\u975c\u614b\u641c\u5c0b\u6cd5
\u5c0d\u975c\u614b\u6a94\u6848(\u7528\u5faa\u5e8f\u8868\u793a\u6cd5\u5132\u5b58)\u9032\u884c\u641c\u5c0b<\/p>\n\n\n\n
\u5faa\u5e8f\u641c\u5c0b\u6cd5<\/strong> binary search algorithm(\u4e8c\u5143\u641c\u5c0b\u6cd5)<\/strong> \u8cbb\u6c0f\u641c\u5c0b\u6cd5<\/strong> \u63d2\u88dc\u641c\u5c0b\u6cd5<\/strong> huffman tree(\u970d\u592b\u66fc\u6a39)<\/strong> optimal binary search tree(\u6700\u4f73\u4e8c\u5143\u641c\u5c0b\u6a39)<\/strong> ……………………………………………………………………………..<\/p>\n\n\n\n \u52d5\u614b\u641c\u5c0b\u6cd5 sorted linked list: insert=O(n) , finddata=O(N) , findmaxormin=O(1) binary search tree(\u4e8c\u5143\u641c\u5c0b\u6a39)<\/strong> void find_great_than_x(struct treenode *root,int x){ \/\/\u6b64\u7a0b\u5f0f\u78bc\u5c1a\u672a\u5b8c\u6210 \u63d2\u5165\u904b\u4f5c avl tree(\u9ad8\u5ea6\u5e73\u8861\u4e8c\u5143\u6a39)<\/strong> \u7bc0\u9ede\u7d50\u69cb \u63d2\u5165\u8207\u522a\u9664\u9700\u8981\u505arotation\u65cb\u8f49,\u5171\u6709\u56db\u7a2e\uff1a m\u5143b\u6a39 \u9ad8\u5ea6\u5e73\u8861m\u5143\u641c\u5c0b\u6a39<\/strong> \u5206\u652f\u5ea6\u70ba3\u7684\u7bc0\u9ede\u7d50\u69cb \u63d2\u5165\u904b\u4f5c\uff1a b’ tree<\/strong> red-black trees(\u7d05\u9ed1\u6a39)<\/strong> hashing function(\u96dc\u6e4a\u51fd\u6578)\uff1a\u4e3b\u8981\u6ce8\u610f\u6709:\u907f\u514dcollision\u78b0\u649e(\u7b97\u51fa\u7684\u4f4d\u7f6e\u6700\u597d\u662f\u5747\u5300\u5206\u914d)\uff0c\u5bb9\u6613\u8a08\u7b97 \u82e5\u8cc7\u6599\u88ab\u522a\u9664\u6642\uff1f<\/p>\n\n\n\n ……………………………………………………………………………..<\/p>\n\n\n\n heap(\u5806\u7a4d\u7d50\u69cb) \u6eff\u8db3heap\u7684\u689d\u4ef6: heap\u5206\u70ba: \u82e5\u6709n\u500b\u7bc0\u9ede,\u5247\u9ad8\u5ea6\u70balog2(n+1)\uff0c\u56e0\u6b64\u63d2\u5165\u8207\u522a\u9664\u8907\u96dc\u5ea6=bigO(log2(n)) \u5728\u7dda\u6027\u8907\u8907\u96dc\u5ea6bigO(N)\u5efa\u7acbmax tree\u6b65\u9a5f \u522a\u9664 \u96d9\u5411\u5806\u7a4d\u7d50\u69cb \u975c\u614b\u641c\u5c0b\u6cd5\u5c0d\u975c\u614b\u6a94\u6848(\u7528\u5faa\u5e8f\u8868\u793a\u6cd5\u5132\u5b58)\u9032\u884c\u641c\u5c0b \u5faa\u5e8f\u641c\u5c0b\u6cd5 …<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"fifu_image_url":"","fifu_image_alt":"","_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[15],"tags":[],"class_list":["post-566","post","type-post","status-publish","format-standard","hentry","category-algorithm"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/systw.net\/note\/wp-json\/wp\/v2\/posts\/566","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/systw.net\/note\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/systw.net\/note\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/systw.net\/note\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/systw.net\/note\/wp-json\/wp\/v2\/comments?post=566"}],"version-history":[{"count":0,"href":"https:\/\/systw.net\/note\/wp-json\/wp\/v2\/posts\/566\/revisions"}],"wp:attachment":[{"href":"https:\/\/systw.net\/note\/wp-json\/wp\/v2\/media?parent=566"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/systw.net\/note\/wp-json\/wp\/v2\/categories?post=566"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/systw.net\/note\/wp-json\/wp\/v2\/tags?post=566"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\u6642\u9593\u8907\u96dc\u5ea6\u6700\u5dee\u6700\u597d\u60c5\u6cc1\u7686\u70babigO(N)
