{"id":73,"date":"2010-02-01T13:35:00","date_gmt":"2010-02-01T05:35:00","guid":{"rendered":"http:\/\/localhost\/?p=73"},"modified":"2010-02-01T13:35:00","modified_gmt":"2010-02-01T05:35:00","slug":"balanced_tree_","status":"publish","type":"post","link":"https:\/\/www.shuizilong.com\/wjmzbmr\/?p=73","title":{"rendered":"\u5e73\u8861\u6811\u3002\u3002"},"content":{"rendered":"<p> \u6211\u5728wiki\u4e0a\u53d1\u73b0\u4e86N\u79cd\u5e73\u8861\u6811\u3002\u3002\u4e0d\u5f97\u4e0d\u611f\u53f9\u6570\u636e\u7ed3\u6784\u7684\u535a\u5927\u7cbe\u6df1\u3002\u3002<br \/>AVL\u548cSBT\u5b9e\u9645\u4e0a\u601d\u60f3\u4e0a\u5dee\u4e0d\u591a\u3002\u3002<br \/>\u90fd\u662f\u8fd0\u7528\u67d0\u79cd\u6570\u503c\u5c06\u6811\u5e73\u8861\u8d77\u6765\u3002\u3002<br \/>AVL\u662f\u9ad8\u5ea6\u3002\u3002SBT\u662f\u5927\u5c0f\u3002\u3002<br \/>\u5728AVL\u4e2d\u4e24\u68f5\u5b50\u6811\u9ad8\u5ea6\u4e0d\u4f1a\u5dee\u592a\u591a\uff08\u4ece\u800c\u4fdd\u8bc1\u5927\u5c0f\u4e0d\u5dee\u592a\u591a\uff09\u3002\u3002<br \/>SBT\u4e2d\u5927\u5c0f\u4e0d\u4f1a\u5dee\u592a\u591a\u3002\u3002<br \/>\u751a\u81f3\u6211\u611f\u89c9SBT\u5c31\u662f\u7b80\u5316\u7248\u7684AVL\u3002\u3002<br \/>\u56e0\u4e3a\u5176\u4e2d\u5de6\u5b69\u5b50\u5927\u5c0f\u4e0d\u5c0f\u4e8e\u53f3\u8fb9\u7684\u4e24\u4e2a\u5b59\u5b50\u5927\u5c0f\u7684\u89c4\u5b9a<br \/>\u592a\u50cf\u9ad8\u5ea6\u4e0d\u5dee\u4e00\u4e86\u3002\u3002<\/p>\n<p>Treap\u6bd4\u8f83NB\u3002\u3002\u5b83\u5229\u7528\u4e86\u968f\u673a\u6811\u662f\u5e73\u8861\u7684<br \/>\u6240\u4ee5\u7528\u4e86\u4e00\u79cdtree+heap\u7684\u65b9\u6cd5\u52a8\u6001\u4ea7\u751f\u968f\u673a\u6811\u3002\u3002<br \/>\u4f46\u6811\u9ad8\u5ea6\u5c31\u4e0d\u600e\u4e48\u6837\u4e86\u3002\u3002<br \/>\u4f46\u4ed6\u662f\u6700\u597d\u5199\u7684\u3002\u3002<\/p>\n<p>\u7ea2\u9ed1\u6811\u662f\u7528\u8282\u70b9\u7684\u989c\u8272\u6765\u662f\u6811\u4e2d\u4efb\u610f\u4e24\u6761\u8def\u5f84\u957f\u5ea6\u4e0d\u5dee2\u500d\u3002\u3002<br \/>\u6240\u4ee5\u4e5f\u662f\u5e73\u8861\u7684\u3002\u3002\u4e0d\u8fc7\u603b\u662f\u8ba9\u6211\u611f\u89c9\u592a\u7cbe\u5de7\u548c\u590d\u6742\u4e86\u3002\u3002<br \/>\u4e0d\u77e5\u662f\u600e\u4e48\u60f3\u51fa\u6765\u7684\u3002\u3002\u7b97\u6cd5\u5bfc\u8bba\u4e0a\u6709\u3002\u3002\u5c31\u4e0d\u591a\u8bf4\u4e86\u3002\u3002<\/p>\n<p>2-3\u6811\u66f4\u8be1\u5f02\u3002\u3002\u5b83\u8ddfAA\u6811\u662f\u540c\u6784\u7684\u3002\u3002<br \/>\u4ed6\u4e00\u4e2a\u8282\u70b9\u53ef\u4ee5\u662f\u666e\u901a\u76842\u8282\u70b9\u3002\u3002\u5c31\u662f\u4e24\u4e2a\u5b69\u5b50\u3002\u3002<br \/>\u4e5f\u53ef\u4ee5\u662f3\u8282\u70b9\u3002\u3002\u5c31\u662f\u8bf43\u4e2a\u5b69\u5b50\u3002\u3002<br \/>\u4e00\u822c\u7684\u8282\u70b9\u5b58\u4e00\u4e2a\u503c\u3002\u6bd4\u5982\u662fx\u3002\u3002<br \/>\u5c06\u5b50\u6811\u5206\u4e3a&lt;x\u548c&gt;x\u7684\u3002\u3002<br \/>\u800c3\u8282\u70b9\u5b58\u4e24\u4e2a\u503cx,y\u3002\u3002<br \/>\u5c06\u5b50\u6811\u5206\u4e3a&lt;x,(x,y),&gt;y\u4e09\u4e2a\u90e8\u5206\u3002\u3002<br \/>\u7136\u540e\u5728\u63d2\u5165\u7684\u65f6\u5019\u5982\u679c2\u8282\u70b9\u53d8\u62103\u8282\u70b9\u4e86\u3002\u3002\u6ca1\u4e8b\u3002\u3002<br \/>\u5982\u679c3\u8282\u70b9\u53d84\u8282\u70b9\u4e86\u3002\u3002\u5c31\u5206\u88c2\u4e00\u4e0b\u3002\u3002\u628a\u4e2d\u95f4\u90a3\u4e2a\u63d0\u4e0a\u53bb\u3002\u3002\u3002\u3002<br \/>2-3\u6811\u9ad8\u5ea6\u662f\u4e25\u683clogn\u7684\u3002\u3002\u4e0d\u8fc73\u8282\u70b9\u5f88\u591a\u3002\u3002<br \/>\u67e5\u8d77\u6765\u4e5f\u5dee\u4e0d\u591a\u662f2logn\u7684\u3002\u3002\u3002<\/p>\n<p>2-3-4\u6811\u3002\u3002\u5c31\u662f\u8bf4\u4e0d\u4f46\u67092\uff0c3\u8282\u70b9\u3002\u3002\u8fd8\u67094\u8282\u70b9\u3002\u3002\u641e\u6b7b\u4eba\u7684\u4e1c\u897f\u3002\u3002<br \/>\u8ddf2-3\u6811\u5dee\u4e0d\u591a\u3002\u3002<\/p>\n<p>splay\u3002\u3002\u6211\u6700\u559c\u6b22\u7684\u3002\u3002\u5b83\u4e3b\u8981\u5c31\u662f\u6bcf\u6b21\u8bbf\u95ee\u5230\u4e00\u4e2a\u8282\u70b9\u3002\u3002\u5c31\u628a\u5b83\u8f6c\u6210\u6839\u3002\u3002<br \/>\u7b97\u662f\u6700NB\u548c\u81ea\u7136\u7684\u6570\u636e\u7ed3\u6784\u4e86\u3002\u3002\u4e0d\u8fc7\u5c31\u662f\u592a\u6162\u4e86\u3002\u3002<br \/>\u4e2a\u4eba\u611f\u89c9\u662f\u6700\u597d\u5199\u7684\u3002\u3002\u8fd9\u5bb6\u4f19\u7684\u957f\u5ea6\u4e00\u822c\u662f3-4*logn\u3002\u3002<\/p>\n<p>\u7ea2\u9ed1\u6811\u6709\u4e00\u4e2a\u5f88BT\u7684\u7279\u70b9\u5c31\u662f\u7ef4\u62a4\u7684\u65f6\u5019\u6700\u591a\u65cb\u8f6c2\u6b21\u3002\u3002\u3002\u6240\u4ee5stl\u5c31\u7528\u8fd9\u4e2a\u4e86\u3002\u3002<br \/>\u800cAA\u6811\u662f\u7ea2\u9ed1\u6811\u7684\u4e00\u4e2a\u53d8\u79cd\u3002\u3002\u89c4\u5b9a\u5de6\u8fb9\u7684\u5b69\u5b50\u4e0d\u80fd\u4e3a\u7ea2\u8272\u3002\u3002\u6240\u4ee5\u7ef4\u62a4\u7684\u65f6\u5019\u53ef\u80fd\u8f6c\u7684<br \/>\u66f4\u591a\u3002\u3002\u4f46\u4f3c\u4e4e\u662fAA\u6811\u66f4\u5feb\u4e00\u70b9\u3002\u3002\u4e0d\u8fc7stl\u8ffd\u6c42\u7684\u662f\u7a33\u5b9a\u3002\u3002<\/p>\n<p><a title=\"Scapegoat tree\" href=\"http:\/\/en.wikipedia.org\/wiki\/Scapegoat_tree\">Scapegoat tree<\/a>\u662f\u8ba9\u4e24\u4e2a\u5b69\u5b50\u7684\u5927\u5c0f\u90fd\u5c0f\u4e8ea*\u7236\u4eb2\u7684\u5927\u5c0f\u3002\u3002<br \/>\u7ef4\u62a4\u8d77\u6765\u5f88\u8be1\u5f02\u3002\u3002\u6bcf\u6b21\u90fd\u662f\u627e\u4e00\u4e2a\u6700\u9ad8\u7684\u90a3\u4e2a\u4e0d\u6ee1\u8db3\u7684\u9876\u70b9\u3002\u3002<br \/>\u76f4\u63a5\u66b4\u529b\u91cd\u5efa\u6210\u8fd1\u5b8c\u51682\u53c9\u6811\u3002\u3002\u5747\u644a\u662flogn\u7684\u3002\u3002<\/p>\n<p> <\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u6211\u5728wiki\u4e0a\u53d1\u73b0\u4e86N\u79cd\u5e73\u8861\u6811\u3002\u3002\u4e0d\u5f97\u4e0d\u611f\u53f9\u6570\u636e\u7ed3\u6784\u7684\u535a\u5927\u7cbe\u6df1\u3002\u3002AVL\u548cSBT\u5b9e\u9645\u4e0a\u601d\u60f3\u4e0a\u5dee\u4e0d\u591a\u3002\u3002\u90fd\u662f\u8fd0\u7528\u67d0\u79cd\u6570\u503c\u5c06\u6811\u5e73\u8861\u8d77\u6765\u3002\u3002AVL\u662f\u9ad8\u5ea6\u3002\u3002SBT\u662f\u5927\u5c0f\u3002\u3002\u5728AVL\u4e2d\u4e24\u68f5\u5b50\u6811\u9ad8\u5ea6\u4e0d\u4f1a\u5dee\u592a\u591a\uff08\u4ece\u800c\u4fdd\u8bc1\u5927\u5c0f\u4e0d\u5dee\u592a\u591a\uff09\u3002\u3002SBT\u4e2d\u5927\u5c0f\u4e0d\u4f1a\u5dee\u592a\u591a\u3002\u3002\u751a\u81f3\u6211\u611f\u89c9SBT\u5c31\u662f\u7b80\u5316\u7248\u7684AVL\u3002\u3002\u56e0\u4e3a\u5176\u4e2d\u5de6\u5b69\u5b50\u5927\u5c0f\u4e0d\u5c0f\u4e8e\u53f3\u8fb9\u7684\u4e24\u4e2a\u5b59\u5b50\u5927\u5c0f\u7684\u89c4\u5b9a\u592a\u50cf\u9ad8\u5ea6\u4e0d\u5dee\u4e00\u4e86\u3002\u3002 Treap\u6bd4\u8f83NB\u3002\u3002\u5b83\u5229\u7528\u4e86\u968f\u673a\u6811\u662f\u5e73\u8861\u7684\u6240\u4ee5\u7528\u4e86\u4e00\u79cdtree+heap\u7684\u65b9\u6cd5\u52a8\u6001\u4ea7\u751f\u968f\u673a\u6811\u3002\u3002\u4f46\u6811\u9ad8\u5ea6\u5c31\u4e0d\u600e\u4e48\u6837\u4e86\u3002\u3002\u4f46\u4ed6\u662f\u6700\u597d\u5199\u7684\u3002\u3002 \u7ea2\u9ed1\u6811\u662f\u7528\u8282\u70b9\u7684\u989c\u8272\u6765\u662f\u6811\u4e2d\u4efb\u610f\u4e24\u6761\u8def\u5f84\u957f\u5ea6\u4e0d\u5dee2\u500d\u3002\u3002\u6240\u4ee5\u4e5f\u662f\u5e73\u8861\u7684\u3002\u3002\u4e0d\u8fc7\u603b\u662f\u8ba9\u6211\u611f\u89c9\u592a\u7cbe\u5de7\u548c\u590d\u6742\u4e86\u3002\u3002\u4e0d\u77e5\u662f\u600e\u4e48\u60f3\u51fa\u6765\u7684\u3002\u3002\u7b97\u6cd5\u5bfc\u8bba\u4e0a\u6709\u3002\u3002\u5c31\u4e0d\u591a\u8bf4\u4e86\u3002\u3002 2-3\u6811\u66f4\u8be1\u5f02\u3002\u3002\u5b83\u8ddfAA\u6811\u662f\u540c\u6784\u7684\u3002\u3002\u4ed6\u4e00\u4e2a\u8282\u70b9\u53ef\u4ee5\u662f\u666e\u901a\u76842\u8282\u70b9\u3002\u3002\u5c31\u662f\u4e24\u4e2a\u5b69\u5b50\u3002\u3002\u4e5f\u53ef\u4ee5\u662f3\u8282\u70b9\u3002\u3002\u5c31\u662f\u8bf43\u4e2a\u5b69\u5b50\u3002\u3002\u4e00\u822c\u7684\u8282\u70b9\u5b58\u4e00\u4e2a\u503c\u3002\u6bd4\u5982\u662fx\u3002\u3002\u5c06\u5b50\u6811\u5206\u4e3a&lt;x\u548c&gt;x\u7684\u3002\u3002\u800c3\u8282\u70b9\u5b58\u4e24\u4e2a\u503cx,y\u3002\u3002\u5c06\u5b50\u6811\u5206\u4e3a&lt;x,(x,y),&gt;y\u4e09\u4e2a\u90e8\u5206\u3002\u3002\u7136\u540e\u5728\u63d2\u5165\u7684\u65f6\u5019\u5982\u679c2\u8282\u70b9\u53d8\u62103\u8282\u70b9\u4e86\u3002\u3002\u6ca1\u4e8b\u3002\u3002\u5982\u679c3\u8282\u70b9\u53d84\u8282\u70b9\u4e86\u3002\u3002\u5c31\u5206\u88c2\u4e00\u4e0b\u3002\u3002\u628a\u4e2d\u95f4\u90a3\u4e2a\u63d0\u4e0a\u53bb\u3002\u3002\u3002\u30022-3\u6811\u9ad8\u5ea6\u662f\u4e25\u683clogn\u7684\u3002\u3002\u4e0d\u8fc73\u8282\u70b9\u5f88\u591a\u3002\u3002\u67e5\u8d77\u6765\u4e5f\u5dee\u4e0d\u591a\u662f2logn\u7684\u3002\u3002\u3002 2-3-4\u6811\u3002\u3002\u5c31\u662f\u8bf4\u4e0d\u4f46\u67092\uff0c3\u8282\u70b9\u3002\u3002\u8fd8\u67094\u8282\u70b9\u3002\u3002\u641e\u6b7b\u4eba\u7684\u4e1c\u897f\u3002\u3002\u8ddf2-3\u6811\u5dee\u4e0d\u591a\u3002\u3002 splay\u3002\u3002\u6211\u6700\u559c\u6b22\u7684\u3002\u3002\u5b83\u4e3b\u8981\u5c31\u662f\u6bcf\u6b21\u8bbf\u95ee\u5230\u4e00\u4e2a\u8282\u70b9\u3002\u3002\u5c31\u628a\u5b83\u8f6c\u6210\u6839\u3002\u3002\u7b97\u662f\u6700NB\u548c\u81ea\u7136\u7684\u6570\u636e\u7ed3\u6784\u4e86\u3002\u3002\u4e0d\u8fc7\u5c31\u662f\u592a\u6162\u4e86\u3002\u3002\u4e2a\u4eba\u611f\u89c9\u662f\u6700\u597d\u5199\u7684\u3002\u3002\u8fd9\u5bb6\u4f19\u7684\u957f\u5ea6\u4e00\u822c\u662f3-4*logn\u3002\u3002 \u7ea2\u9ed1\u6811\u6709\u4e00\u4e2a\u5f88BT\u7684\u7279\u70b9\u5c31\u662f\u7ef4\u62a4\u7684\u65f6\u5019\u6700\u591a\u65cb\u8f6c2\u6b21\u3002\u3002\u3002\u6240\u4ee5stl\u5c31\u7528\u8fd9\u4e2a\u4e86\u3002\u3002\u800cAA\u6811\u662f\u7ea2\u9ed1\u6811\u7684\u4e00\u4e2a\u53d8\u79cd\u3002\u3002\u89c4\u5b9a\u5de6\u8fb9\u7684\u5b69\u5b50\u4e0d\u80fd\u4e3a\u7ea2\u8272\u3002\u3002\u6240\u4ee5\u7ef4\u62a4\u7684\u65f6\u5019\u53ef\u80fd\u8f6c\u7684\u66f4\u591a\u3002\u3002\u4f46\u4f3c\u4e4e\u662fAA\u6811\u66f4\u5feb\u4e00\u70b9\u3002\u3002\u4e0d\u8fc7stl\u8ffd\u6c42\u7684\u662f\u7a33\u5b9a\u3002\u3002 Scapegoat tree\u662f\u8ba9\u4e24\u4e2a\u5b69\u5b50\u7684\u5927\u5c0f\u90fd\u5c0f\u4e8ea*\u7236\u4eb2\u7684\u5927\u5c0f\u3002\u3002\u7ef4\u62a4\u8d77\u6765\u5f88\u8be1\u5f02\u3002\u3002\u6bcf\u6b21\u90fd\u662f\u627e\u4e00\u4e2a\u6700\u9ad8\u7684\u90a3\u4e2a\u4e0d\u6ee1\u8db3\u7684\u9876\u70b9\u3002\u3002\u76f4\u63a5\u66b4\u529b\u91cd\u5efa\u6210\u8fd1\u5b8c\u51682\u53c9\u6811\u3002\u3002\u5747\u644a\u662flogn\u7684\u3002\u3002<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[10],"tags":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/www.shuizilong.com\/wjmzbmr\/index.php?rest_route=\/wp\/v2\/posts\/73"}],"collection":[{"href":"https:\/\/www.shuizilong.com\/wjmzbmr\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.shuizilong.com\/wjmzbmr\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.shuizilong.com\/wjmzbmr\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.shuizilong.com\/wjmzbmr\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=73"}],"version-history":[{"count":0,"href":"https:\/\/www.shuizilong.com\/wjmzbmr\/index.php?rest_route=\/wp\/v2\/posts\/73\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.shuizilong.com\/wjmzbmr\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=73"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.shuizilong.com\/wjmzbmr\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=73"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.shuizilong.com\/wjmzbmr\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=73"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}