{"id":936,"date":"2014-08-08T05:32:49","date_gmt":"2014-08-07T21:32:49","guid":{"rendered":"http:\/\/www.shuizilong.com\/house\/?p=936"},"modified":"2014-08-08T05:48:44","modified_gmt":"2014-08-07T21:48:44","slug":"codeforces-round-129-div-1-problem-e-little-elephant-and-strings","status":"publish","type":"post","link":"https:\/\/www.shuizilong.com\/house\/archives\/codeforces-round-129-div-1-problem-e-little-elephant-and-strings\/","title":{"rendered":"Codeforces Round #129 (Div. 1) Problem E. Little Elephant and Strings"},"content":{"rendered":"

http:\/\/codeforces.com\/problemset\/problem\/204\/E<\/a><\/p>\n

Brief description:<\/h3>\n

\u7ed9\u5b9a n \u4e2a\u4e32\u3002\u3002\u95ee\u5bf9\u4e8e\u6bcf\u4e00\u4e2a\u5b57\u7b26\u4e32\uff0c\u6709\u591a\u5c11\u5b83\u7684\u5b50\u4e32\uff0c\u53ef\u4ee5\u81f3\u5c11\u5339\u914d k \u4e2a\u5b57\u7b26\u4e32\u3002\uff08\u5305\u542b\u81ea\u8eab\uff09<\/p>\n

Analysis:<\/h3>\n

\u540e\u7f00\u6570\u7ec4<\/h4>\n

\u7b97\u6cd51. \u4e8c\u5206 + \u53ef\u6301\u4e45\u5316\u7ebf\u6bb5\u6811<\/p>\n

\u9996\u5148\u5f53\u7136\u8fd8\u662f\u8981\u628a\u6240\u6709\u4e32\u62fc\u4e00\u8d77\u8dd1\u540e\u7f00\u6570\u7ec4\u3002\u3002\u3002\u4ee5aaa$aba$aaa<\/code> \u4e3a\u4f8b<\/p>\n

\u8003\u5bdf\u7b2c\u4e00\u4e2a\u4e32\u3002\u3002\u8bb0\u4f5c s0 = aaa<\/code> \u3002\u3002\u3002\u6211\u4eec\u679a\u4e3e\u8d77\u59cb\u4f4d x\u3002\u3002
\n\u3002\u3002\u8bbe f(x, len)\u3002\u3002\u8868\u793a \u3002\u3002\u3002s0[x, x+len] \u8fd9\u4e2a\u5b50\u4e32\u3002\u3002\u662f\u5426\u51fa\u73b0\u5728\u4e86 k \u4e2a\u5b50\u4e32\u4e2d\u3002
\n\u3002\u3002\u3002\uff08\u3002\u6211\u4eec\u5e0c\u671b\u6c42\u6700\u5927\u7684 len<\/code>\u3002\u3002\u3002\u3002\u663e\u7136 len<\/code> \u8d8a\u957f\u5bf9\u8fd9\u4e2a\u6027\u8d28\u8d8a\u4e0d\u5229\u3002\u3002
\n\u3002\u3002\u3002\uff08\u8003\u8651\u4e8c\u5206\u3002\u3002\u3002<\/p>\n