\u4e00\u7b46\u7b46\u8cc7\u6599\u9010\u4e00\u6bd4\u8f03
unsorted array:insert=bigO(1) , finddata=bigO(n) , findminormax=bigO(n)<\/p>\n\n\n\n
\u6642\u9593\u8907\u96dc\u5ea6\u70babigO(2\u5e95log N)
\u8cc7\u6599\u9700\u5148\u6392\u5217\uff0c\u5f9e\u4e2d\u9593\u4f4d\u7f6e\u958b\u59cb\u6bd4\u8f03\uff0c\u4f9d\u5927\u5c0f\u5728\u5230\u5de6\u534a\u908a\u6216\u53f3\u534a\u908a\u7684\u4e2d\u9593\u6bd4\u8f03
\u905e\u8ff4\u65b9\u6cd5
int binary_search(int list[],int first,int last,int data){ \/\/data\u4ee3\u8868\u8cc7\u6599
\u3000if(first>last)return(-1); \/\/\u8cc7\u6599\u4e0d\u5728list\u5167
\u3000else{
\u3000\u3000middle=(first+last)\/2;
\u3000\u3000if(list[middle]==data)return(middle); \/\/\u50b3\u56dedata\u7684\u4f4d\u7f6e
\u3000\u3000else{
\u3000\u3000\u3000if(list[middle]>data)binary_search(list,middle-1,last,data); \/\/data\u5728\u5de6\u534a\u908a
\u3000\u3000\u3000else if(list[middle]
\u3000\u3000}
\u3000}
}
\u975e\u905e\u8ff4\u65b9\u6cd5
int binary_search(int list[],int first,int last,int data){
\u3000int middle;
\u3000while(first<=last){
\u3000\u3000middle=(first+last)\/2;
\u3000\u3000if(data==list[middle])return(middle);
\u3000\u3000else if(data>list[middle])first=middle+1; \/\/data\u5728\u53f3\u908a
\u3000\u3000else last=middle-1; \/\/data\u5728\u5de6\u908a
\u3000}
\u3000if(first>last)return(-1); \/\/\u8cc7\u6599\u4e0d\u5728list\u5167
}<\/p>\n\n\n\n
\u6642\u9593\u8907\u96dc\u5ea6\u70babigO(2\u5e95log N)
\u8cc7\u6599\u9700\u5148\u6392\u5217\uff0c\u4f7f\u7528\u8cbb\u6c0f\u6578\u5217\u5207\u5272\u6a94
\u8cbb\u6c0f\u6578\u5217\uff1af(0)=0,f(1)=1,f(2)=1,f(3)=2,f(4)=3,f(5)=5,f(6)=8,f(7)=13
\u5047\u8a2dn\u7b46\u8cc7\u6599=f(x)-1 ex:12=f(7)-1=13-1,x=7
\u3000\u6a39\u6839=f(x-1) ex:f(7-1)=f(6)=8
\u3000\u5de6\u5b50\u6a39\u7bc0\u9ede\u6578=f(x-1)-1 ex:f(6)-1=7
\u3000\u53f3\u5b50\u6a39\u7bc0\u9ede\u6578=f(x-1)-2 ex:f(6)-2=4
\u3000\u6a39\u6839\u8207son\u5dee\u8ddd=f(x-3) ex:f(7-3)=3,\u56e0\u6b64\u6a39\u6839-3\u5230\u5de6\u5b50\u6a39\u6a39\u6839\uff0c+3\u5230\u53f3\u5b50\u6a39\u6a39\u6839
\u5047\u8a2d\u6a39\u6839\u503c=f(j) ex:8=f(6),j=6
\u3000\u6a39\u6839\u8207son\u5dee\u8ddd=f(j-2) ex:f(6-2)=3,\u7d50\u679c\u540c\u4e0a\u505a\u6cd5\u4e0d\u540c\u800c\u5df1
\u5047\u8a2d\u7956\u7236\u8207\u7236\u89aa\u5dee\u8ddd=f(r) ex:\u5dee\u8ddd=8-5=3 , 3=f(4),r=4
\u3000\u5728\u5de6\u5b50\u6a39\u7684\u7236\u7bc0\u9ede\u548cson\u7684\u5dee\u8ddd=f(r-1) ex:f(r-1)=f(4-1)=2
\u3000\u5728\u53f3\u5b50\u6a39\u7684\u7236\u7bc0\u9ede\u548cson\u7684\u5dee\u8ddd=f(r-2) ex:f(r-2)=f(4-2)=1
