{"id":841,"date":"2013-10-24T09:35:34","date_gmt":"2013-10-24T01:35:34","guid":{"rendered":"http:\/\/www.shuizilong.com\/house\/?p=841"},"modified":"2013-10-31T21:14:29","modified_gmt":"2013-10-31T13:14:29","slug":"bzoj-3230-%e7%9b%b8%e4%bc%bc%e5%ad%90%e4%b8%b2","status":"publish","type":"post","link":"https:\/\/www.shuizilong.com\/house\/archives\/bzoj-3230-%e7%9b%b8%e4%bc%bc%e5%ad%90%e4%b8%b2\/","title":{"rendered":"BZOJ 3230. \u76f8\u4f3c\u5b50\u4e32"},"content":{"rendered":"<h3>Brief description:<\/h3>\n<p>\u8bbe\u4e24\u4e2a\u5b57\u7b26\u4e32\u7684\u6700\u957f\u516c\u5171\u524d\u7f00\u548c\u540e\u7f00\u7684\u957f\u5ea6\u5206\u522b\u4e3a $$a$$, $$b$$\u3002<br \/>\n\u5219\u5b83\u4eec\u76f8\u4f3c\u7a0b\u5ea6\uff0c\u5b9a\u4e49\u4e3a $$a^2 + b^2$$\u3002<br \/>\n\u7ed9\u5b9a\u4e00\u4e2a\u5b57\u7b26\u4e32\uff0c\u6bcf\u6b21\u8be2\u95ee\u5176\u5b57\u5178\u5e8f\u7b2c <code>k1-th<\/code> \u5927\u548c\u7b2c <code>k2-th<\/code> \u5927\u7684\u4e24\u4e2a\u5b50\u4e32\u95f4\u7684\u76f8\u4f3c\u7a0b\u5ea6\u3002<\/p>\n<p><!--more--><\/p>\n<h3>Analysis:<\/h3>\n<p>\u6c42\u4e00\u4e2a\u5b57\u7b26\u4e32\u7684\u5b57\u5178\u5e8f\u7b2c <code>k-th<\/code> \u5927\u5b50\u4e32\u53ef\u4ee5\u7528 <code>SA<\/code> \u505a\u5230\u6bcf\u6b21\u8be2\u95ee<code>log(n)<\/code>\u3002<br \/>\n\u65b9\u6cd5\u662f\uff0c\u5728\u641e\u51fa\u9ad8\u5ea6\u51fd\u6570\u7684\u65f6\u5019\uff0c\u987a\u4fbf\u5f00\u4e00\u4e2a\u6570\u7ec4\u8bb0\u5f55\u5230 SA \u4e2d\u7684\u7684\u67d0\u4e2a\u4e3a\u6b62\uff0c\u5171\u4f1a\u51fa\u73b0\u591a\u5c11\u5b50\u4e32\u3002\u6bcf\u6b21\u8be2\u95ee\u76f4\u63a5\u5728\u8fd9\u4e2a\u6570\u7ec4\u4e0a\u4e8c\u5206\u5373\u53ef\u3002<\/p>\n<p>\uff08Open Problem: \u8fd9\u91cc\u6211\u4eec\u53ea\u9700\u8981\u8f93\u51fa\u5b50\u4e32\u7684\u5de6\u53f3\u4e0b\u6807\uff0c\u7c7b\u4f3c\u5bf9\u4e8e <code>Rank<\/code> \u6211\u4eec\u7ed9\u51fa\u5b50\u4e32\u7684\u4e0b\u6807\uff0c\u540c\u6837 SA \u53ef\u4ee5\u7528\u7c7b\u4f3c\u65b9\u6cd5\u5728 <code>log(n)<\/code> \u65f6\u95f4\u5185\u89e3\u51b3\u95ee\u9898\u3002\u5bf9\u4e8e <code>Select<\/code> \u4ee5\u53ca <code>Rank<\/code>\uff0c\u7528 <code>SAM<\/code> \u662f\u5426\u4e5f\u53ef\u4ee5\u8fbe\u5230 <code>log(n)<\/code> \u7684\u590d\u6742\u5ea6\uff1f\u3002<\/p>\n<p>\u4e4b\u540e\u5c31\u662f lcp \u4e86\u3002\u3002\u3002\uff08\u8fd9\u9898\u6211\u7528 hash \u6c42 lcp \u6302\u4e86\u3002\u3002= =\uff09\u3002<\/p>\n<p><a href=\"https:\/\/gist.github.com\/lychees\/7079186\">https:\/\/gist.github.com\/lychees\/7079186<\/a><\/p>\n<pre class=\"brush: cpp; light: false; title: ; toolbar: true; notranslate\" title=\"\">\r\nconst int N = int(1e5)+9, M = 26+1, LV = 20;\r\n \r\nLL a&#x5B;N]; char s&#x5B;N]; int n;\r\nint C&#x5B;N], key&#x5B;N], t1&#x5B;N], t2&#x5B;N];\r\n \r\nstruct SA{\r\n \r\n    int a&#x5B;3*N], sa&#x5B;3*N], rk&#x5B;N], h&#x5B;N];\r\n \r\n    inline void rs(int*x,int*y,int*sa,int n,int m){\r\n        REP(i, n)key&#x5B;i]=i&#x5B;y]&#x5B;x];\r\n        