{"id":383,"date":"2013-04-07T21:34:00","date_gmt":"2013-04-07T13:34:00","guid":{"rendered":"http:\/\/nike0good.jp1.rpvhost.net\/287"},"modified":"2013-04-07T21:34:00","modified_gmt":"2013-04-07T13:34:00","slug":"bzoj_3097_hash_killer_i-hash_u64_infeasible","status":"publish","type":"post","link":"https:\/\/nike0good.com\/?p=383","title":{"rendered":"BZOJ 3097(Hash Killer I-\u54c8\u5e0c%u64\u7684\u4e0d\u53ef\u884c)"},"content":{"rendered":"

<\/p>\n

3097: Hash Killer I<\/h2>\n

Time Limit: <\/span>5 Sec  Memory Limit: <\/span>128 MBSec  Special Judge<\/span>
\nSubmit: <\/span>76  Solved: <\/span>34
\n[Submit<\/a>][Status<\/a>][Discuss<\/a>]<\/center><\/p>\n

Description<\/h2>\n
\n

\u8fd9\u5929\u5929\u6c14\u4e0d\u9519\uff0chzhwcmhf\u795e\u7287\u7ed9VFleaKing\u51fa\u4e86\u4e00\u9053\u9898\uff1a
\n\u7ed9\u4f60\u4e00\u4e2a\u957f\u5ea6\u4e3aN\u7684\u5b57\u7b26\u4e32S\uff0c\u6c42\u6709\u591a\u5c11\u4e2a\u4e0d\u540c\u7684\u957f\u5ea6\u4e3aL\u7684\u5b50\u4e32\u3002
\n\u5b50\u4e32\u7684\u5b9a\u4e49\u662fS[l]\u3001S[l + 1]\u3001... S[r]\u8fd9\u6837\u8fde\u7eed\u7684\u4e00\u6bb5\u3002
\n\u4e24\u4e2a\u5b57\u7b26\u4e32\u88ab\u8ba4\u4e3a\u662f\u4e0d\u540c\u7684\u5f53\u4e14\u4ec5\u5f53\u67d0\u4e2a\u4f4d\u7f6e\u4e0a\u7684\u5b57\u7b26\u4e0d\u540c\u3002<\/span><\/p>\n

VFleaKing\u4e00\u770b\u89c9\u5f97\u8fd9\u4e0d\u662fHash\u7684\u88f8\u9898\u4e48\uff01\u4e8e\u662f\u679c\u65ad\u5199\u4e86\u54c8\u5e0c + \u6392\u5e8f\u3002
\n\u800chzhwcmhf\u795e\u7287\u5fc3\u91cc\u81ea\u7136\u77e5\u9053\uff0c\u8fd9\u9898\u5c31\u662f\u540e\u7f00\u6570\u7ec4\u7684height\u4e2d < L\u7684\u4e2a\u6570 + 1\uff0c\u5c31\u662f\u540e\u7f00\u81ea\u52a8\u673a\u4e0a\u4ee3\u8868\u7684\u957f\u5ea6\u533a\u95f4\u5305\u542bL\u7684\u7ed3\u70b9\u4e2a\u6570\uff0c\u5c31\u662f\u540e\u7f00\u6811\u6df1\u5ea6\u4e3aL\u7684\u7ed3\u70b9\u7684\u6570\u91cf\u3002
\n\u4f46\u662fhzhwcmhf\u795e\u7287\u770b\u4e86\u770bVFleaKing\u7684\u505a\u6cd5\u8868\u793a\u975e\u5e38\u6c57\u3002\u4e8e\u662f\u60f3\u5361\u6389\u4ed6\u3002<\/span><\/p>\n