\u5047\u8a2d\u9ad8\u5ea6\u70bah(root=0)\uff0c\u5247\u7bc0\u9ede\u6578\u70baf(h+3)-1
\u3000f(0)=1,f(1)=2,f(2)=4,f(3)=7,f(4)=12,f(5)=20…<\/p>\n\n\n\n
\u8cc7\u6599\u9700\u5148\u6392\u5217\uff0c\u548c\u4e8c\u5143\u641c\u5c0b\u6cd5\u985e\u4f3c\uff0c\u5dee\u5225\u5728middle\u7684\u8a08\u7b97\u4e0d\u540c\uff0c\u82e5\u8cc7\u6599\u5206\u4f48\u5747\u5300\u5247\u70babigO(1),\u5426\u5247\u6700\u5dee\u60c5\u6cc1\u70babigO(n)
\u5047\u8a2dlist[lower]=\u7b2c\u4e00\u7b46\u8cc7\u6599\u4e14\u503c\u6700\u5c0f\uff0clist[upper]=\u6700\u5f8c\u4e00\u7b46\u8cc7\u6599\u4e14\u503c\u6700\u5927
middle=(key-list[lower])\/(list[upper]-list[lower])*(upper-lower)+lower<\/p>\n\n\n\n
\u64f4\u5145\u4e8c\u5143\u6a39<\/strong>\uff1d\u539f\u6a39\uff0bexternal node\u5916\u90e8\u7bc0\u9ede
\u539f\u5167\u90e8\u7bc0\u9ede\u6307\u5411\u7a7a\u7684\u6b04\u4f4d\uff0c\u6539\u6210\u6307\u5411\u7279\u6b8a\u7684\u5916\u90e8\u7bc0\u9ede(\u4e5f\u7a31\u5931\u6557\u7bc0\u9ede\uff0c\u4e14\u6709n+1\u500b)
internal path length\u5167\u90e8\u8def\u5f91\u9577\u5ea6(i)=\u641c\u5c0b\u6210\u529f\u7684\u6210\u672c,\u7531\u6a39\u6839\u5230\u6240\u6709\u5167\u90e8\u7bc0\u9ede\u7684\u8def\u5f91\u9577\u5ea6\u7684\u7e3d\u548c
external path length\u5916\u90e8\u8def\u5f91\u9577\u5ea6(e)=\u641c\u5c0b\u5931\u6557\u7684\u6210\u672c,\u4e14e=i+2*n\uff0c\u7531\u6a39\u6839\u5230\u6240\u6709\u5916\u90e8\u7bc0\u9ede\u7684\u8def\u5f91\u9577\u5ea6\u7684\u7e3d\u548c
\u82e5\u7b49\u65bc\u5b8c\u6574\u4e8c\u5143\u6a39\uff0c\u64f4\u5145\u4e8c\u5143\u6a39\u5247\u6709\u6700\u5c0f\u7684i\u8207e\uff0c(\u5047\u8a2d\u5404\u7bc0\u9ede\u9577\u5ea6\u70ba1)\u5247i\u7684\u9577\u5ea6=n\u70ba0~n\u5404\u5225\u653e\u5165ceil(log2(n+1))-1\u5f8c\u76f8\u52a0
ex:n=7,\u5c31\u662f0+1+1+2+2+2+2
\u82e5\u7b49\u65bc\u50be\u659c\u4e8c\u5143\u6a39\uff0c\u64f4\u5145\u4e8c\u5143\u6a39\u5247\u6709\u6700\u5927\u7684i\u8207e\uff0c(\u5047\u8a2d\u5404\u7bc0\u9ede\u9577\u5ea6\u70ba1)\u5247i\u7684\u9577\u5ea6=n*(n-1)\/2=0+1+2+3+…(n-1)
\u8a2did1=\u6a39\u6839\u5230\u7b2c\u4e00\u500b\u5167\u90e8\u7bc0\u9ede\u7684\u8ddd\u96e2\uff0cip1=\u7b2c\u4e00\u500b\u5167\u90e8\u7bc0\u9ede\u7684\u52a0\u6b0a\uff0c
weighted internal path length\u52a0\u6b0a\u5167\u90e8\u8def\u5f91\u9577\u5ea6=id1*ip1+id2*ip2+….idn*ipn (\u641c\u5c0b\u6210\u529f\u7684\u6210\u672c)
\u8a2ded1=\u7b2c\u4e00\u500b\u5916\u90e8\u7bc0\u9ede\u7684\u8ddd\u96e2\uff0cep1=\u7b2c\u4e00\u500b\u5916\u90e8\u7bc0\u9ede\u7684\u52a0\u6b0a
weighted external path length\u52a0\u6b0a\u5916\u90e8\u8def\u5f91\u9577\u5ea6=ed1*ep1+ed2*ep2+…..ed(n+1)*ep(n+1) (\u641c\u5c0b\u5931\u6557\u7684\u6210\u672c)<\/p>\n\n\n\n
\u8aaa\u660e\uff1a\u5177\u6709\u6700\u5c0f\u52a0\u6b0a\u5916\u90e8\u8def\u5f91\u9577\u5ea6(\u7de8\u78bc\u8207\u89e3\u78bc\u6210\u672c)\u7684\u64f4\u5145\u4e8c\u5143\u6a39(\u5167\u90e8\u7bc0\u9ede\u7684\u52a0\u6b0a\u7e3d\u5408=\u52a0\u6b0a\u5916\u90e8\u8def\u5f91\u9577\u5ea6)
\u6f14\u7b97\u6cd5\uff1a\u8caa\u5a6a\u6cd5\uff0c\u9078\u64c7\u7a0b\u5f0f=\u5916\u90e8\u7bc0\u9ede\u7684\u52a0\u6b0a
