{"id":1418,"date":"2020-03-08T23:24:43","date_gmt":"2020-03-08T15:24:43","guid":{"rendered":"http:\/\/149.129.74.185\/?p=1418"},"modified":"2020-03-16T20:35:51","modified_gmt":"2020-03-16T12:35:51","slug":"%e9%ab%98%e7%ba%a7%e6%95%b0%e6%8d%ae%e7%bb%93%e6%9e%84-week-2-note","status":"publish","type":"post","link":"http:\/\/www.magicmipamipa.com\/?p=1418","title":{"rendered":"[\u9ad8\u7ea7\u6570\u636e\u7ed3\u6784] Week 2 Note"},"content":{"rendered":"

Red-Black Trees<\/h2>\n
\n

\u3010\u4e8c\u53c9\u5e73\u8861\u641c\u7d22\u6811\u3011<\/p>\n

\u7ea2\u9ed1\u6811\u7684\u6027\u8d28<\/h3>\n
\n
\n
\n
<\/div>\n
\n
\uff081\uff09 \u6bcf\u4e2a\u8282\u70b9\u90fd\u662f\u7ea2\u8272\u6216\u9ed1\u8272\u7684\u3002<\/div>\n
\uff082\uff09 \u6839\u662f\u9ed1\u8272\u7684\u3002<\/div>\n
\uff083\uff09 \u6bcf\u7247\u53f6\u5b50\uff08\u65e0\uff09\u90fd\u662f\u9ed1\u8272\u7684\u3002\u9650\u5236\u51fa\u73b0\u76f8\u90bb\u7684\u7ea2\u8282\u70b9<\/span><\/div>\n
\uff084\uff09 \u5982\u679c\u4e00\u4e2a\u8282\u70b9\u662f\u7ea2\u8272\u7684\uff0c\u90a3\u4e48\u5b83\u7684\u4e24\u4e2a\u5b50\u8282\u70b9\u90fd\u662f\u9ed1\u8272\u7684\u3002<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
\n
\n
\n
\n

\uff085\uff09 <\/span>\u5bf9\u4e8e\u6bcf\u4e2a\u8282\u70b9\uff0c\u4ece\u8282\u70b9\u5230\u5b50\u4ee3\u53f6\u5b50\u7684\u6240\u6709\u7b80\u5355\u8def\u5f84\u90fd\u5305\u542b\u76f8\u540c\u6570\u91cf\u7684\u9ed1\u8272\u8282\u70b9\u3002<\/span><\/p>\n

\u7ea2\u9ed1\u6811\u7684\u7ed3\u6784<\/h3>\n

<\/p>\n

\u7a7a\u53f6\u7ed3\u70b9\u7b97\u4f5c\u3010\u5916\u90e8\u8282\u70b9\u3011<\/p>\n

Black-height<\/h3>\n

\u3010\u4e00\u4e2a\u7ea2\u9ed1\u6811\u7684\u9ed1\u9ad8\u6700\u591a\u662f2ln(N+1)\u3011<\/p>\n

\u8bc1\u660e\uff1a<\/p>\n

(1) \u5bf9\u4efb\u610f\u8282\u70b9x\uff0csizeof(x) >= 2bh(x)\u00a0<\/sup>– 1<\/p>\n

\u5982\u679ch(x) = 0, x \u4e3a null -> sizeof(x) >= 20<\/sup> – 1 = 0<\/p>\n

\u5047\u8bbe\u5bf9\u6240\u6709h(x)<=k\u6210\u7acb\uff0c\u5bf9x\u4e14h(x)=k+1\uff1a<\/p>\n

bh(child) = bh(x) \u6216 bh(x) – 1<\/p>\n

\u7531\u4e8e h(child) <= k\uff0csizeof(child) >= 2bh(child) – 1 >= 2bh(x) – 1<\/p>\n

\u56e0\u6b64 sizeof(x) = 1 + 2sizeof(child) >= 2bh(x) – 1<\/p>\n

(2) bh(Tree) >= h(Tree)\/2<\/p>\n

Insert \u63d2\u5165<\/h3>\n

(1) \u57fa\u7840\u63d2\u5165\u64cd\u4f5c\uff0c\u540c\u4e8c\u53c9\u641c\u7d22\u6811<\/p>\n

