\u56e0\u6b64\u5148\u751f\u6210\u4e00\u4e2a\u5b50\u8282\u70b9R1\uff0c\u5e76\u5c06\u6570\u636e\u8bb0\u5f55\u653e\u7f6e\u81f3R1\u8282\u70b9\u4e2d\u3002\n<ul class=\"wp-block-list\">\n<li><\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n<figure class=\"wp-block-image aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"286\" height=\"94\" src=\"http:\/\/www.algmain.com\/wp-content\/uploads\/2023\/02\/v2-dbe23abd7f760e0aa5e0009cf3f57c85_1440w.jpg\" alt=\"\" class=\"wp-image-1234\"\/><figcaption class=\"wp-element-caption\">\u56fe4 \u5c06\u6570\u636e\u8bb0\u5f55\u653e\u81f3R1\u8282\u70b9\u4e2d<\/figcaption><\/figure>\n\n\n\n<p>\uff08\u6b65\u9aa42\uff09\u5728\u6b64\u6b21\u64cd\u4f5c\u5b8c\u6210\u4e4b\u540e\uff0c\u7ee7\u7eed\u65b0\u63d2\u5165\u4e00\u6761\u6570\u636e\u8bb0\u5f55&nbsp;(\\(key=12\\))&nbsp;\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"486\" height=\"94\" src=\"http:\/\/www.algmain.com\/wp-content\/uploads\/2023\/02\/v2-13b65595ff759f9a1682a2eff01ece2e_1440w.jpg\" alt=\"\" class=\"wp-image-1236\" srcset=\"http:\/\/www.algmain.com\/wp-content\/uploads\/2023\/02\/v2-13b65595ff759f9a1682a2eff01ece2e_1440w.jpg 486w, http:\/\/www.algmain.com\/wp-content\/uploads\/2023\/02\/v2-13b65595ff759f9a1682a2eff01ece2e_1440w-300x58.jpg 300w\" sizes=\"(max-width: 486px) 100vw, 486px\" \/><figcaption class=\"wp-element-caption\">\u56fe5\u5728\u54c8\u5e0c\u6811\u4e2d\u63d2\u5165\u4e00\u6761\u65b0\u6570\u636e\u8bb0\u5f55<\/figcaption><\/figure>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u67e5\u8be2\u9664\u6570\u5e8f\u5217\u53ef\u77e5\uff0c\u6839\u8282\u70b9\u4e0b\u5e94\u8be5\u6709\\(M(1)=2\\)\u4e2a\u8282\u70b9\u3002\u6839\u636e\u524d\u9762\u6240\u63cf\u8ff0\u5f97\u7b97\u6cd5\uff0c\u5c06\u5173\u952e\u5b57\u6570\u503c\u53d6\u4f59\u53ef\u5f97\\(0\\,(12\\, mod \\,&nbsp;2)&nbsp;\\)\u3002\u7531\u4e8e\u6839\u8282\u70b9\u4e0b\u76ee\u524d\u6ca1\u6709\u4efb\u4f55\u5b50\u8282\u70b9\uff0c\u56e0\u6b64\u5148\u751f\u6210\u4e00\u4e2a\u5b50\u8282\u70b9R0\uff0c\u5e76\u5c06\u6570\u636e\u8bb0\u5f55\u653e\u7f6e\u81f3R0\u8282\u70b9\u4e2d\u3002<\/li>\n<\/ol>\n\n\n\n<figure class=\"wp-block-image aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"286\" height=\"108\" src=\"http:\/\/www.algmain.com\/wp-content\/uploads\/2023\/02\/v2-f53b3af0247e593777b1fc6ec13ac588_1440w.jpg\" alt=\"\" class=\"wp-image-1239\"\/><figcaption class=\"wp-element-caption\">\u56fe6 \u5c06\u6570\u636e\u8bb0\u5f55\u653e\u81f3R0\u8282\u70b9\u4e2d<\/figcaption><\/figure>\n\n\n\n<p>\uff08\u6b65\u9aa43\uff09\u5728\u6b64\u6b21\u64cd\u4f5c\u5b8c\u6210\u4e4b\u540e\uff0c\u7ee7\u7eed\u65b0\u63d2\u5165\u4e00\u6761\u6570\u636e\u8bb0\u5f55&nbsp;(\\(key=13\\))&nbsp;\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"486\" height=\"108\" src=\"http:\/\/www.algmain.com\/wp-content\/uploads\/2023\/02\/v2-deb2f2afff8ecf958f88e04916bbc85b_1440w.jpg\" alt=\"\" class=\"wp-image-1240\" srcset=\"http:\/\/www.algmain.com\/wp-content\/uploads\/2023\/02\/v2-deb2f2afff8ecf958f88e04916bbc85b_1440w.jpg 486w, http:\/\/www.algmain.com\/wp-content\/uploads\/2023\/02\/v2-deb2f2afff8ecf958f88e04916bbc85b_1440w-300x67.jpg 300w\" sizes=\"(max-width: 486px) 100vw, 486px\" \/><figcaption class=\"wp-element-caption\">\u56fe7\u5728\u54c8\u5e0c\u6811\u4e2d\u63d2\u5165\u4e00\u6761\u65b0\u6570\u636e\u8bb0\u5f55<\/figcaption><\/figure>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u67e5\u8be2\u9664\u6570\u5e8f\u5217\u53ef\u77e5\uff0c\u6839\u8282\u70b9\u4e0b\u5e94\u8be5\u6709\\(M(1)=2\\)\u4e2a\u8282\u70b9\u3002\u6839\u636e\u524d\u9762\u6240\u63cf\u8ff0\u5f97\u7b97\u6cd5\uff0c\u5c06\u5173\u952e\u5b57\u6570\u503c\u53d6\u4f59\u53ef\u5f97\\(1\\,(13\\,&nbsp;mod \\,&nbsp;2)\\)&nbsp;\u3002\u8c03\u53d6\u8282\u70b9R1\u7684\u72b6\u6001\uff0c\u53d1\u73b0\u8be5\u8282\u70b9\u5df2\u7ecf\u5b58\u50a8\u4e86\u4e00\u6761\u6570\u636e\u8bb0\u5f55\u3002\u56e0\u6b64\u9700\u8981\u7ee7\u7eed\u67e5\u8be2R1\u4e0b\u7684\u5b50\u8282\u70b9\u5bfb\u627e\u7a7a\u51fa\u7684\u5b58\u50a8\u4f4d\u7f6e\u3002<\/li>\n\n\n\n<li>\u67e5\u8be2\u9664\u6570\u5e8f\u5217\u53ef\u77e5\uff0cR1\u8282\u70b9\u4e0b\u5e94\u8be5\u6709\\(M(2)=3\\)\u4e2a\u8282\u70b9\u3002\u5c06\u5173\u952e\u5b57\u6570\u503c\u53d6\u4f59\u53ef\u5f97&nbsp;\uff09\\(1\\,(13\\, mod \\,&nbsp;3)\\)&nbsp;\u3002\u7531\u4e8eR1\u8282\u70b9\u4e0b\u7684R11\u8282\u70b9\u5e76\u672a\u751f\u6210\uff0c\u53ef\u4ee5\u5148\u751f\u6210R11\u8282\u70b9\uff0c\u5e76\u5c06\u6570\u636e\u8bb0\u5f55\u653e\u7f6e\u5176\u4e2d\u3002<\/li>\n<\/ol>\n\n\n\n<figure class=\"wp-block-image aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"423\" height=\"108\" src=\"http:\/\/www.algmain.com\/wp-content\/uploads\/2023\/02\/v2-6249fd018998ed78d0db70f89e0b0ea5_1440w.jpg\" alt=\"\" class=\"wp-image-1241\" srcset=\"http:\/\/www.algmain.com\/wp-content\/uploads\/2023\/02\/v2-6249fd018998ed78d0db70f89e0b0ea5_1440w.jpg 423w, http:\/\/www.algmain.com\/wp-content\/uploads\/2023\/02\/v2-6249fd018998ed78d0db70f89e0b0ea5_1440w-300x77.jpg 300w\" sizes=\"(max-width: 423px) 100vw, 423px\" \/><figcaption class=\"wp-element-caption\">\u56fe8 \u5c06\u6570\u636e\u8bb0\u5f55\u653e\u81f3R11\u8282\u70b9\u4e2d<\/figcaption><\/figure>\n\n\n\n<p>\u6309\u7167\u4e0a\u8ff0\u7684\u65b9\u6cd5\u5c06\u5173\u952e\u5b57\u5e8f\u5217\\(key=\\{25,12,13,30,128,77,1,9,18,1024\\}\\)\u4f9d\u6b21\u6dfb\u52a0\u5230\u54c8\u5e0c\u6811\u6570\u636e\u7ed3\u6784\u4e2d\uff0c\u6700\u540e\u53ef\u4ee5\u5f97\u5230\u54c8\u5e0c\u6811\u6570\u636e\u7ed3\u6784\u5982\u4e0b\u56fe\u6240\u793a\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"571\" height=\"923\" src=\"http:\/\/www.algmain.com\/wp-content\/uploads\/2023\/02\/v2-a389aa0a18921fb3ed23b2776d55851c_1440w.webp\" alt=\"\" class=\"wp-image-1242\" srcset=\"http:\/\/www.algmain.com\/wp-content\/uploads\/2023\/02\/v2-a389aa0a18921fb3ed23b2776d55851c_1440w.webp 571w, http:\/\/www.algmain.com\/wp-content\/uploads\/2023\/02\/v2-a389aa0a18921fb3ed23b2776d55851c_1440w-186x300.webp 186w\" sizes=\"(max-width: 571px) 100vw, 571px\" \/><figcaption class=\"wp-element-caption\">\u56fe9 \u6309\u7167\u5173\u952e\u5b57\u5e8f\u5217K\u63d2\u5165\u6570\u636e\u540e\u7684\u7ed3\u679c<\/figcaption><\/figure>\n\n\n\n<p>\u8fd9\u79cd\u6570\u636e\u63d2\u5165\u65b9\u6cd5\u7684\u4e00\u4e2a\u597d\u5904\u5c31\u662f\uff0c\u53ef\u4ee5\u4f18\u5148\u5360\u636e\u63a5\u8fd1\u6839\u8282\u70b9\u7684\u5b50\u8282\u70b9\uff0c\u964d\u4f4e\u5355\u6b21\u64cd\u4f5c\u4e2d\u8bbf\u95ee\u7684\u6b21\u6570\uff0c\u540c\u65f6\u4f7f\u6811\u7ed3\u6784\u5747\u8861\u5316\u3002\u6309\u7167\u8fd9\u79cd\u6570\u636e\u63d2\u5165\u65b9\u6cd5\uff0c\u6b64\u54c8\u5e0c\u6811\u6570\u636e\u7ed3\u6784\u4e2d\uff0c\u6700\u591a\u53ef\u4ee5\u5b58\u50a8\u7684\u6570\u636e\u8bb0\u5f55\u6570\u91cf\u5e94\u5927\u4e8e\u8be5\u54c8\u5e0c\u7b97\u6cd5\u7684\u603b\u4f53\u5206\u8fa8\u80fd\u529b\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u67e5\u627e\u6570\u636e<\/h2>\n\n\n\n<p>\u5728\u56fe9\u6240\u793a\u7684\u54c8\u5e0c\u6811\u72b6\u6001\u4e0b\uff0c\u8fdb\u884c\u6570\u636e\u67e5\u627e\u3002<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u67e5\u627e\u7684\u6570\u636e\u8bb0\u5f55&nbsp;(\\(key=128\\))&nbsp;\u3002\n<ul class=\"wp-block-list\">\n<li>\u67e5\u8be2\u9664\u6570\u5e8f\u5217\u53ef\u77e5\uff0c\u6839\u8282\u70b9\u4e0b\u5e94\u8be5\u6709\u4e2a\u8282\u70b9\u3002\u6839\u636e\u524d\u9762\u6240\u63cf\u8ff0\u5f97\u7b97\u6cd5\uff0c\u5c06\u5173\u952e\u5b57\u6570\u503c\u53d6\u4f59\u53ef\u5f97\\(0\\,(128\\,mod\\,2)\\)\u3002\u8c03\u53d6\u8282\u70b9R0\u7684\u72b6\u6001\uff0c\u53d1\u73b0\u8be5\u8282\u70b9\u5df2\u7ecf\u5b58\u50a8\u4e86\u4e00\u6761\u6570\u636e\u8bb0\u5f55\uff0c\u800c\u4e14\u5173\u952e\u5b57\u4e0d\u7b49\u4e8e128\u3002\u56e0\u6b64\u9700\u8981\u7ee7\u7eed\u67e5\u8be2R0\u4e0b\u7684\u5b50\u8282\u70b9\u3002<\/li>\n\n\n\n<li>\u67e5\u8be2\u9664\u6570\u5e8f\u5217\u53ef\u77e5\uff0cR0\u8282\u70b9\u4e0b\u5e94\u8be5\u6709\u4e2a\u8282\u70b9\u3002\u5c06\u5173\u952e\u5b57\u6570\u503c\u53d6\u4f59\u53ef\u5f97\\(2\\,(128\\,mod\\,3)\\)\u3002\u7531\u4e8eR0\u8282\u70b9\u4e0b\u7684R02\u8282\u70b9\u8282\u70b9\u5df2\u7ecf\u5b58\u50a8\u4e86\u4e00\u6761\u6570\u636e\u8bb0\u5f55\uff0c\u4e14\u5173\u952e\u5b57\u7b49\u4e8e128\uff0c\u56e0\u6b64\u8be5\u8282\u70b9\u5373\u4e3a\u6240\u67e5\u627e\u7684\u8282\u70b9\u3002<\/li>\n\n\n\n<li>\u7a0b\u5e8f\u64cd\u4f5c\u5230\u6b64\u5373\u53ef\u7ed3\u675f\u3002<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u67e5\u627e\u7684\u6570\u636e\u8bb0\u5f55&nbsp;(\\(key=31\\))&nbsp;\u3002\n<ul