\u512a\u9ede\uff1a\u7de8\u78bc\u8207\u89e3\u78bc\uff0c\u6700\u4f73\u5408\u4f75\u904e\u7a0b
huffman tree\u5efa\u7acb\u65b9\u6cd5\uff1a\u5c07\u4e00\u7b46\u6599\u7d93\u6392\u5e8f\u5f8c\uff0c\u6bcf\u4e00\u6b21\u627e\u51fa\u5169\u500b\u6700\u5c0f\u52a0\u6b0a\u7684\u503c\u7576\u7236\u7bc0\u9ede\uff0c\u4e26\u53cd\u8986\u4e00\u76f4\u5230\u5efa\u51fa\u6a39\u6839\u7bc0\u9ede
huffman code\u5efa\u7acb\u65b9\u6cd5\uff1a\u5c07\u5de6\u5206\u652f\u8868\u793a0\uff0c\u53f3\u5206\u652f\u8868\u793a1\uff0c\u6bcf\u500b\u8cc7\u6599\u5373\u53ef\u5f97\u5230\u4e00\u500b\u7de8\u78bc
\u6700\u5dee\u72c0\u6cc1\u4e0b\u7684\u5408\u4f75\u6b21\u6578\uff1a\u5167\u90e8\u7bc0\u9ede\u76f8\u52a0<\/p>\n\n\n\n
\u8aaa\u660e\uff1a\u9ad8\u5ea6\u6700\u5c0f\u7684\u4e8c\u5143\u641c\u5c0b\u6a39\uff0c\u4e14\u52a0\u6b0a\u5167\u90e8\u8def\u5f91\u9577\u5ea6\u8207\u52a0\u6b0a\u5916\u90e8\u8def\u5f91\u9577\u5ea6\u7e3d\u548c\u6700\u5c0f
\u76ee\u5730\uff1a\u70ba\u4e86\u80fd\u8b93\u641c\u5c0b\u6210\u672c\u6700\u5c11\uff0c\u4e5f\u5c31\u662f\u641c\u5c0b\u7684\u5e73\u5747\u6bd4\u8f03\u6b21\u6578\u6700\u5c11\uff0c\u4ee5\u63d0\u6607\u641c\u5c0b\u6548\u7387
\u505a\u6cd5\uff1a\u53ef\u5148\u7522\u751f\u6240\u6709\u53ef\u80fd\u7684\u4e8c\u5143\u6a39\uff0c\u518d\u8a08\u7b97\u5404\u4e0d\u540c\u4e8c\u5143\u6a39\u7684\u641c\u5c0b\u6210\u672c\uff0c\u5373\u53ef\u627e\u51fa\u6210\u672c\u6700\u5c0f\u7684\u6700\u4f73\u641c\u5c0b\u4e8c\u5143\u6a39
\u52d5\u614b\u898f\u756b\u6cd5\u7684\u8a2d\u8a08\u65b9\u5f0f\uff1a\u8b93\u6a39\u6839\u7bc0\u9ede\u7684\u5de6\u5b50\u6a39\u641c\u5c0b\u6210\u672c\u8207\u53f3\u5b50\u6a39\u641c\u5c0b\u6210\u672c\u76f8\u52a0\u6703\u6700\u5c0f\u7684\u64f4\u5145\u4e8c\u5143\u6a39\uff0c\u5c31\u662f\u641c\u5c0b\u6210\u672c\u6700\u5c0f\u7684\u6700\u4f73\u4e8c\u5143\u641c\u5c0b\u6a39
\u905e\u8ff4\u95dc\u4fc2\u5f0f\uff1acost(i,j)={
\u30000 , if i=j
\u3000min{cost(i,k-1)+cost(k,j)}+weight(i,j) , i<=j<\/p>\n\n\n\n
\u5141\u8a31\u8cc7\u6599\u80fd\u96a8\u6642\u9032\u884c\u63d2\u5165\u8207\u522a\u9664\u904b\u4f5c\uff0c\u9069\u5408\u4f7f\u7528\u93c8\u7d50\u8868\u793a\u6cd5<\/p>\n\n\n\n
unsorted linked list:insert=O(1) , finddata=O(N) , findmaxormin=O(N)<\/p>\n\n\n\n
\u8aaa\u660e\uff1a\u4e8c\u5143\u6a39\u7684\u4e00\u7a2e\uff0c\u82e5\u975e\u7a7a\u96c6\u5408\uff0c\u5247\u6a39\u6839\u7bc0\u9ede\u7684\u5de6\u5b50\u6a39\u6240\u6709\u7bc0\u9ede\u6bd4\u6a39\u6839\u7bc0\u9ede\u7684\u503c\u5c0f\uff0c\u53f3\u5b50\u6a39\u6240\u6709\u7bc0\u9ede\u5247\u6bd4\u6a39\u6839\u7bc0\u9ede\u5927\uff0c\u5de6\u53f3\u5b50\u6a39\u4e5f\u7b49\u65bc\u4e8c\u5143\u641c\u5c0b\u6a39
\u82e5\u4f7f\u7528\u4e2d\u5e8f\u8d70\u8a2a\uff0c\u5247\u53ef\u5c07\u503c\u7531\u5c0f\u5230\u5927\u5217\u51fa
\u512a\u9ede\uff1a\u52d5\u614b\u8cc7\u6599\u63d2\u5165\u522a\u9664\u8207\u641c\u5c0b
\u7279\u8cea:\u5de6\u5b50\u6a39\u5c0f\u65bc\u7236\u7bc0\u9ede,\u53f3\u5b50\u6a39\u5927\u65bc\u7236\u7bc0\u9ede
worst case:O(n),average case:O(2\u5e95log n)<\/p>\n\n\n\n
