{"id":313,"date":"2013-01-20T23:58:00","date_gmt":"2013-01-20T15:58:00","guid":{"rendered":"http:\/\/nike0good.jp1.rpvhost.net\/218"},"modified":"2013-01-20T23:58:00","modified_gmt":"2013-01-20T15:58:00","slug":"cf_264b_prime_factor_decomposition","status":"publish","type":"post","link":"https:\/\/nike0good.com\/?p=313","title":{"rendered":"CF 264B(\u8d28\u56e0\u6570\u5206\u89e3)"},"content":{"rendered":"
\n
\n
\n
\n
\n
D. Good Sequences<\/div>\n
\n
\ntime limit per test<\/div>\n

2 seconds<\/p><\/div>\n

\n
\nmemory limit per test<\/div>\n

256 megabytes<\/p><\/div>\n

\n
\ninput<\/div>\n

standard input<\/p><\/div>\n

\n
\noutput<\/div>\n

standard output<\/p><\/div>\n<\/div>\n

\n

\n\u6570\u5217 n<\/em><\/span> \u6709 a<\/em>1<\/sub>,\u2009a<\/em>2<\/sub>,\u2009...,\u2009a<\/em>n<\/em><\/sub><\/span> \u4e2a\u6570\uff08\u4e25格\u9012\u589e\uff09\uff0c\u8bf7\u4ece\u4e2d\u4efb\u610f\u5220\u53bb\u4e00\u4e9b\u6570\uff0c\u4f7f\u5e8f\u5217\u76f8\u90bb2\u6570\u90fd\u4e0d\u4e92\u8d28\u3002<\/p>\n

\n

\n\u95ee\u5220\u540e\u5e8f\u5217\u6700\u957f\u957f\u5ea6.<\/p>\n<\/div>\n

\n
\nInput<\/div>\n

\n\u7b2c\u4e00\u884c n<\/em><\/span> (1\u2009\u2264\u2009n<\/em>\u2009\u2264\u2009105<\/sup><\/span>)
\n \u7b2c\u4e8c\u884c\u5e8f\u5217 a<\/em>1<\/sub>,\u2009a<\/em>2<\/sub>,\u2009...,\u2009a<\/em>n<\/em><\/sub><\/span> (1\u2009\u2264\u2009a<\/em>i<\/em><\/sub>\u2009\u2264\u2009105<\/sup>; a<\/em>i<\/em><\/sub>\u2009<\u2009a<\/em>i<\/em>\u2009+\u20091<\/sub><\/span>).<\/p>\n<\/div>\n

\n
\nOutput<\/div>\n

\n\u5220\u540e\u5e8f\u5217\u6700\u957f\u957f\u5ea6<\/span>.<\/p>\n<\/div>\n

\n
\nSample test(s)<\/div>\n
\n
\n
\ninput<\/div>\n
5\n2 3 4 6 9\n<\/pre>\n<\/div>\n
\n
\noutput<\/div>\n
4\n<\/pre>\n<\/div>\n
\n
\ninput<\/div>\n
9\n1 2 3 5 6 7 8 9 10\n<\/pre>\n<\/div>\n
\n
\noutput<\/div>\n
4\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n
\n
\nNote<\/div>\n
\nIn the first example, the following sequences are examples of good sequences: [2; 4; 6; 9], [2; 4; 6], [3; 9], [6]. The length of the longest good sequence is 4.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
\n<\/p>\n
\u9519\u89e3\uff1a\u679a\u4e3e\u5f00\u5934\u5373\u53ef\u3002<\/span>X<\/del><\/u><\/strong><\/span><\/p>\n
<\/span><\/p>\n
#include<cstdio>\n#include<iostream>\n#include<cstdlib>\n#include<cstring>\n#include<cmath>\n#include<functional>\n#include<algorithm>\n#include<cctype>\nusing namespace std;\n#define MAXN (100000+10)\nint n,a[MAXN];\nbool b[MAXN]={0};\nint gcd(int a,int b){return (b==0)?a:gcd(b,a%b);};\nint main()\n{\n\tscanf("%d",&n);for (int i=1;i<=n;i++) scanf("%d",&a[i]);\n\tint ans=0;\n\tfor (int i=1;i<=n;i++)\n\tif (!b[i])\n\t{\n\t\tint len=1;\n\t\tb[i]=1;\n\t\tint head=i,tail=i+1;\n\t\twhile (tail<=n)\n\t\t{\n\t\t\tif (gcd(a[tail],a[head])==1) tail++;\n\t\t\telse {b[head]=1;head=tail;tail++;len++;\t}\n\t\t}\n\t\tans=max(ans,len);\n\t}\n\tcout<<ans<<endl;\n\n\treturn 0;\n}<\/pre>\n
\u66f4\u6b63\uff1a<\/span><\/p>\n
<\/span>\u679a\u4e3e\u5f00\u5934\u4e0d\u884c\uff0c\u56e0\u4e3a\u4e00\u4e2a\u5f00\u5934\u53ef\u80fd\u8ddf\u6709\u591a\u4e2a\u5e8f\u5217\uff082\uff0c6\uff0c9\uff09\/\uff082\uff0c4\uff09\u2190\u9009\u8fd9\u4e2a\u4e0d\u5fe7<\/span><\/p>\n
\u6545\u679a\u4e3e\u8d28\u56e0\u6570\uff0c\u8bc1\u660e\u4e0b\uff1a<\/span><\/p>\n
\u82e5a\u548cb\u4e0d\u4e92\u8d28,\u5219\u5fc5\u5b58\u5728\u8d28\u6570k\uff0c\u4f7fk|a&&k|b<\/span><\/p>\n
\u6545Dp\u5982\u4e0b:<\/span><\/p>\n
<\/span> f[i,j]=max(f[i-1,k]+1) (k| a[i] \u4e14j|a[i] ) \u6700\u5927值len=f[i,j] <\/em><\/span><\/span><\/p>\n
\/\/  f[i,j]  \u8868\u793a\u5230\u7b2ci\u4e2a\u6570\u4e3a\u6b62\uff0c\u7ed3\u5c3e\u662f\u8d28\u6570 j \u7684\u500d\u6570\u7684\u6700\u5927\u957f\u5ea6\u3002<\/span><\/p>\n
+\u4e0a\u6eda\u52a8\u6570\u7ec4\u540e\uff0c\u5f97\u5230\u5982\u4e0b\u7684Dp\u65b9\u7a0b<\/span><\/p>\n
\u8ba1\u7b97<\/span>\uff1a <\/span>len=max(f[k])+1 (k| a[i] )<\/em><\/span><\/span><\/p>\n
\u66f4\u65b0\uff1af[j]=max(f[j],len) (j|a[i])<\/em><\/span><\/span><\/em><\/span> <\/em><\/span><\/p>\n