\r\n$aaa \r\n$aba$aaa \r\na \r\na$aaa \r\na$aba$aaa \r\naa \r\naa$aba$aaa \r\naaa \r\naaa$aba$aaa \r\naba$aaa \r\nba$aaa  \r\n<\/pre>\n
\u3002\u3002\u5bf9\u4e8e\u4efb\u610f\u4e00\u4e2a x<\/code> \u548c len<\/code>\u3002\u3002\u3002
\n\u3002\u3002\u6211\u4eec\u9700\u8981\u5728\u540e\u7f00\u6570\u7ec4\u4e2d\uff0c\u627e\u5230\u6700\u5927\u7684\u5305\u542b x<\/code> \u7684 [l, r]<\/code> \u533a\u95f4\u3002\u3002\u6ee1\u8db3 lcp(l, r) \u2265 len<\/code>\u3002<\/p>\n
\u3002\u3002\u800c\u8fd9\u53c8\u662f\u4e00\u4e2a\u4e8c\u5206\u8fc7\u7a0b\u3002\u3002\u3002\uff08\u3002\u3002\u8fd9\u91cc\u9700\u8981\u7528\u5230 SA<\/code> \u7684\u4e00\u4e2a\u6027\u8d28\u3002\u3002\u7136\u540e\u5bf9\u4e8e\u4efb\u4e00\u4e2a\u4e32 P<\/code>\uff0clcp(P, SA[i])<\/code> \u662f\u5355\u5cf0\u7684\u3002
\n\u3002\u3002\u627e\u5230 [l, r] \u533a\u95f4\u540e\u3002\u3002\u3002\u5c31\u662f\u3002\u3002\u3002\u3002<\/p>\n
\u3002\u3002\u3002\u5224\u65ad\u8fd9\u4e2a\u533a\u95f4\u7684\u540e\u7f00\u51fa\u73b0\u5728\u4e86\u51e0\u4e2a\u4e0d\u540c\u7684\u5b57\u7b26\u4e32\u4e2d\u3002\u3002\u3002
\n\u3002\u3002\u3002\u800c\u8fd9\u4e2a\u662f\u4e2a\u53ef\u6301\u4e45\u5316\u7ebf\u6bb5\u6811\u7684\u5165\u95e8\u9898\u3002\u3002\uff08\u53c2\u89c1 SPOJ Dquery \u3002\u3002<\/p>\n
\u3002\u3002\u3002\u8fd9\u6837\u8fd9\u4e2a\u9898\u6211\u4eec\u5c31\u5f97\u5230\u4e86\u6700\u50bb\u903c\u7684\u505a\u6cd5\u3002\u3002\u3002\u590d\u6742\u5ea6  $O(nlog^2n)$\u3002
\nhttp:\/\/codeforces.com\/contest\/204\/submission\/4545205<\/a><\/p>\n
\u7b97\u6cd5 2. two-point
\nhttp:\/\/www.cppblog.com\/hanfei19910905\/archive\/2012\/07\/26\/185139.html<\/p>\n
\u3002\u3002\u3002\u4e0a\u9762\u7684\u505a\u6cd5\u4e2d\u3002\u53ef\u6301\u4e45\u5316\u7ebf\u6bb5\u6811\u3002\u672a\u514d\u6709\u70b9 overkill\u3002\u3002\u6ce8\u610f\u6bd5\u7adf\u53ea\u662f\u8be2\u95ee\u662f\u5426 >= k\u3002\u3002\u3002
\n\u3002\u800c\u8fd9\u4e2a\u53ef\u4ee5\u901a\u8fc7 two-point \u79bb\u7ebf\u641e\u51fa\u5bf9\u4e8e\u6bcf\u4e2a\u5de6\u7aef\u70b9\u3002\u6700\u65e9\u7684\u5408\u6cd5\u4f4d\u7f6e\u3002\u3002\u3002
\n\u5177\u4f53\u505a\u6cd5\u662f prd[], suc[] \u5206\u522b\u8868\u793a\u5de6\u53f3\u7b2c\u4e00\u4e2a\u4e0e b[i] \u76f8\u540c\u7684\u4f4d\u7f6e\u3002\u3002<\/p>\n
\r\nint last[N], prd[N], suc[N];\r\n<\/pre>\n
\u4e24\u904d\u5faa\u73af\u3002\u3002<\/p>\n
\r\n    FOR_1(i, nn, n) prd[i] = last[bb(i)], last[bb(i)] = i;\r\n    REP_1(i, nn) last[i] = n + 1;\r\n    DWN_1(i, n, nn) suc[i] = last[bb(i)], last[bb(i)] = i;\r\n<\/pre>\n
\u4e4b\u540e two-point\u3002\u3002
\n\uff08l \u589e\u5927\u7684\u65f6\u5019\u3002\u3002\u5982\u679c suc[l] > r \u3002\u3002c -= 1
\n\uff08r \u589e\u5927\u7684\u65f6\u5019\u3002\u3002\u5982\u679c prd[++r] < l\u3002\u3002\u5219 c += 1\n[cpp]\n    for(int l=nn,r=nn-1,c;l<=n;c-=(suc[l++]>r)){\n        if (r<l) r=l,c=1; while(c<k&&r<=n) if(prd[++r]<l)++c; if (c<k){n=l-1;break;}\n        last[l] = r;\n    }\n[\/cpp] \n\n\u5176\u4ed6\u5730\u65b9\u4e0d\u53d8\u3002\u3002\u3002\u3002\u3002\u590d\u6742\u5ea6\u4f9d\u65e7\u662f  O(nlog^2n)\nhttp:\/\/codeforces.com\/contest\/204\/submission\/4544775\n\n\n\n\n\u7b97\u6cd5 