(2) \u67d3\u8272\u64cd\u4f5c\u3002\u5982\u679c\u67d3\u6210\u9ed1\u8272\uff0c\u4f1a\u5f71\u54cd\u6574\u4e2a\u6811\u7684\u9ed1\u9ad8\uff1b\u5982\u679c\u67d3\u6210\u7ea2\u8272\uff0c\u4f1a\u5b58\u5728\u76f8\u90bb\u7ea2\u8282\u70b9\uff0c\u6216\u63d2\u5165\u4e3a\u6839\uff0c\u7834\u574f\u4e86\u6839\u8282\u70b9\u4e3a\u9ed1\u7684\u6027\u8d28\u3002<\/p>\n

->\u63d2\u5165\u601d\u60f3\uff1a\u6309\u7167\u4e8c\u53c9\u6811\u63d2\u5165\u5e76\u67d3\u6210\u7ea2\u8272\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n

<\/p>\n

*\u5982\u679c\u80fd\u591f\u5c40\u90e8\u8c03\u6574\uff0c\u5c31\u4f7f\u7528\u5c40\u90e8\u8c03\u6574\u89e3\u51b3\u3002\u5982\u679c\u5c40\u90e8\u8c03\u6574\u89e3\u51b3\u4e0d\u4e86\uff0c\u5c31\u5c06\u95ee\u9898\u8f6c\u79fb\u5230\u6839\u8282\u70b9\uff0c\u901a\u8fc7\u6839\u8282\u70b9\u6362\u8272\u89e3\u51b3\u3002<\/p>\n

Delete \u5220\u9664<\/h3>\n

(1) \u67e5\u627e\u6811\u7684\u5220\u9664<\/p>\n

\u5220\u9664\u53f6\u7ed3\u70b9\uff1a\u628a\u7236\u8282\u70b9\u7684\u6307\u9488\u7f6e\u4e3aNULL<\/p>\n

\u5220\u9664\u5355\u5b69\u8282\u70b9\uff1a\u628a\u7236\u8282\u70b9\u7684\u6307\u9488\u6307\u5411\u5355\u5b69\u8282\u70b9<\/p>\n

\u5220\u9664\u6ee1\u8282\u70b9\uff1a\u627e\u51fa\u66ff\u6362\u5f53\u524d\u4f4d\u7f6e\u8282\u70b9\u7684\u65b0\u8282\u70b9\uff08\u5de6\u5b50\u6811\u6700\u5927<\/span>or\u53f3\u5b50\u6811\u6700\u5c0f\uff09\u628a\u66ff\u6362\u8282\u70b9\u4fdd\u6301\u4f4f\u88ab\u5220\u9664\u8282\u70b9\u7684\u989c\u8272\u3002<\/p>\n

(2) \u5220\u9664\u9ed1\u8282\u70b9\u7684\u60c5\u51b5\u9700\u8981\u8c03\u6574\u3002<\/p>\n

<\/p>\n

<\/p>\n

\u7528\u4f8b\uff1a<\/p>\n

<\/p>\n

\u2460\u5144\u5f1f\u7ea2\u6613\u5144\u5f1f\u9ed1\uff0c\u6362\u8272\u659c\u65cb\u63a5\u7740\u63a8\uff1b<\/span>
\n\u2461\u4f84\u9ed1\u7236\u7ea2\u6362\u5144\u8272\uff0c\u7236\u4f84\u5168\u9ed1\u5144\u67d3\u7ea2\uff0c\u4e0a\u63a8\uff1b<\/span>
\n\u2462\u8fd1\u4f84\u7ea2\u6765\u8fdc\u4f84\u9ed1\uff0c\u6362\u8272\u659c\u65cb\u6a21\u6837\u6539\uff1b<\/span>
\n\u2463\u8fdc\u4f84\u7ea2\u6765\u4ee4\u5176\u9ed1\uff0c\u7236\u5144\u6362\u8272\u659c\u65cb\u5760\u3002<\/span><\/p>\n