\u3000if(root==null)printf(“there is no data y>x”); \/\/\u82e5\u662f\u7a7a\u6a39\u5247\u6c92\u6709
\u3000else if(root->dataright,x); \/\/\u82e5x\u6bd4\u6a39\u6839\u5927\u5247\u5f80\u53f3\u5b50\u6a39\u641c\u5c0b
\u3000else if(root->data>x) find_great_than_x(root->left,x); \/\/\u82e5x\u6bd4\u6a39\u6839\u5c0f\u5247\u5f80\u5de6\u5b50\u6a39\u641c\u5c0b
\u3000else printf(“y=%d”,root->data”);
}<\/p>\n\n\n\n
treenode insert(struct treenode *root,int value){ \/\/\u65b0\u589evalue\u9032\u6a39
}
\u641c\u5c0b\u904b\u4f5c
treenode search(struct treenode *node,int value){
}
\u522a\u9664\u904b\u4f5c
\u82e5\u8981\u522a\u9664\u7684\u8cc7\u6599\u7bc0\u9ede\u5206\u652f\u5ea6<2 \u5247\u76f4\u63a5\u522a\u9664\uff0c\u5426\u5247\u627e\u8a72\u7bc0\u9ede\u5de6\u5b50\u6a39\u4e2d\u6700\u5927\u503c\u7bc0\u9ede\u6216\u53f3\u5b50\u6a39\u4e2d\u6700\u5c0f\u503c\u7bc0\u9ede\u53d6\u4ee3\u6b32\u522a\u9664\u7bc0\u9ede\uff0c\u5728\u522a\u9664\u6700\u5927\u6216\u6700\u5c0f\u503c\u7bc0\u9ede
treenode delete(struct treenode *root,int value,struct treenode *parent){
}
\u6700\u5dee\u60c5\u6cc1\u662f\u5efa\u7acb\u50be\u659c\u4e8c\u5143\u6a39\uff0c\u5247\u63d2\u5165\u522a\u9664\u641c\u5c0b\u90fd\u70babigO(N)\uff0c\u6700\u4f73\u60c5\u6cc1\u662f\u5efa\u7acb\u8da8\u8fd1\u5e73\u8861\u7684\u4e8c\u5143\u6a39\uff0c\u5247\u63d2\u5165\u522a\u9664\u641c\u5c0b\u90fd\u70babigO(2\u5e95log n)<\/p>\n\n\n\n
\u8aaa\u660e\uff1a\u7279\u6b8a\u4e8c\u5143\u641c\u5c0b\u6a39,\u5b9a\u7fa9\u548c\u4e8c\u5143\u641c\u5c0b\u6a39\u4e00\u6a23\uff0c\u5dee\u5225\u5728\u65bc\u63d2\u5165\u6216\u522a\u9664\u4e00\u7bc0\u9ede\u5f8c\u8981\u5c0d\u90e8\u4efd\u5b50\u6a39\u9032\u884c\u8abf\u6574\u4ee5\u4fdd\u6301\u9ad8\u5ea6\u5e73\u8861
\u512a\u9ede\uff1a\u52d5\u614b\u8cc7\u6599\u63d2\u5165\u522a\u9664\u8207\u641c\u5c0b\uff0c\u6700\u5dee\u60c5\u6cc1(log n)\u512a\u65bc\u4e8c\u5143\u641c\u5c0b\u6a39
\u63d2\u5165\u522a\u9664\u63d2\u5c0b\u90fd\u70babigO(2\u5e95log n)\uff0c\u4e5f\u5c31\u662f\u6a39\u7684\u9ad8\u5ea6<\/p>\n\n\n\n
typedef struct avltreenode *treenode;
typedef struct avltreenode{
\u3000treenode left;
\u3000int data;
\u3000int balance_factor; \/\/\u5de6\u53f3\u5b50\u6a39\u9ad8\u5ea6\u5dee\uff0c\u53ea\u6709-1,0,1\u4e09\u7a2e\u503c
\u3000treenode right;
}<\/p>\n\n\n\n
LL:\u9edea\u5de6\u6a39\u6839b\u53d6\u4ee3\u9edea,\u9edea\u548c\u9edea\u53f3\u6a39\u8b8a\u6210\u9edeb\u53f3\u6a39,\u9edeb\u539f\u53f3\u6a39\u8b8a\u6210\u9edea\u5de6\u6a39(a\u8b8ab\u7684\u53f3\u6a39,b\u7684\u53f3\u6a39\u8b8a\u6210a\u7684\u5de6\u6a39)
RR:\u548cLL\u76f8\u53cd(a\u8b8ab\u7684\u5de6\u6a39,b\u7684\u5de6\u6a39\u8b8a\u6210a\u7684\u53f3\u6a39)
LR:\u9edea\u5de6\u5152b\u7684\u53f3\u5152\u9edec\u53d6\u4ee3\u9edea,\u9edeb\u8b8a\u6210\u9edec\u5de6\u6a39,\u9edea\u548c\u9edea\u53f3\u6a39\u8b8a\u6210\u9edec\u53f3\u6a39,\u9edec\u5de6\u6a39\u8b8a\u6210\u9edeb\u53f3\u6a39,\u9edec\u53f3\u6a39\u8b8a\u6210\u9edea\u5de6\u6a39
RL:\u548cLR\u76f8\u53cd<\/p>\n\n\n\n