3. \u6807\u8bb0\n\u3002\u3002\u4e3a\u4e86\u675c\u7edd\u6389\u4e8c\u5206\u7684\u8fc7\u7a0b\u3002\u3002\u3002\u6211\u4eec\u6ce8\u610f\u5230\u4e0a\u9762 two-point \u5f97\u5230\u4e00\u7ec4\u6700\u5c0f\u7684\u5408\u6cd5 (l, r, lcp) \u7684\u65f6\u5019\u3002\u3002\u3002\n\u3002\u3002\u53ef\u4ee5\u6cbf\u9014\u6253\u4e0a\u4e8b\u4ef6\u6807\u8bb0\u3002\u3002\u3002\u7528\u626b\u63cf\u7ebf\u7684\u65b9\u6cd5\u3002\u5f04\u4e00\u4e2a\u5e73\u8861\u6811\u3002\u3002\u6bcf\u6b21\u53d6\u51fa\u6700\u5927\u7684 lcp \u597d\u50cf\u5c31\u884c\u4e86\u3002\u3002\n\nhttp:\/\/hi.baidu.com\/wyl8899\/item\/04772d462eeb6797823ae16d\n..\u4f3c\u4e4e\u5df2\u7ecf\u505a\u5b8c\u4e86\u4e48...\u5176\u5b9e\u88ab\u5751\u4e86\uff0c\u6837\u4f8b2\u5c31\u53ef\u4ee5\u628a\u8fd9\u4e2a\u505a\u6cd5\u64b8\u6b7b\u3002\n\u7a76\u5176\u539f\u56e0\uff0c\u662f\u5b58\u5728\u67d0\u4e2ak\uff0c\u4ed6\u7684\u771f\u6b63\u53ef\u7528\u7684\u6700\u5927\u503c\u5e76\u4e0d\u80fd\u88ab\u4e0a\u9762\u6240\u8ff0\u7684\u65b9\u6cd5\u66f4\u65b0\u5230\u3002\n\u8fd9\u5c31\u5751\u7239\u4e86..\u56e0\u4e3a\u80fd\u66f4\u65b0\u5230k\u7684\u6700\u5927\u503c\u7684\u90a3\u4e2a\u533a\u95f4\uff0c\u5047\u8bbe\u662f[x,y']\uff0c\u4f1a\u51fa\u73b0y'>y(\u4f7f\u5f97rank\u4e3ax..y\u7684\u540e\u7f00\u5206\u5c5eK\u4e2a\u4e32\u7684\u6700\u5c0fy\u503c)\u7684\u60c5\u5f62\u3002<\/p>\n
\u3002\u3002\u7136\u800c\u8fd9\u70b9\u4e5f\u6b63\u662f\u8fd9\u9898\u6700\u7cbe\u5f69\u7684\u5730\u65b9\u3002\u3002\u3002\u56e0\u4e3a\u5bf9\u4e8e\u4e00\u7ec4\u6807\u8bb0 (l, r, lcp) \u6765\u8bf4\u3002\u3002
\n\u3002\u3002\u3002r \u4e4b\u540e\u5e76\u4e0d\u4ee3\u8868\u8fd9\u4e2a\u6807\u8bb0\u5c31\u5b8c\u5168\u5931\u6548\u4e86\u3002\u3002\u800c\u662f\u4ee5\u8fd9\u4e2a\u65f6\u523b\u5f00\u59cb\u3002\u3002\u3002
\n\u3002\u3002\u968f\u7740\u65f6\u95f4\u7684\u6d41\u901d\u3002\u3002\u4ea7\u751f\u8870\u51cf\u3002\u3002\uff08\u8bf4\u7684\u795e\u4e4e\u5176\u795e\u7684\u3002\u3002\u5177\u4f53\u6765\u8bf4\u5c31\u662f\u6bcf\u6b21 checkMin(delay, height[i])\u3002\u3002<\/p>\n
\u56e0\u6b64\u3002\u3002\u6211\u4eec\u6bcf\u6b21\u9664\u4e86\u8981\u53d6\u51fa\u5e73\u8861\u6811\u4e2d\u7684\u6700\u5927\u503c\u4ee5\u5916\u3002\u3002\u8fd8\u9700\u8981\u90a3\u4e9b\u8fc7\u4e86 \u201c\u4fdd\u8d28\u671f\u201d \u7684\u6807\u8bb0\u4e2d\u7684\u6700\u5927\u503c\u3002\u3002
\n\u3002\u3002\u3002\u7136\u540e\u4ece\u8fd9\u4e24\u8005\u4e4b\u95f4\u3002\u53d6\u6700\u5927\u503c\u3002\u3002\u3002\u3002<\/p>\n
\u3002\u3002  \u5e73\u8861\u6811\u5185\u7684\u6807\u8bb0\u3002\u3002\u6d89\u53ca\u589e\u5220\u64cd\u4f5c\u3002\u3002\u6700\u597d\u7684\u65b9\u6cd5\u4f7f\u7528 multiset \u5b9e\u73b0\u3002\u3002\u3002
\n\u3002\u3002  \u5e73\u8861\u6811\u4ee5\u5916\u7684\u6807\u8bb0\u3002\u3002\u53ea\u9700\u4fdd\u7559\u4e00\u4e2a\u6700\u5927\u503c\u5373\u53ef\uff08\u8bb0\u4f5c delay\uff09\u3002\u3002\u7136\u540e\u968f\u7740\u65f6\u95f4\u7684\u63a8\u79fb\u3002\u6bcf\u6b21 checkMin(delay, height[i])\u3002\u3002
\nhttp:\/\/codeforces.com\/contest\/204\/submission\/4544928<\/p>\n