VFleaKing\u4f7f\u7528\u7684\u662f\u5b57\u5178\u5e8f\u54c8\u5e0c\uff0c\u5176\u4ee3\u7801\u5927\u81f4\u5982\u4e0b\uff1a
\nu64 val = 0;
\nfor (int i = 0; i < l; i++)
\n val = val * base + s[i] - 'a';
\nu64\u662f\u65e0\u7b26\u53f7int64\uff0c\u8303\u56f4\u662f[0, 2^64)\u3002VFleaKing\u8ba9val\u81ea\u7136\u6ea2\u51fa\u3002
\nbase\u662f\u4e00\u4e2a\u5e38\u91cf\uff0cVFleaKing\u4f1a\u6839\u636e\u5fc3\u60c5\u51b3\u5b9a\u5176值\u3002
\nVFleaKing\u8fd8\u6c42\u51fa\u6765\u4e86base ^ l\uff0c\u5373base\u7684l\u6b21\u65b9\uff0c\u8fd9\u6837\u5c31\u80fd\u65b9\u4fbf\u5730\u6c42\u51fa\u6240\u6709\u957f\u5ea6\u4e3aL\u7684\u5b50\u4e32\u7684\u54c8\u5e0c值\u3002
\n\u7136\u540eVFleaKing\u7ed9\u54c8\u5e0c值\u6392\u5e8f\uff0c\u53bb\u91cd\uff0c\u6c42\u51fa\u6709\u591a\u5c11\u4e2a\u4e0d\u540c\u7684\u54c8\u5e0c值\uff0c\u628a\u8fd9\u4e2a\u6570\u4f5c\u4e3a\u7ed3\u679c\u3002
\n\u5176\u7b97\u6cd5\u7684C++\u4ee3\u7801\u5982\u4e0b\uff1a<\/span><\/p>\n

typedef unsigned long long u64;<\/span><\/p>\n

const int MaxN = 100000;<\/span><\/p>\n

inline int hash_handle(const char *s, const int &n, const int &l, const int &base)
\n{
\n u64 hash_pow_l = 1;
\n for (int i = 1; i <= l; i++)
\n  hash_pow_l *= base;<\/span><\/p>\n

 int li_n = 0;
\n static u64 li[MaxN];<\/span><\/p>\n

 u64 val = 0;
\n for (int i = 0; i < l; i++)
\n  val = val * base + s[i] - 'a';
\n li[li_n++] = val;
\n for (int i = l; i < n; i++)
\n {
\n  val = val * base + s[i] - 'a';
\n  val -= (s[i - l] - 'a') * hash_pow_l;
\n  li[li_n++] = val;
\n }<\/span><\/p>\n

 sort(li, li + li_n);
\n li_n = unique(li, li + li_n) - li;
\n return li_n;
\n}<\/span><\/p>\n

hzhwcmhf\u5f53\u7136\u77e5\u9053\u600e\u4e48\u5361\u5566\uff01\u4f46\u662f\u4ed6\u60f3\u8003\u8003\u4f60\u3002
\n<\/span><\/p>\n<\/div>\n

Input<\/h2>\n
\n

\u6ca1\u6709\u8f93\u5165\u3002
\n<\/span><\/p>\n<\/div>\n

Output<\/h2>\n
\n

\u4f60\u9700\u8981\u8f93\u51fa\u4e00\u7ec4\u6570\u636e\u4f7f\u5f97VFleaKing\u7684\u4ee3\u7801WA\u6389\u3002\u6211\u4eec\u4f1a\u4f7f\u7528Special Judge\u68c0\u67e5\u4f60\u7684\u7ed3\u679c\u7684\u6b63\u786e\u6027\u3002
\n\u8f93\u51fa\u6587\u4ef6\u5171\u4e24\u884c\u3002
\n\u7b2c\u4e00\u884c\u4e24\u4e2a\u7528\u7a7a格\u9694\u5f00\u7684\u6570n\u3001l\u3002
\n\u7b2c\u4e8c\u884c\u662f\u4e00\u4e2a\u957f\u5ea6\u4e3an\u7684\u5b57\u7b26\u4e32\u3002\u53ea\u80fd\u5305\u542b'a'~'z'\u3002
\n\u9700\u8981\u4fdd\u8bc11 <= n <= 10^5, 1 <= l <= n\uff0c
\n\u4e0d\u7b26\u5408\u4ee5\u4e0a格\u5f0f\u4f1aWA\u3002
\n\u4e0d\u8981\u6709\u591a\u4f59\u5b57\u7b26\uff0c\u5f88\u53ef\u80fd\u5bfc\u81f4\u4f60WA\u3002<\/span><\/p>\n<\/p>\n<\/div>\n