\u7279\u6b8a\u7684m-way\u641c\u5c0b\u6a39\uff0c\u5206\u652f\u5ea6\u70bam\uff0c\u6a39\u6839\u5206\u652f\u5ea6\u81f3\u5c11\u70ba2\uff0c\u5931\u6557\u7bc0\u9ede\u5728\u6700\u4e0b\u5c64\u4e14\u540c\u4e00\u5c64\uff0c\u6bcf\u500b\u7bc0\u9ede\u81f3\u5c11\u6709ceil(M\/2)\u500b\u5b50\u6a39
\u512a\u9ede\uff1a\u52d5\u614b\u8cc7\u6599\u63d2\u5165\u522a\u9664\u8207\u641c\u5c0b
2-3tree<\/strong>:\u5206\u652f\u5ea6\u70ba3\u7684btree,\u9664\u5931\u6557\u7bc0\u9ede\u5916,\u6240\u6709\u7bc0\u9ede\u5206\u652f\u5ea6\u4e0d\u662f2\u5c31\u662f3
insert,delete\u8907\u96dc\u5ea6\uff1d\u6a39\u7684\u9ad8\u5ea6\uff1dO(log3(N))
2-3-4tree<\/strong>:\u5206\u652f\u5ea64\u7684btree,\u9664\u5931\u6557\u7bc0\u9ede\u5916,\u6240\u6709\u7bc0\u9ede\u5206\u652f\u5ea6\u4e0d\u662f2\u5c31\u662f3\u62164\uff0c\u8a2d\u9ad8\u70bah\uff1a
\u7576\u5404\u5167\u90e8\u7bc0\u9ede\u5206\u652f\u5ea6\u662f4\u6642\u5177\u6709\u6700\u5c0f\u9ad8\u5ea6,\u5247\u8cc7\u6599\u6578=4^h-1,\u82e5\u4e0d\u8003\u616e\u5931\u6557\u7bc0\u9ede\u5247h=ceil(log4(n+1))
\u7576\u5404\u5167\u90e8\u7bc0\u9ede\u5206\u652f\u5ea6\u662f2\u6642\u5177\u6709\u6700\u5927\u9ad8\u5ea6,\u5247\u8cc7\u6599\u6578=2^h-1,\u82e5\u4e0d\u8003\u616e\u5931\u6557\u7bc0\u9ede\u5247h\uff1dceil(log2(n+1))
insert,delete\u8907\u96dc\u5ea6\uff1dO(log4(N))
\u641c\u5c0b\u65b0\u589e\u522a\u9664\u90fd\u70babigO(logm(N))<\/p>\n\n\n\n
struct treenode{
\u3000struct treenode *child1; \/\/\u6307\u5411\u7b2c\u4e00\u8cc7\u6599\u6b04\u4f4d\u7684\u5de6\u5152\u5b50\u7bc0\u9ede
\u3000int data1;
\u3000struct treenode *child2; \/\/\u6307\u5411\u7b2c\u4e00\u8cc7\u6599\u6b04\u4f4d\u7684\u53f3\u5152\u5b50\u7bc0\u9ede
\u3000int data2;
\u3000struct treenode *child3; \/\/\u6307\u5411\u7b2c\u4e8c\u8cc7\u6599\u6b04\u7684\u53f3\u5152\u5b50\u7bc0\u9ede
\u3000int degree;
}treenode<\/p>\n\n\n\n
1, \u7531\u6a39\u6839\u5f80\u4e0b\u627e\uff0c\u82e5\u8cc7\u6599\u4e0d\u5728b\u6a39\u4e2d\u5247\u505c\u5728\u5931\u6557\u7bc0\u9ede,\u7136\u5f8c\u63d2\u5165\u8cc7\u6599\u5728\u5931\u6557\u7bc0\u9ede\u7684\u4e0a\u5c64\u7bc0\u9edec\u4e2d
2, \u82e5\u7bc0\u9edec\u672a\u586b\u6eff(\u5206\u652f\u5ea6
\u82e5\u7bc0\u9edec\u586b\u6eff(\u5206\u652f\u5ea6=M)\uff0c\u5c07c\u7bc0\u9ede\u5728\u540c\u4e00\u5c64\u5206\u6210\u4e8c\u500b\u7bc0\u9ede\uff0c\u4e26\u5c07c\u7bc0\u9ede\u4e2d\u9593\u7684\u8cc7\u6599\u63d2\u5165\u5230\u7236\u89aa\u7bc0\u9ede
3, \u91cd\u8986\u6b65\u9a5f2\u76f4\u5230\u5b8c\u6210\u63d2\u5165(\u5206\u652f\u5ea6=
\u522a\u9664\u904b\u4f5c\uff1a\u3002\u3002\u3002
\u7bc0\u9ede\u500b\u6578\uff1a\u5206\u652f\u5ea6\u70ba3\u7684b\u6a39\uff0c\u82e5\u9ad8\u70bah\uff0c\u5247\u7bc0\u9ede\u6578\u70ba1+3^1+3^2+….3^(h-1)=(3^h-1)\/2\uff0c1\u7bc0\u9ede\u67092\u8cc7\u6599\uff0c\u6240\u4ee5\u8cc7\u6599\u6578\u70ba3^h-1
\u7bc4\u570d\u67e5\u8a62\uff1a\u3002\u3002\u3002<\/p>\n\n\n\n
btree\u7684\u4e00\u7a2e\u8b8a\u5316\uff0c\u53ef\u63d0\u4f9b\u55ae\u4e00\u8cc7\u6599\u7684\u7c21\u55ae\u67e5\u8a62\u8207\u591a\u500b\u8cc7\u6599\u7684\u7bc4\u570d\u67e5\u8a62