class=\"wp-block-list\">\n<li>\u67e5\u8be2\u9664\u6570\u5e8f\u5217\u53ef\u77e5\uff0c\u6839\u8282\u70b9\u4e0b\u5e94\u8be5\u6709\u4e2a\u8282\u70b9\u3002\u6839\u636e\u524d\u9762\u6240\u63cf\u8ff0\u5f97\u7b97\u6cd5\uff0c\u5c06\u5173\u952e\u5b57\u6570\u503c\u53d6\u4f59\u53ef\u5f97\\(1\\,(31\\,mod\\,2)\\)&nbsp;\u3002\u8c03\u53d6\u8282\u70b9R1\u7684\u72b6\u6001\uff0c\u53d1\u73b0\u8be5\u8282\u70b9\u5df2\u7ecf\u5b58\u50a8\u4e86\u4e00\u6761\u6570\u636e\u8bb0\u5f55\uff0c\u800c\u4e14\u5173\u952e\u5b57\u4e0d\u7b49\u4e8e31\u3002\u56e0\u6b64\u9700\u8981\u7ee7\u7eed\u67e5\u8be2R1\u4e0b\u7684\u5b50\u8282\u70b9\u3002<\/li>\n\n\n\n<li>\u67e5\u8be2\u9664\u6570\u5e8f\u5217\u53ef\u77e5\uff0cR1\u8282\u70b9\u4e0b\u5e94\u8be5\u6709\u4e2a\u8282\u70b9\u3002\u5c06\u5173\u952e\u5b57\u6570\u503c\u53d6\u4f59\u53ef\u5f97\\(1\\,(31\\,mod\\,3)\\)\u3002\u7531\u4e8eR1\u8282\u70b9\u4e0b\u7684R11\u8282\u70b9\u8282\u70b9\u5df2\u7ecf\u5b58\u50a8\u4e86\u4e00\u6761\u6570\u636e\u8bb0\u5f55\uff0c\u4e14\u5173\u952e\u5b57\u4e0d\u7b49\u4e8e31\u3002\u56e0\u6b64\u9700\u8981\u7ee7\u7eed\u67e5\u8be2R11\u8282\u70b9\u4e0b\u7684\u5b50\u8282\u70b9\u3002<\/li>\n\n\n\n<li>\u67e5\u8be2\u9664\u6570\u5e8f\u5217\u53ef\u77e5\uff0cR11\u8282\u70b9\u4e0b\u5e94\u8be5\u6709\u4e2a\u8282\u70b9\u3002\u5c06\u5173\u952e\u5b57\u6570\u503c\u53d6\u4f59\u53ef\u5f97\\(1\\,&nbsp;(31\\,mod\\,5)\\)\u3002\u8c03\u53d6\u8282\u70b9R111\u7684\u72b6\u6001\uff0c\u53d1\u73b0\u8be5\u8282\u70b9\u5df2\u7ecf\u5b58\u50a8\u4e86\u4e00\u6761\u8bb0\u5f55\uff0c\u4e14\u5173\u952e\u5b57\u4e0d\u7b49\u4e8e31\u3002<\/li>\n\n\n\n<li>\u7531\u4e8e\u8282\u70b9R111\u662f\u6700\u5e95\u5c42\u8282\u70b9\uff0c\u56e0\u6b64\u54c8\u5e0c\u6811\u4e2d\u4e0d\u5b58\u5728\u5173\u952e\u5b57\u6240\u5bf9\u5e94\u7684\u6570\u636e\u8bb0\u5f55\u3002\u7a0b\u5e8f\u5230\u6b64\u5373\u53ef\u7ed3\u675f\u3002<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n<h2 class=\"wp-block-heading\">\u5220\u9664\u6570\u636e<\/h2>\n\n\n\n<p>\u5728\u56fe9\u6240\u793a\u7684\u54c8\u5e0c\u6811\u72b6\u6001\u4e0b\uff0c\u8fdb\u884c\u6570\u636e\u5220\u9664\u3002\u663e\u7136\u5220\u9664\u6570\u636e\u7684\u524d\u63d0\u662f\u80fd\u627e\u5230\u6570\u636e\u8bb0\u5f55\u3002\u56e0\u6b64\u5728\u67e5\u627e\u7b97\u6cd5\u4e0a\uff0c\u4e24\u8005\u5177\u6709\u4e00\u81f4\u6027\uff0c\u8fd9\u91cc\u5c31\u4e0d\u518d\u8d58\u8ff0\u3002<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u5220\u9664&nbsp;(\\(key=13\\))&nbsp;\u7684\u6570\u636e\u8bb0\u5f55\u3002\n<ul