Sample Input<\/h2>\n
\n\u6ca1\u6709

\n<\/span><\/div>\n

Sample Output<\/h2>\n
\n8 4

\nbuaabuaa

\n\uff08\u5f53\u7136\u8fd9\u4e2a\u8f93\u51fa\u662f\u4f1aWA\u7684\uff09

\n

\n<\/span><\/div>\n

HINT<\/h2>\n
\n

orz \u6ce2\u5170\u4eba & fotile96 & sillycross<\/p>\n<\/p>\n<\/div>\n

\n<\/p>\n

\u8fd9\u9898\u8981\u4e00\u5b9a\u7684\u6570\u8bba\u77e5\u8bc6\uff08\u5176\u5b9e\u4e0d\u8981\u2026\u2026\uff09<\/span><\/p>\n

\u5982\u679cs[1]=1 s[i]=s[i-1]+s[i-1].flip(1...size)<\/span><\/p>\n

\u5219\u6709<\/span><\/p>\n

strlen(s[i])=2^(i-1)<\/span><\/p>\n

\u82e5\u8bbef[i]=hash(s[i])-(hash(!s[i]))=2^k * t \uff08t\u662f\u5947\u6570\uff09<\/span><\/p>\n

\u5219\u6613\u8bc1(\u628ahash值\u6709base\u5e26\uff0c\u6162\u6162\u7b97\u2026\u2026\uff09<\/span><\/p>\n

<\/span>f[i]=f[i-1]*(base^[2^(i-2)]-1)<\/span><\/p>\n

\u22352^i-1=(2^(i-1)-1)*(2^(i-1)+1),<\/span><\/span><\/p>\n

\u6240\u4ee5k\u5f88\u5927\u3002<\/span>  <\/span><\/p>\n

\u5982\u679cbase\u662f\u5076\u6570\uff0c\u90a3\u4e48\u53ea\u8981\u6700\u9ad8\u4f4d\u4e0d\u540c\uff0c\u5176\u5b83\u90fd\u76f8\u540c\u8ba9\u5176\u6ea2\u51fa\u5c31\u884c\u3002<\/span><\/p>\n