memset(C, 0,sizeof(C&#x5B;0])*m);\r\n        REP(i, n) ++C&#x5B;key&#x5B;i]];\r\n        FOR(i, 1, m) C&#x5B;i] += C&#x5B;i-1];\r\n        DWN(i, n, 0) sa&#x5B;--C&#x5B;key&#x5B;i]]] = y&#x5B;i];\r\n    }\r\n \r\n    void da(int*a,int*sa,int n,int m){\r\n        int *x = t1, *y = t2;\r\n        memset(C,0,sizeof(C&#x5B;0])*m);\r\n        REP(i, n)++C&#x5B;x&#x5B;i]=a&#x5B;i]];\r\n        FOR(i, 1, m)C&#x5B;i]+=C&#x5B;i-1];\r\n        DWN(i, n, 0)sa&#x5B;--C&#x5B;x&#x5B;i]]]=i;\r\n        for(int l=1,p=1;p&lt;n;l&lt;&lt;=1,m=p){\r\n            p=0; FOR(i, n-l, n) y&#x5B;p++]=i;\r\n            REP(i, n) if (sa&#x5B;i]&gt;=l) y&#x5B;p++]=sa&#x5B;i]-l;\r\n            rs(x,y,sa,n,m),swap(x,y),x&#x5B;sa&#x5B;0]]=p=0;FOR(i, 1, n)\r\n                x&#x5B;sa&#x5B;i]]=(y&#x5B;sa&#x5B;i]]==y&#x5B;sa&#x5B;i-1]]&amp;&amp;y&#x5B;sa&#x5B;i]+l]==y&#x5B;sa&#x5B;i-1]+l])?p:++p;\r\n            ++p;\r\n        }\r\n    }\r\n \r\n#define F(x) ((x)\/3+((x)%3==1?0:tb))\r\n#define G(x) ((x)&lt;tb?(x)*3+1:((x)-tb)*3+2)\r\nint c0(int*r,int a,int b)\r\n{return r&#x5B;a]==r&#x5B;b]&amp;&amp;r&#x5B;a+1]==r&#x5B;b+1]&amp;&amp;r&#x5B;a+2]==r&#x5B;b+2];}\r\nint c12(int k,int*r,int a,int b)\r\n{if(k==2) return r&#x5B;a]&lt;r&#x5B;b]||r&#x5B;a]==r&#x5B;b]&amp;&amp;c12(1,r,a+1,b+1);\r\n else return r&#x5B;a]&lt;r&#x5B;b]||r&#x5B;a]==r&#x5B;b]&amp;&amp;key&#x5B;a+1]&lt;key&#x5B;b+1];}\r\n \r\nvoid dc3(int*a,int*sa,int n,int m){\r\n    int i, j, *an=a+n, *san=sa+n, ta=0, tb=(n+1)\/3, tbc=0, p;\r\n    a&#x5B;n] = a&#x5B;n+1] = 0; REP(i, n) if (i%3) t1&#x5B;tbc++]=i;\r\n \r\n    rs(a+2,t1,t2,tbc,m),rs(a+1,t2,t1,tbc,m),rs(a,t1,t2,tbc,m);\r\n    p=0,an&#x5B;F(t2&#x5B;0])]=0;FOR(i, 1, tbc)\r\n        an&#x5B;F(t2&#x5B;i])]=c0(a,t2&#x5B;i-1],t2&#x5B;i])?p:++p;\r\n \r\n    if (++p &lt; tbc) dc3(an,san,tbc,p);\r\n    else REP(i, tbc) san&#x5B;an&#x5B;i]] = i;\r\n \r\n    REP(i, tbc) if(san&#x5B;i] &lt; tb) t2&#x5B;ta++] = san&#x5B;i] * 3;\r\n    if (n%3==1) t2&#x5B;ta++] = n-1; rs(a,t2,t1,ta,m);\r\n    REP(i, tbc) key&#x5B;t2&#x5B;i]=G(san&#x5B;i])] = i;\r\n \r\n    for(i=0,j=0,p=0; i&lt;ta &amp;&amp; j&lt;tbc; p++)\r\n        sa&#x5B;p]=c12(t2&#x5B;j]%3,a,t1&#x5B;i],t2&#x5B;j]) ? t1&#x5B;i++] : t2&#x5B;j++];\r\n    for(;i&lt;ta;p++) sa&#x5B;p]=t1&#x5B;i++]; for(;j&lt;tbc;p++) sa&#x5B;p]=t2&#x5B;j++];\r\n}\r\n \r\nvoid get_h(){\r\n    REP_1(i, n) rk&#x5B;sa&#x5B;i]] = i;\r\n    int k=0;for(int i=0;i&lt;n;h&#x5B;rk&#x5B;i++]]=k){\r\n        if (k)--k;for(int j=sa&#x5B;rk&#x5B;i]-1];a&#x5B;i+k]==a&#x5B;j+k];++k);\r\n    }\r\n}\r\n \r\nint ST&#x5B;LV]&#x5B;N];\r\n \r\n#define cmp(a, b) (h&#x5B;a]&lt;h&#x5B;b]?a:b)\r\n \r\ninline int lcp(int l, int r){\r\n    int lv = lg2(r - l); ++l, ++r;\r\n    return min(h&#x5B;ST&#x5B;lv]&#x5B;l]], h&#x5B;ST&#x5B;lv]&#x5B;r-_1(lv)]]);\r\n}\r\n \r\ninline int lcpp(int l, int r){\r\n    if (l == r) return n-l;\r\n    l = rk&#x5B;l], r = rk&#x5B;r]; if (l &gt; r) swap(l, r);\r\n    return lcp(l, r);\r\n}\r\n \r\nvoid get_lcp(){\r\n    REP_1(i, n) ST&#x5B;0]&#x5B;i] = i;\r\n    for (int lv = 1; _1(lv) &lt;= n; ++lv){\r\n        for (int i = 1; i + _1(lv) &lt;= n + 1; ++i)\r\n            ST&#x5B;lv]&#x5B;i] = cmp(ST&#x5B;lv-1]&#x5B;i], ST&#x5B;lv-1]&#x5B;i+_1(lv-1)]);\r\n    }\r\n}\r\n \r\nvoid bd(){\r\n    dc3(a,sa,n+1,M),get_h(),get_lcp();\r\n}\r\n} A, B;\r\n \r\nPII get(LL k){\r\n    int r = lower_bound(a, a+n, k) - a; k -= a&#x5B;r-1];\r\n    return MP(A.sa&#x5B;r]+1, A.h&#x5B;r]+k);\r\n}\r\n \r\nLL f(LL x, LL y){\r\n    if (x&gt;a&#x5B;n] || y&gt;a&#x5B;n]) return -1;\r\n    PII a = get(x), b = get(y); int t = min(a.se, b.se);\r\n    return sqr(LL(min(t,A.lcpp(a.fi-1, b.fi-1)))) + sqr(LL(min(t,B.lcpp(n-(a.fi+a.se-1), n-(b.fi+b.se-1)))));\r\n}\r\n \r\n \r\nint main(){\r\n \r\n#ifndef ONLINE_JUDGE\r\n    freopen(&quot;in.txt&quot;, &quot;r&quot;, stdin);\r\n    \/\/freopen(&quot;out.txt&quot;, &quot;w&quot;, stdout);\r\n#endif\r\n \r\n    int m; RD(n, m); strlen(RS(s));  REP(i, n) B.a&#x5B;n-i-1]=A.a&#x5B;i]=s&#x5B;i]-='a'-1;\r\n    A.bd(); B.bd(); REP_1(i, n) a&#x5B;i]=a&#x5B;i-1]+n-A.sa&#x5B;i]-A.h&#x5B;i];\r\n    DO(m) OT(f(RD(), RD()));\r\n}\r\n<\/pre>\n<h3>External link:<\/h3>\n<p><a href=\"http:\/\/www.lydsy.com:808\/JudgeOnline\/problem.php?id=3230\">http:\/\/www.lydsy.com:808\/JudgeOnline\/problem.php?id=3230<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Brief description: \u8bbe\u4e24\u4e2a\u5b57\u7b26\u4e32\u7684\u6700\u957f\u516c\u5171\u524d\u7f00\u548c\u540e\u7f00\u7684\u957f\u5ea6\u5206\u522b\u4e3a $$a$$, $$b$$\u3002 \u5219\u5b83\u4eec\u76f8\u4f3c\u7a0b\u5ea6\uff0c\u5b9a\u4e49\u4e3a $$a^2 + b^2$$\u3002 \u7ed9\u5b9a\u4e00\u4e2a\u5b57\u7b26\u4e32\uff0c\u6bcf\u6b21\u8be2\u95ee\u5176\u5b57\u5178\u5e8f\u7b2c k1-th \u5927\u548c\u7b2c k2-th \u5927\u7684\u4e24\u4e2a\u5b50\u4e32\u95f4\u7684\u76f8\u4f3c\u7a0b\u5ea6\u3002<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","enabled":false}}},"categories":[22],"tags":[123],"class_list":["post-841","post","type-post","status-publish","format-standard","hentry","category-bzoj","tag-123"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_shortlink":"https:\/\/wp.me\/p2tdP7-dz","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts\/841","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/comments?post=841"}],"version-history":[{"count":1,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts\/841\/revisions"}],"predecessor-version":[{"id":842,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts\/841\/revisions\/842"}],"wp:attachment":[{"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/media?parent=841"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/categories?post=841"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/tags?post=841"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}