\n<\/span><\/p>\n
\u6ce8\u610f\u8d28\u56e0\u6570\u7684\u5206\u89e3\u4e2d \u5148\u5206\u89e3\u5230\u221an\uff0c\u82e5\u6b64\u65f6\u672a\u9664\u5c3d\uff0c\u90a3\u4e00\u90e8\u5206\u4e5f\u8981\u7b97\u8fdb\u53bb\uff08\u80af\u5b9a\u662f\u8d28\u6570\uff0c\u5426\u5219\u5fc5\u80fd\u518d\u5206\uff09<\/span><\/p>\n
eg\uff1a14=2*7\uff087=\u221a49>\u221a14\uff09<\/span><\/p>\n

\n<\/span><\/p>\n
<\/span><\/p>\n
#include<cstdio>\n#include<iostream>\n#include<cstdlib>\n#include<cstring>\n#include<cmath>\n#include<functional>\n#include<algorithm>\n#include<cctype>\nusing namespace std;\n#define MAXN (100000+10)\nint n,a[MAXN],f[MAXN]={0},st[MAXN],size;\nint gcd(int a,int b){return (b==0)?a:gcd(b,a%b);};\nvoid fac_prime(int x)\n{\n\tsize=0;\n\tfor (int j=2;j*j<=x;j++)\n\t{\n\t\tif (x%j==0)\n\t\t{\n\t\t\twhile (x%j==0) x\/=j;\n\t\t\tst[++size]=j;\n\t\t}\n\t}\n\tif (x>1) st[++size]=x;\n}\nint main()\n{\n\tscanf("%d",&n);\n\tint ans=0;\n\tfor (int i=1;i<=n;i++)\n\t{\n\t\tscanf("%d",&a[i]);\n\t\tif (a[i]==1) {ans=max(ans,1);continue;}\n\t\tfac_prime(a[i]);\n\t\tint len=0;\n\t\tif (st[1]==a[i]) {len=1;f[a[i]]=1;}\n\t\telse\n\t\t\tfor (int j=1;j<=size;j++)\n\t\t\t\tlen=max(len,f[st[j]]+1);\n\n\t\tfor (int j=1;j<=size;j++) f[st[j]]=max(f[st[j]],len);\n\t\tans=max(ans,len);\n\/\/\t\tfor (int j=1;j<=a[i];j++) cout<<f[j]<<' ';\n\/\/\t\tcout<<endl;\n\t}\n\tcout<<ans<<endl;\n\treturn 0;\n}<\/pre>\n<\/p>\n

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

\n<\/span><\/p>\n
<\/p>\n","protected":false},"excerpt":{"rendered":"
D. Good Sequences time limit per test 2 seconds memory  […]<\/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":[107],"class_list":["post-313","post","type-post","status-publish","format-standard","hentry","category-defaultcategory","tag-prime_number"],"yoast_head":"\nCF 264B(\u8d28\u56e0\u6570\u5206\u89e3) - 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=313\" \/>\n<meta property=\"og:locale\" content=\"zh_CN\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"CF 264B(\u8d28\u56e0\u6570\u5206\u89e3) - nike0good\" \/>\n<meta property=\"og:description\" content=\"D. 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