class=\"wp-block-list\">\n<li>\u627e\u5230\u6240\u5bf9\u5e94\u7684\u6570\u636e\u8282\u70b9R11\uff0c\u5e76\u5c06\u6570\u636e\u8282\u70b9R11\u7684\u72b6\u6001\u8bbe\u7f6e\u4e3a\u65e0\u6570\u636e\u72b6\u6001\u3002<\/li>\n\n\n\n<li>\u7a0b\u5e8f\u5230\u6b64\u5373\u53ef\u8fd4\u56de\u3002<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u5220\u9664&nbsp;(\\(key=18\\))&nbsp;\u7684\u6570\u636e\u8bb0\u5f55\u3002\n<ul class=\"wp-block-list\">\n<li>\u627e\u5230\u6240\u5bf9\u5e94\u7684\u6570\u636e\u8282\u70b9R003\uff0c\u5e76\u5c06\u6570\u636e\u8282\u70b9R11\u7684\u72b6\u6001\u8bbe\u7f6e\u4e3a\u65e0\u6570\u636e\u72b6\u6001\u3002<\/li>\n\n\n\n<li>\u7a0b\u5e8f\u5230\u6b64\u5373\u53ef\u8fd4\u56de\u3002<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n<p>\u7ecf\u8fc7\u4e24\u6b21\u5220\u9664\u64cd\u4f5c\u540e\uff0c\u54c8\u5e0c\u6811\u7684\u5f53\u524d\u72b6\u6001\u5982\u4e0b\u56fe\u6240\u793a\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"521\" height=\"923\" src=\"http:\/\/www.algmain.com\/wp-content\/uploads\/2023\/02\/v2-bd03d322c7f26b1ef4e89d37ddd04678_1440w.webp\" alt=\"\" class=\"wp-image-1248\" srcset=\"http:\/\/www.algmain.com\/wp-content\/uploads\/2023\/02\/v2-bd03d322c7f26b1ef4e89d37ddd04678_1440w.webp 521w, http:\/\/www.algmain.com\/wp-content\/uploads\/2023\/02\/v2-bd03d322c7f26b1ef4e89d37ddd04678_1440w-169x300.webp 169w\" sizes=\"(max-width: 521px) 100vw, 521px\" \/><figcaption class=\"wp-element-caption\">\u56fe10 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class=\"wp-block-heading\">\u54c8\u5e0c\u6811\u7684\u7279\u70b9<\/h2>\n\n\n\n<p>\uff081\uff09\u7ed3\u6784\u7b80\u5355<\/p>\n\n\n\n<p>\u54c8\u5e0c\u6811\u7684\u7ed3\u6784\u975e\u5e38\u7b80\u5355\uff0c\u6bcf\u5c42\u8282\u70b9\u7684\u5b50\u8282\u70b9\u4e2a\u6570\u7531\u9664\u6570\u5e8f\u5217\u6307\u5b9a\uff0c\u5b50\u8282\u70b9\u53ef\u4ee5\u968f\u65f6\u52a8\u6001\u521b\u5efa\u3002\u54c8\u5e0c\u6811\u7ed3\u6784\u662f\u52a8\u6001\u7684\uff0c\u4e0d\u9700\u8981\u957f\u65f6\u95f4\u7684\u521d\u59cb\u5316\u8fc7\u7a0b\uff0c\u6ca1\u6709\u5fc5\u8981\u4e3a\u4e0d\u5b58\u5728\u7684\u5173\u952e\u5b57\u8282\u70b9\u63d0\u524d\u5206\u914d\u5b58\u50a8\u7a7a\u95f4\u3002<\/p>\n\n\n\n<p>\uff082\uff09\u6613\u4e8e\u5b9e\u73b0<\/p>\n\n\n\n<p>\u4ece\u4e0a\u9762\u6240\u8bb2\u8ff0\u7684\u64cd\u4f5c\u8fc7\u7a0b\u6765\u8bf4\u662f\u76f8\u5f53\u7b80\u5355\u7684\u3002\u7a0b\u5e8f\u4e0a\u7279\u522b\u5bb9\u6613\u5b9e\u73b0\uff0c\u6bd4\u8d77\\(B^\u2212\\)\u6811\u66f4\u5bb9\u6613\u7406\u89e3\u548c\u5b9e\u73b0\u3002<\/p>\n\n\n\n<p>\uff083\uff09\u67e5\u627e\u8fc5\u901f<\/p>\n\n\n\n<p>\u4ece\u524d\u9762\u7684\u5206\u6790\u53ef\u4ee5\u770b\u51fa\uff0c\u65f6\u95f4\u590d\u6742\u5ea6\u662f\\(O(n)\\)\uff08\u5176\u4e2d\\(n\\)\u4e3a\u9664\u6570\u6570\u5217\u7684\u957f\u5ea6\uff09\u3002\u5b9e\u9645\u5e94\u7528\u4e2d\uff0c\u5e73\u5747\u67e5\u627e\u957f\u5ea6\u5e94\u8be5\u5c0f\u4e8e\\(n\\)<\/p>\n\n\n\n<p> 