\u539f\u5931\u6557\u7bc0\u9ede\u4e2d\u653e\u6240\u6709\u8cc7\u6599\uff0c\u4e26\u7528\u93c8\u7bc0\u6b04\u4f4d\u9023\u6210\u4e00\u93c8\u7bc0\u4e32\u5217\uff0c\u4e14\u8cc7\u6599\u503c\u7531\u5de6\u81f3\u53f3\u9010\u4e00\u905e\u589e
\u539f\u975e\u5931\u6557\u7bc0\u9ede\u4e2d\u53ea\u5b58\u65bc\u90e8\u4efd\u7684\u503c\u7528\u4f86\u7576\u6210\u7d22\u5f15\u7d50\u69cb\uff0c\u8868\u793a\u7bc0\u9ede\u7684\u5b50\u6a39\u4e2d\u7684\u6700\u5927\u503c\u6216\u6700\u5c0f\u503c\u4ee5\u65b9\u4fbf\u7bc4\u570d\u67e5\u8a62<\/p>\n\n\n\n
2-3-4\u6a39\u7684\u4e8c\u5143\u6a39\u5f62\u5f0f\u8868\u793a\uff0c\u70ba\u4e8c\u5143\u641c\u5c0b\u6a39
\u5404\u7bc0\u9ede\u6307\u6a19\u6709\u7d05\u6307\u6a19(234\u6a39\u7d93\u8f49\u63db\u5f8c\u591a\u51fa\u4f86\u7684\u6307\u6a19)\u8207\u9ed1\u6307\u6a19(\u539f\u5148234\u6a39\u6307\u6a19)
\u7531\u6a39\u6839\u7bc0\u9ede\u5230\u5916\u90e8\u7bc0\u9ede\u7684\u6240\u6709\u8def\u5f91\u4e0a\uff0c\u9ed1\u6307\u6a19\u7684\u500b\u6578\u76f8\u540c
\u7531\u6a39\u6839\u7bc0\u9ede\u5230\u5916\u90e8\u7bc0\u9ede\u7684\u6240\u6709\u8def\u5f91\u4e0a\uff0c\u4e0d\u6703\u6709\u9023\u7e8c\u5169\u500b\u7d05\u6307\u6a19<\/p>\n\n\n\n
hashing search(\u96dc\u6e4a\u641c\u5c0b\u6cd5)<\/strong>
\u4e3b\u8981\u7528\u5728\u63d2\u5165\u548c\u641c\u5c0b\u6216\u522a\u9664
\u6700\u6709\u7528\u7684\u8cc7\u6599\u7d50\u69cb\u4e4b\u4e00
\u904b\u4f5c\u6642\u9593\u548c\u8cc7\u6599\u500b\u6578\u7121\u95dc,\u6642\u9593\u8907\u96dc\u5ea6\u70babigO(1)
\u7d93\u904e\u4e00\u500b\u7b97\u8853\u904b\u7b97\u51fd\u6578\u8a08\u7b97\uff0c\u800c\u5f97\u5230\u8cc7\u6599\u4f4d\u5740(\u96dc\u6e4a\u4f4d\u5740)
collision:\u4e0d\u540c\u7684\u8cc7\u6599\u8a08\u7b97\u51fa\u76f8\u540c\u7684\u96dc\u6e4a\u4f4d\u7f6e\uff0c\u7b2cn\u7b46\u8cc7\u6599\u672a\u78b0\u649e\u7684\u6a5f\u7387=\u8cc7\u65991\u672a\u78b0\u649e\u6a5f\u7387*\u8cc7\u65992\u672a\u78b0\u649e\u6a5f\u7387…*\u8cc7\u6599n\u672a\u78b0\u649e\u6a5f\u7387
overflow:\u767c\u751fcollision\u4e14\u6c92\u6709\u7a7a\u9593\u53ef\u4ee5\u5b58\u653e\u8cc7\u6599
\u82e5\u7121\u767c\u751foverflow\u6ea2\u4f4d\uff0c\u5247\u641c\u5c0b\u63d2\u5165\u522a\u9664\u6240\u9700\u6642\u9593\u7a7a\u9593\u548c\u8cc7\u6599\u500b\u6578\u7121\u95dc<\/p>\n\n\n\n
\u5e38\u7528\u6709\u5e73\u65b9\u4e2d\u9593\u6cd5\uff0c\u9664\u6cd5\uff0c\u647a\u758a\u6cd5\uff0c\u6578\u5b57\u5206\u6790\u6cd5
\u9664\u6cd5\uff1a\u8cc7\u6599 mod \u96dc\u6e4a\u8868\u5927\u5c0f(\u6700\u597d\u662f\u8cea\u6578)\uff1d\u96dc\u6e4a\u4f4d\u7f6e
\u56e0\u70ba\u96dc\u6e4a\u8868\u7a7a\u9593\u6709\u9650\u6240\u4ee5\u6ea2\u4f4d\u4e00\u5b9a\u6703\u767c\u751f\uff0c\u89e3\u6c7a\u8fa6\u6cd5\uff1a
\u3000linear probing(\u7dda\u6027\u641c\u5c0b\u6cd5)\uff1a\u5c07hash\u8868\u8996\u70ba\u74b0\u72c0\uff0c\u767c\u751f\u6ea2\u4f4d\u6642\uff0c\u5f80\u4e0b\u627e\u6700\u8fd1\u7684\u7a7a\u4f4d\u5b58\u653e\u8cc7\u6599
