{"id":282,"date":"2012-11-21T11:33:00","date_gmt":"2012-11-21T03:33:00","guid":{"rendered":"http:\/\/nike0good.jp1.rpvhost.net\/187"},"modified":"2012-11-21T11:33:00","modified_gmt":"2012-11-21T03:33:00","slug":"poj_1631_o_n_log_n_lis_practice","status":"publish","type":"post","link":"https:\/\/nike0good.com\/?p=282","title":{"rendered":"POJ 1631(O(nlogn)LIS\u76842\u79cd\u505a\u6cd5)"},"content":{"rendered":"\n\n\n
\n
Language:\n\n\n\n
Time Limit:<\/strong> 1000MS<\/td>\n <\/td>\nMemory Limit:<\/strong> 10000K<\/td>\n<\/tr>\n
Total Submissions:<\/strong> 8574<\/td>\n <\/td>\nAccepted:<\/strong> 4635<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n

\nDescription<\/p>\n

\n\u5bf9\u4e8e\u4e00\u4e2a\u4e8c\u5206\u56fe\u7684\u5b8c\u5168\u5339\u914d\uff0c\u8bf7\u627e\u51fa\u6700\u591a\u7684\u8fb9\u4f7f\u5176\u4e24\u4e24\u4e0d\u76f8\u4ea4\u3002
\n
\"\"
\n<\/center>\n<\/div>\n

\nInput<\/p>\n

\n\u7b2c\u4e00\u884c\u4e3a\u6d4b\u8bd5\u6570\u636e\u6570t\uff0c<\/div>\n
\n\u5bf9\u4e8e\u6bcf\u7ec4\u6570\u636e\uff0c\u7b2c\u4e00\u884c\u4e3a\u5339\u914d\u6570 p < 40000\uff0c<\/div>\n
\n\u63a5\u4e0b\u6765p\u884c\uff0c\u6bcf\u884c1\u4e2a\u6570a[i]\uff0c\u8868\u793a\u5de6\u8fb9\u7b2ci\u4e2a\u7aef\u70b9\u4e0e\u53f3\u8fb9\u7b2ca[i]\u4e2a\u7aef\u70b9\u76f8\u8fde<\/div>\n

\nOutput<\/p>\n

\n\u5bf9\u6bcf\u7ec4\u6570\u636e\uff0c\u8f93\u51fa\u4e00\u884cans\uff0c\u8868\u793a\u6700\u5927\u4e0d\u76f8\u4ea4\u5339\u914d\u6570<\/div>\n