\n

<\/h2>\n

B+ Trees<\/h2>\n
\n

\u3010\u7528\u4e8e\u4e8c\u7ea7\u5b58\u50a8\u3011<\/p>\n

*I\/O\u8bbf\u95ee\u4e0e\u5185\u5b58\u8bbf\u95ee\u76f8\u6bd4\u901f\u5ea6\u5dee\u4e07\u500d\u5355\u4f4d\u3002<\/p>\n

B+\u6811\u7684\u6027\u8d28<\/h3>\n

M\u9636B+\u6811\u662f\u5177\u6709\u4ee5\u4e0b\u7ed3\u6784\u5c5e\u6027\u7684\u6811\uff1a<\/p>\n

\uff081\uff09 \u6839\u8981\u4e48\u662f\u4e00\u7247\u53f6\u5b50\uff0c\u8981\u4e48\u67092\u5230M\u4e2a\u5b69\u5b50<\/span>\u3002<\/p>\n

\uff082\uff09 \u6240\u6709\u975e\u53f6\u8282\u70b9\uff08\u6839\u9664\u5916\uff09\u90fd\u6709\u2308M\/2\u2309\u5230M\u4e2a\u5b50\u8282\u70b9<\/span>\u3002<\/p>\n

\uff083\uff09 \u6240\u6709\u7684\u53f6\u5b50\u90fd\u5728\u540c\u4e00\u6df1\u5ea6<\/span>\u3002<\/p>\n

\u5047\u8bbe\u6bcf\u4e2a\u975e\u6839\u53f6\u4e5f\u6709\u2308M\/2\u2309\u5230M\u4e2a\u5b50\u53f6<\/span>\u3002<\/p>\n

\u53f6\u7ed3\u70b9\u653e\u6570\u636e\uff0c\u975e\u53f6\u7ed3\u70b9\u653e\u7d22\u5f15\u3002<\/p><\/blockquote>\n

4\u9636B+\u6811\uff082-3-4\u6811\uff09<\/h3>\n

<\/p>\n

B+\u6811\u7684\u63d2\u5165<\/h3>\n
Btree  Insert ( ElementType X,  Btree T ) \r\n{ \r\n  Search from root to leaf for X and find the proper leaf node;\r\n  Insert X;\r\n  while ( this node has M+1 keys ) {\r\n    \t\tsplit it into 2 nodes with \uf0e9(M+1)\/2\uf0f9 and \uf0eb(M+1)\/2 \uf0fb keys, respectively;\r\n    \t\tif (this node is the root)\r\n        \t\tcreate a new root with two children;\r\n    \t\tcheck its parent;\r\n  }\r\n} \r\n<\/pre>\n
<\/p>\n
<\/p>\n
*The best choice of M is 3 or 4.<\/p>\n","protected":false},"excerpt":{"rendered":"
Red-Black Trees \u3010\u4e8c\u53c9\u5e73\u8861\u641c\u7d22\u6811\u3011 \u7ea2\u9ed1\u6811\u7684\u6027\u8d28 \uff081\uff09 \u6bcf\u4e2a\u8282\u70b9\u90fd\u662f\u7ea2\u8272\u6216\u9ed1\u8272\u7684\u3002 […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[38,16],"tags":[],"_links":{"self":[{"href":"http:\/\/www.magicmipamipa.com\/index.php?rest_route=\/wp\/v2\/posts\/1418"}],"collection":[{"href":"http:\/\/www.magicmipamipa.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/www.magicmipamipa.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/www.magicmipamipa.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/www.magicmipamipa.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1418"}],"version-history":[{"count":6,"href":"http:\/\/www.magicmipamipa.com\/index.php?rest_route=\/wp\/v2\/posts\/1418\/revisions"}],"predecessor-version":[{"id":1463,"href":"http:\/\/www.magicmipamipa.com\/index.php?rest_route=\/wp\/v2\/posts\/1418\/revisions\/1463"}],"wp:attachment":[{"href":"http:\/\/www.magicmipamipa.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1418"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/www.magicmipamipa.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1418"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/www.magicmipamipa.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1418"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}