\u3000chaining(\u93c8\u4e32\u6cd5)\uff1ahash\u8868\u5404\u4f4d\u5740\u7528\u93c8\u7d50\u4e32\u5217\u5b58\u653e\u8cc7\u6599\uff0c\u76f8\u540c\u4f4d\u5740\u7684\u8cc7\u6599\u6703\u5b58\u653e\u5728\u540c\u4e00\u500b\u93c8\u7d50\u4e32\u5217\u4e2d
\u3000rehashing(\u91cd\u65b0\u96dc\u6e4a)\uff1a\u82e5\u767c\u751f\u6ea2\u4f4d\u5247\u7528\u53e6\u4e00\u500b\u96dc\u6e4a\u5bd2\u6578\u91cd\u65b0\u8a08\u7b97\u8cc7\u6599\u4f4d\u5740<\/p>\n\n\n\n
\u53ef\u61c9\u7528\u5728priority queue
heap\u9069\u5408\u7528\u5faa\u5e8f\u8868\u793a\u6cd5\u5132\u5b58
ps:
heap\u662f\u6a39\u72c0\u7d50\u69cb,\u800c\u5806\u758a\u662f\u7dda\u6027\u7d50\u69cb<\/p>\n\n\n\n
1\u70ba\u4e00\u5b8c\u6574\u4e8c\u5143\u6a39
2\u88e1\u9762\u7684\u5143\u7d20\u9700\u7b26\u5408heap condition(\u4e5f\u7a31heap property)
ps:
heap condition:
\u5404node\u5167\u7684data\u6bd4\u5b83\u5de6\u53f3\u5169\u908achild nodes\u5167\u7684data\u5c0f,\u800c\u5de6\u53f3\u5169child nodes\u9593\u4e26\u7121\u4e00\u5b9a\u7684\u95dc\u4fc2
\u4e5f\u5c31\u7b49\u65bc,\u6bcf\u68f5\u5b50\u6a39\u4e2d\u6700\u5c0f\u7684\u5143\u7d20\u7e3d\u662f\u5728\u6a39\u6839<\/p>\n\n\n\n
max heap(\u6700\u5927\u5806\u7a4d),\u7236\u7bc0\u9ede\u6703\u6bd4\u5b50\u7bc0\u9ede\u5927
min heap(\u6700\u5c0f\u5806\u7a4d),\u7236\u7bc0\u9ede\u6703\u6bd4\u5b50\u7bc0\u9ede\u5c0f<\/p>\n\n\n\n
\u641c\u5c0b\u6700\u5927\u503c\u8207\u6700\u5c0f\u503c\u7686\u70babigO(1)\uff0c\u4f46\u82e5\u8981\u641c\u5c0b\u6307\u5b9a\u7684\u503c\u70babigO(n)
\u6574\u500b\u5efa\u7acb\u6700\u5927\u6700\u5c0f\u5806\u7a4d\u7d50\u69cb\u7684\u8907\u96dc\u5ea6\u70babigO(n)
\u8b49\u660e\uff1a\u3002\u3002\u3002<\/p>\n\n\n\n
1\uff0c\u5c07\u9663\u5217\u8cc7\u6599\u8996\u70ba\u5b8c\u6574\u4e8c\u5143\u6a39\uff0c\u4e26\u53d6\u4e00\u503c\u7576\u65b0\u8cc7\u6599\u63d2\u5165\u5806\u7a4d\u6a39\u5167\uff0c\u65b0\u8cc7\u6599\u9700\u63d2\u5728\u6700\u5f8c\u4e00\u500b\u7bc0\u9ede
2\uff0c\u82e5\u662fmax tree,\u5247\u65b0\u8cc7\u6599\u6bd4\u7236\u7bc0\u9ede\u5927\u5247\u8abf\u63db\uff0c\u4e26\u5f80\u4e0a\u9010\u4e00\u6aa2\u67e5\u5b50\u7bc0\u9ede\u662f\u5426\u5927\u65bc\u7236\u7bc0\u9ede\uff0c\u82e5\u662f\u5247\u8abf\u63db
2\uff0c\u82e5\u662fmin tree,\u5247\u65b0\u8cc7\u6599\u6bd4\u7236\u7bc0\u9ede\u5c0f\u5247\u8abf\u63db\uff0c\u4e26\u5f80\u4e0a\u9010\u4e00\u6aa2\u67e5\u5b50\u7bc0\u9ede\u662f\u5426\u5c0f\u65bc\u7236\u7bc0\u9ede\uff0c\u82e5\u662f\u5247\u8abf\u63db
void insertitem(p,data){
\u3000pos=rear+1; \/\/pos\u53d6\u5f97\u6700\u5f8c\u4e00\u500b\u7bc0\u9ede\u7684\u4f4d\u7f6e
\u3000p[pos]=data;
\u3000while(pos>front){ \/\/front\u662f\u7b2c\u4e00\u500b\u7bc0\u9ede\u7684\u4f4d\u7f6e
\u3000if(p[pos] < p[pos\/2]){ break;}
\u3000else{
\u3000\u3000swap(p[pos],p[pos\/2]);
\u3000\u3000pos=pos\/2;
\u3000\u3000}
\u3000}
}<\/p>\n\n\n\n
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removeroot(p){
…
}<\/p>\n\n\n\n
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\u63d2\u5165\u8207\u522a\u9664\u6700\u5927\u6216\u6700\u5c0f\u904b\u4f5c\u7686\u70babigO(log2(n))<\/p>\n","protected":false},"excerpt":{"rendered":"