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

#include<cstdio>\n#include<iostream>\n#include<functional>\n#include<bitset>\n#include<string>\nusing namespace std;\n#define MAXN (100000+10)\nint n,l;\nbitset<MAXN> s;\nint main()\n{\n\tn=MAXN-10;\n\tint bin=1;\n\ts[1]=1;\n\tfor (int i=2;i<=13;i++,bin<<=1)\n\t{\n\t\tfor(int j=bin+1;j<=bin*2;j++)\n\t\t\ts[j]=s[j-bin]^1;\n\t}\n\tcout<<n<<' '<<bin\/2<<endl;\n\tfor (int i=1;i<=bin;i++)\n\t{\n\t\tif (s[i]) cout<<'a';\n\t\telse cout<<'b';\n\t}\n\tcout<<'b';\n\tfor (int i=bin+2;i<=n;i++) cout<<'a';\n\n\tcout<<endl;\n\treturn 0;\n}<\/pre><\/p>\n","protected":false},"excerpt":{"rendered":"
3097: Hash Killer I Time Limit: 5 Sec  M […]<\/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":[64],"class_list":["post-383","post","type-post","status-publish","format-standard","hentry","category-defaultcategory","tag-hash_table"],"yoast_head":"\nBZOJ 3097(Hash Killer I-\u54c8\u5e0c%u64\u7684\u4e0d\u53ef\u884c) - 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=383\" \/>\n<meta property=\"og:locale\" content=\"zh_CN\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"BZOJ 3097(Hash Killer I-\u54c8\u5e0c%u64\u7684\u4e0d\u53ef\u884c) - nike0good\" \/>\n<meta property=\"og:description\" content=\"3097: Hash Killer I Time Limit: 5 Sec  M […]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/nike0good.com\/?p=383\" \/>\n<meta property=\"og:site_name\" content=\"nike0good\" \/>\n<meta property=\"article:published_time\" content=\"2013-04-07T13:34:00+00:00\" \/>\n<meta name=\"author\" content=\"nike0good\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"\u4f5c\u8005\" \/>\n\t<meta name=\"twitter:data1\" content=\"nike0good\" \/>\n\t<meta name=\"twitter:label2\" content=\"\u9884\u8ba1\u9605\u8bfb\u65f6\u95f4\" \/>\n\t<meta name=\"twitter:data2\" content=\"2 \u5206\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\\\/\\\/nike0good.com\\\/?p=383#article\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/nike0good.com\\\/?p=383\"},\"author\":{\"name\":\"nike0good\",\"@id\":\"https:\\\/\\\/nike0good.com\\\/#\\\/schema\\\/person\\\/4defa38da89de87e400861e73396baad\"},\"headline\":\"BZOJ 3097(Hash Killer I-\u54c8\u5e0c%u64\u7684\u4e0d\u53ef\u884c)\",\"datePublished\":\"2013-04-07T13:34:00+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\\\/\\\/nike0good.com\\\/?p=383\"},\"wordCount\":299,\"commentCount\":0,\"keywords\":[\"\u54c8\u5e0c\u8868\"],\"articleSection\":[\"DefaultCategory\"],\"inLanguage\":\"zh-Hans\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\\\/\\\/nike0good.com\\\/?p=383#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/nike0good.com\\\/?p=383\",\"url\":\"https:\\\/\\\/nike0good.com\\\/?p=383\",\"name\":\"BZOJ 3097(Hash Killer I-\u54c8\u5e0c%u64\u7684\u4e0d\u53ef\u884c) - nike0good\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/nike0good.com\\\/#website\"},\"datePublished\":\"2013-04-07T13:34:00+00:00\",\"author\":{\"@id\":\"https:\\\/\\\/nike0good.com\\\/#\\\/schema\\\/person\\\/4defa38da89de87e400861e73396baad\"},\"breadcrumb\":{\"@id\":\"https:\\\/\\\/nike0good.com\\\/?p=383#breadcrumb\"},\"inLanguage\":\"zh-Hans\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\\\/\\\/nike0good.com\\\/?p=383\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\\\/\\\/nike0good.com\\\/?p=383#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\\\/\\\/nike0good.com\\\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"BZOJ 3097(Hash Killer I-\u54c8\u5e0c%u64\u7684\u4e0d\u53ef\u884c)\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\\\/\\\/nike0good.com\\\/#website\",\"url\":\"https:\\\/\\\/nike0good.com\\\/\",\"name\":\"nike0good\",\"description\":\"\u6709\u6240\u4f5c\u4e3a\u662f\u4eba\u751f\u7684\u6700\u9ad8\u5883\u754c\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\\\/\\\/nike0good.com\\\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"zh-Hans\"},{\"@type\":\"Person\",\"@id\":\"https:\\\/\\\/nike0good.com\\\/#\\\/schema\\\/person\\\/4defa38da89de87e400861e73396baad\",\"name\":\"nike0good\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"zh-Hans\",\"@id\":\"https:\\\/\\\/secure.gravatar.com\\\/avatar\\\/8e5fa08d5c367a1a6fb5ff13bb10ed5a331f981513256951290ae42322da6854?s=96&d=identicon&r=g\",\"url\":\"https:\\\/\\\/secure.gravatar.com\\\/avatar\\\/8e5fa08d5c367a1a6fb5ff13bb10ed5a331f981513256951290ae42322da6854?s=96&d=identicon&r=g\",\"contentUrl\":\"https:\\\/\\\/secure.gravatar.com\\\/avatar\\\/8e5fa08d5c367a1a6fb5ff13bb10ed5a331f981513256951290ae42322da6854?s=96&d=identicon&r=g\",\"caption\":\"nike0good\"},\"sameAs\":[\"https:\\\/\\\/nike0good.com\"],\"url\":\"https:\\\/\\\/nike0good.com\\\/?author=1\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"BZOJ 