\u3002\u3002\u9664\u53bb\u4e0d\u591a\u7684\u51e0\u6b21\u5e73\u8861\u6811\u64cd\u4f5c\u3002\u3002\u8fd9\u4e2a\u7b97\u6cd5\u7684\u590d\u6742\u5ea6\u5df2\u7ecf\u5f88\u63a5\u8fd1 O(n) \u4e86\u3002\u3002\u800c\u4e14\u975e\u5e38\u597d\u5199\u3002\u3002
\n\u3002\u3002\u3002\u3002\u662f\u4e00\u4e2a\u4f18\u79c0\u7684\u7b97\u6cd5\u3002<\/p>\n
\u7b97\u6cd5 4. \u540e\u7f00\u81ea\u52a8\u673a
\nhttps:\/\/www.13331.org\/205.html
\nhttp:\/\/codeforces.com\/contest\/204\/submission\/2579006<\/p>\n
\u2014\u2014\u2014\u2014\u2014\u2014
\n\u666e\u901a\u5e76\u67e5\u96c6\u3002\u3002\u3002
\nhttp:\/\/codeforces.com\/contest\/204\/submission\/4601790  \uff08280ms\u3002\u3002
\n\u52a0\u6309\u79e9\u5408\u5e76\u3002\u3002
\nhttp:\/\/codeforces.com\/contest\/204\/submission\/4601803 \uff08248ms\u3002\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"
http:\/\/codeforces.com\/problemset\/problem\/204\/E Brief description: \u7ed9\u5b9a n \u4e2a\u4e32\u3002\u3002\u95ee\u5bf9\u4e8e\u6bcf\u4e00\u4e2a\u5b57\u7b26\u4e32\uff0c\u6709\u591a\u5c11\u5b83\u7684\u5b50\u4e32\uff0c\u53ef\u4ee5\u81f3\u5c11\u5339\u914d k \u4e2a\u5b57\u7b26\u4e32\u3002\uff08\u5305\u542b\u81ea\u8eab\uff09 Analysis: \u540e\u7f00\u6570\u7ec4 \u7b97\u6cd51. \u4e8c\u5206 + \u53ef\u6301\u4e45\u5316\u7ebf\u6bb5\u6811 \u9996\u5148\u5f53\u7136\u8fd8\u662f\u8981\u628a\u6240\u6709\u4e32\u62fc\u4e00\u8d77\u8dd1\u540e\u7f00\u6570\u7ec4\u3002\u3002\u3002\u4ee5aaa$aba$aaa \u4e3a\u4f8b \u8003\u5bdf\u7b2c\u4e00\u4e2a\u4e32\u3002\u3002\u8bb0\u4f5c s0 = aaa \u3002\u3002\u3002\u6211\u4eec\u679a\u4e3e\u8d77\u59cb\u4f4d x\u3002\u3002 \u3002\u3002\u8bbe f(x, len)\u3002\u3002\u8868\u793a \u3002\u3002\u3002s0[x, x+len] \u8fd9\u4e2a\u5b50\u4e32\u3002\u3002\u662f\u5426\u51fa\u73b0\u5728\u4e86 k \u4e2a\u5b50\u4e32\u4e2d\u3002 \u3002\u3002\u3002\uff08\u3002\u6211\u4eec\u5e0c\u671b\u6c42\u6700\u5927\u7684 len\u3002\u3002\u3002\u3002\u663e\u7136 len \u8d8a\u957f\u5bf9\u8fd9\u4e2a\u6027\u8d28\u8d8a\u4e0d\u5229\u3002\u3002 \u3002\u3002\u3002\uff08\u8003\u8651\u4e8c\u5206\u3002\u3002\u3002 $aaa $aba$aaa a a$aaa a$aba$aaa aa aa$aba$aaa aaa aaa$aba$aaa aba$aaa ba$aaa \u3002\u3002\u5bf9\u4e8e\u4efb\u610f\u4e00\u4e2a x \u548c len\u3002\u3002\u3002 \u3002\u3002\u6211\u4eec\u9700\u8981\u5728\u540e\u7f00\u6570\u7ec4\u4e2d\uff0c\u627e\u5230\u6700\u5927\u7684\u5305\u542b x \u7684 [l, r] […]<\/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":[1],"tags":[],"class_list":["post-936","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_shortlink":"https:\/\/wp.me\/p2tdP7-f6","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts\/936","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=936"}],"version-history":[{"count":1,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts\/936\/revisions"}],"predecessor-version":[{"id":937,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts\/936\/revisions\/937"}],"wp:attachment":[{"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/media?parent=936"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/categories?post=936"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/tags?post=936"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}