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class=\"wp-block-heading\">\u62d3\u5c55\u9605\u8bfb<\/h2>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p><strong>CSDN :&nbsp;<\/strong><a rel=\"noreferrer noopener\" href=\"https:\/\/blog.csdn.net\/wuprogrammer\/article\/details\/105425170\" target=\"_blank\">\u67e5\u627e\u7b97\u6cd5<\/a><br>CSDN : <a rel=\"noreferrer noopener\" href=\"https:\/\/blog.csdn.net\/u014600626\/article\/details\/108242417\" target=\"_blank\">\u54c8\u5e0c\u6811 (HashTree)<\/a><br>CSDN : <a rel=\"noreferrer noopener\" href=\"https:\/\/blog.csdn.net\/yang_yulei\/article\/details\/46337405\" target=\"_blank\">\u67e5\u627e\u2014\u2014\u56fe\u6587\u7fd4\u89e3HashTree\uff08\u54c8\u5e0c\u6811\uff09<\/a><br>CNBlogs : <a rel=\"noreferrer noopener\" href=\"https:\/\/www.cnblogs.com\/tlnshuju\/p\/6740754.html\" target=\"_blank\">\u67e5\u627e\u2014\u2014\u56fe\u6587\u7fd4\u89e3HashTree\uff08\u54c8\u5e0c\u6811\uff09<\/a><\/p>\n<\/blockquote>\n","protected":false},"excerpt":{"rendered":"<p>\u77e5\u4e4e\uff1a\u54c8\u5e0c\u6811\uff08HashTree\uff09\u67e5\u627e\u7b97\u6cd5CSDN :\u00a0\u54c8\u5e0c\u6811\uff08HashTree\uff09\u67e5\u627e\u7b97\u6cd5\u767e\u5ea6\u6587\u5e93\uff1a\u54c8\u5e0c\u6811\uff08Ha [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":363,"menu_order":2,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-754","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"http:\/\/www.algmain.com\/index.php\/wp-json\/wp\/v2\/pages\/754"}],"collection":[{"href":"http:\/\/www.algmain.com\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"http:\/\/www.algmain.com\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"http:\/\/www.algmain.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/www.algmain.com\/index.php\/wp-json\/wp\/v2\/comments?post=754"}],"version-history":[{"count":23,"href":"http:\/\/www.algmain.com\/index.php\/wp-json\/wp\/v2\/pages\/754\/revisions"}],"predecessor-version":[{"id":1302,"href":"http:\/\/www.algmain.com\/index.php\/wp-json\/wp\/v2\/pages\/754\/revisions\/1302"}],"up":[{"embeddable":true,"href":"http:\/\/www.algmain.com\/index.php\/wp-json\/wp\/v2\/pages\/363"}],"wp:attachment":[{"href":"http:\/\/www.algmain.com\/index.php\/wp-json\/wp\/v2\/media?parent=754"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}