3097(Hash Killer I-\u54c8\u5e0c%u64\u7684\u4e0d\u53ef\u884c) - nike0good","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/nike0good.com\/?p=383","og_locale":"zh_CN","og_type":"article","og_title":"BZOJ 3097(Hash Killer I-\u54c8\u5e0c%u64\u7684\u4e0d\u53ef\u884c) - nike0good","og_description":"3097: Hash Killer I Time Limit: 5 Sec  M […]","og_url":"https:\/\/nike0good.com\/?p=383","og_site_name":"nike0good","article_published_time":"2013-04-07T13:34:00+00:00","author":"nike0good","twitter_card":"summary_large_image","twitter_misc":{"\u4f5c\u8005":"nike0good","\u9884\u8ba1\u9605\u8bfb\u65f6\u95f4":"2 \u5206"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/nike0good.com\/?p=383#article","isPartOf":{"@id":"https:\/\/nike0good.com\/?p=383"},"author":{"name":"nike0good","@id":"https:\/\/nike0good.com\/#\/schema\/person\/4defa38da89de87e400861e73396baad"},"headline":"BZOJ 3097(Hash Killer I-\u54c8\u5e0c%u64\u7684\u4e0d\u53ef\u884c)","datePublished":"2013-04-07T13:34:00+00:00","mainEntityOfPage":{"@id":"https:\/\/nike0good.com\/?p=383"},"wordCount":299,"commentCount":0,"keywords":["\u54c8\u5e0c\u8868"],"articleSection":["DefaultCategory"],"inLanguage":"zh-Hans","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/nike0good.com\/?p=383#respond"]}]},{"@type":"WebPage","@id":"https:\/\/nike0good.com\/?p=383","url":"https:\/\/nike0good.com\/?p=383","name":"BZOJ 3097(Hash Killer I-\u54c8\u5e0c%u64\u7684\u4e0d\u53ef\u884c) - nike0good","isPartOf":{"@id":"https:\/\/nike0good.com\/#website"},"datePublished":"2013-04-07T13:34:00+00:00","author":{"@id":"https:\/\/nike0good.com\/#\/schema\/person\/4defa38da89de87e400861e73396baad"},"breadcrumb":{"@id":"https:\/\/nike0good.com\/?p=383#breadcrumb"},"inLanguage":"zh-Hans","potentialAction":[{"@type":"ReadAction","target":["https:\/\/nike0good.com\/?p=383"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/nike0good.com\/?p=383#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/nike0good.com\/"},{"@type":"ListItem","position":2,"name":"BZOJ 3097(Hash Killer I-\u54c8\u5e0c%u64\u7684\u4e0d\u53ef\u884c)"}]},{"@type":"WebSite","@id":"https:\/\/nike0good.com\/#website","url":"https:\/\/nike0good.com\/","name":"nike0good","description":"\u6709\u6240\u4f5c\u4e3a\u662f\u4eba\u751f\u7684\u6700\u9ad8\u5883\u754c","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/nike0good.com\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"zh-Hans"},{"@type":"Person","@id":"https:\/\/nike0good.com\/#\/schema\/person\/4defa38da89de87e400861e73396baad","name":"nike0good","image":{"@type":"ImageObject","inLanguage":"zh-Hans","@id":"https:\/\/secure.gravatar.com\/avatar\/8e5fa08d5c367a1a6fb5ff13bb10ed5a331f981513256951290ae42322da6854?s=96&d=identicon&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/8e5fa08d5c367a1a6fb5ff13bb10ed5a331f981513256951290ae42322da6854?s=96&d=identicon&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/8e5fa08d5c367a1a6fb5ff13bb10ed5a331f981513256951290ae42322da6854?s=96&d=identicon&r=g","caption":"nike0good"},"sameAs":["https:\/\/nike0good.com"],"url":"https:\/\/nike0good.com\/?author=1"}]}},"_links":{"self":[{"href":"https:\/\/nike0good.com\/index.php?rest_route=\/wp\/v2\/posts\/383","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/nike0good.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/nike0good.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/nike0good.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/nike0good.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=383"}],"version-history":[{"count":0,"href":"https:\/\/nike0good.com\/index.php?rest_route=\/wp\/v2\/posts\/383\/revisions"}],"wp:attachment":[{"href":"https:\/\/nike0good.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=383"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/nike0good.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=383"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/nike0good.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=383"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}