\nSample Input<\/p>\n

4\n6\n4\n2\n6\n3\n1\n5\n10\n2\n3\n4\n5\n6\n7\n8\n9\n10\n1\n8\n8\n7\n6\n5\n4\n3\n2\n1\n9\n5\n8\n9\n2\n3\n1\n7\n4\n6<\/pre>\n
\nSample Output<\/p>\n
3\n9\n1\n4<\/pre>\n
\nSource<\/p>\n
\nNorthwestern Europe 2003<\/a><\/div>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
\u8fd9\u9898\u663e\u7136\u53ef\u4ee5\u8f6c\u5316\u4e3aa[i]\u7684LIS<\/span><\/p>\n
LIS\u7684\u4e00\u822c\u505a\u6cd5\u5982\u4e0b\uff1a<\/span><\/p>\n
f[i]\u8868\u793a\u4ee5i\u4e3a\u6700\u540e\u4e00\u4e2a\u5143\u7d20\u7684\u6700\u957f\u5e8f\u5217\u6570\uff0c<\/span><\/p>\n
f[i]=f[j]+1(a[j]<a[i]\uff0cj<i)<\/span><\/p>\n
nLogn \u7b97\u6cd51\uff1a<\/span><\/p>\n
\u663e\u7136\u4e0a\u9762\u7684\u65b9\u7a0b\u67091\u7ef4n\u662f\u7528\u6765\u6c42\u2018\u5c0f\u4e8ea[i]\u4e14\u5728a[i]\u524d\u9762\u7684\uff0c\u6700\u5927\u7684\u6570\u2018<\/span><\/p>\n
\u5355\u4ece\u8fd9\u4e2a\u5b9a\u4e49\u8003\u8651\uff0c<\/span><\/p>\n
\n<\/p>\n
\"\"\n<\/p>\n
\n<\/p>\n
\u4e8e\u662f\u95ee\u9898\u8f6c\u5316\u6210-\u7ef4\u62a4\u5e8f\u5217max\uff08f[i])\uff0c\u6bcf\u4e00\u6b21\u589e\u52a01\u4e2a\u70b9\u7684值\uff0c\u6c42[1,value_i)\u7684\u6700\u5927值\uff08\u82e5\u65e0值\u5219\u4e3a0\uff09<\/span><\/p>\n
\u4e0d\u59a8\u7528\u4e00\u4e2azkw\u7ebf\u6bb5\u6811\u7ef4\u62a4\uff08\u672c\u9898max(f[i])\u7684\u957f\u5ea6=n\uff0c\u82e5\u6ca1\u6709\u8fd9\u4e2a\u6761\u4ef6\u65f6\u95f4\u4f1a\u9000\u5316\u5230O(nLogT)(T\u4e3aa[i]\u7684\u6700\u5927值\uff09\uff0c\u90a3\u4e48\u8bf7\u628a\u539f\u5e8f\u5217\u6392\u5e8fO(nLogn)+\u79bb\u6563\u5316O(n),\u8fd9\u6837\u590d\u6742\u5ea6\u5c31\u6709O(nLogT)\u964d\u81f3O(nLogn)    \uff09.<\/span><\/span><\/p>\n
\u7a0b\u5e8f1\u5982\u4e0b\uff1a<\/span><\/p>\n
<\/span><\/p>\n
#include<cstdio>\n#include<cstring>\n#include<cstdlib>\n#include<iostream>\n#include<functional>\n#include<algorithm>\nusing namespace std;\n#define MAXN (40000+10)\n#define NDEBUG\nint t,n;\nstruct SegMentTree\n{\n\tint a[MAXN*10],n;\n\tint M;\n\tSegMentTree(){}\n\tSegMentTree(int _n):n(_n)\n\t{\n\t\tM=1;\n\t\twhile (M-2<n) M<<=1;\n\t\tmemset(a,0,sizeof(a));\n\t}\n\tvoid insert(int _x,int c)\n\t{\n\t\t_x+=M;\n\t\tif (a[_x]<c)\n\t\t{\n\t\t\ta[_x]=c;\n\t\t\tfor (_x>>=1;_x;_x>>=1) a[_x]=max(a[_x<<1],a[(_x<<1)^1]);\n\t\t}\n\t}\n\tint find(int l,int r)\n\t{\n\t\tint ans=0;\n\t\tl--;r++;\n\t\tl+=M;r+=M;\n\t\twhile (l^r^1)\n\t\t{\n\t\t\tif (~l&1) ans=max(ans,a[l+1]);\n\t\t\tif (r&1) ans=max(ans,a[r-1]);\n\t\t\tl>>=1;r>>=1;\n\t\t}\n\t\treturn ans;\n\t}\n}a;\nint main()\n{\n\t#ifndef NDEBUG\n\tfreopen("poj1631.in","r",stdin);\n\t#endif\n\tscanf("%d",&t);\n\twhile (t--)\n\t{\n\t\tcin>>n;\n\t\ta=SegMentTree(n);\n\t\tfor (int i=1;i<=n;i++)\n\t\t{\n\t\t\tint value;\n\t\t\tscanf("%d",&value);\n\t\t\ta.insert(value,a.find(1,value-1)+1);\n\t\t}\n\t\tprintf("%dn",a.find(1,n));\n\n\t}\n\treturn 0;\n}<\/pre>\n
\n\u7b97\u6cd52\uff1a<\/p>\n
\u4ed4\u7ec6\u89c2\u5bdf\u63a8\u5bfc\u5e8f\u5217\u6c42\u6700\u5927值\u90e8\u5206\uff0c\u53d1\u73b0i\u603b\u4ece1\u5f00\u59cb[1,value_i)<\/span><\/p>\n
\u4e8e\u662f\u53ef\u4e8c\u5206\u67e5\u627e\u5e8f\u5217Max[I]'=Max[ F[p] ] (1\u2264p\u2264i)<\/span><\/p>\n
\n<\/p>\n
<\/span><\/p>\n
Program LCS;\nvar\n   a,d,f:array[1..100000] of longint;\n   n,i,j,len,test:longint;\nfunction search(k:longint):longint;\nvar\n   i,j,m:longint;\nbegin\n   i:=1; j:=len;\n   m:=d[(i+j) div 2];\n   while (i<=j) do\n   begin\n      m:=(i+j) div 2;\n      if (d[m]<k) and (d[m+1]>=k) then exit(m)\n      else if (d[m]<k) then i:=m+1\n      else j:=m-1;\n   end;\nend;\nbegin\n   read(test);\n   while (test>0) do\n   begin\n      read(n);\n      len:=1;\n      fillchar(d,sizeof(d),0);\n      for i:=1 to n do read(a[i]);\n      d[1]:=a[1];\n      f[1]:=1;\n      for i:=2 to n do\n      begin\n         if (a[i]>d[len]) then\n         begin\n            inc(len);\n            d[len]:=a[i];\n            f[i]:=len;\n         end\n         else if (a[i]<=d[1]) then\n         begin\n            d[1]:=a[i];\n            f[i]:=1;\n         end\n         else\n         begin\n            j:=search(a[i]);\n            d[j+1]:=a[i];\n            f[i]:=j+1;\n         end;\n      end;\n      writeln(len);\n      dec(test);\n   end;\nend.<\/pre>\n<\/p>\n

\n<\/span><\/p>\n

\n<\/span><\/p>\n

\n<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"
Language: Default Bridging signals Time Limit: 100 […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_coblocks_attr":"","_coblocks_dimensions":"","_coblocks_responsive_height":"","_coblocks_accordion_ie_support":"","footnotes":""},"categories":[3],"tags":[30,52,55,81],"class_list":["post-282","post","type-post","status-publish","format-standard","hentry","category-defaultcategory","tag-dp","tag-the_zkw_segment_tree","tag-dichotomy","tag-series"],"yoast_head":"\nPOJ 1631(O(nlogn)LIS\u76842\u79cd\u505a\u6cd5) - nike0good<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/nike0good.com\/?p=282\" \/>\n<meta property=\"og:locale\" content=\"zh_CN\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"POJ 1631(O(nlogn)LIS\u76842\u79cd\u505a\u6cd5) - 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